data.complex.basic ⟷ Mathlib.Data.Complex.Basic

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

@@ -952,71 +952,71 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 /-! ### Cast lemmas -/
 
 
-#print Complex.ofReal_nat_cast /-
+#print Complex.ofReal_natCast /-
 @[simp, norm_cast]
-theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_natCast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
   map_natCast ofReal n
-#align complex.of_real_nat_cast Complex.ofReal_nat_cast
+#align complex.of_real_nat_cast Complex.ofReal_natCast
 -/
 
-#print Complex.nat_cast_re /-
+#print Complex.natCast_re /-
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
-#align complex.nat_cast_re Complex.nat_cast_re
+theorem natCast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
+#align complex.nat_cast_re Complex.natCast_re
 -/
 
-#print Complex.nat_cast_im /-
+#print Complex.natCast_im /-
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
-#align complex.nat_cast_im Complex.nat_cast_im
+theorem natCast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
+#align complex.nat_cast_im Complex.natCast_im
 -/
 
-#print Complex.ofReal_int_cast /-
+#print Complex.ofReal_intCast /-
 @[simp, norm_cast]
-theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_intCast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
   map_intCast ofReal n
-#align complex.of_real_int_cast Complex.ofReal_int_cast
+#align complex.of_real_int_cast Complex.ofReal_intCast
 -/
 
-#print Complex.int_cast_re /-
+#print Complex.intCast_re /-
 @[simp, norm_cast]
-theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← of_real_int_cast, of_real_re]
-#align complex.int_cast_re Complex.int_cast_re
+theorem intCast_re (n : ℤ) : (n : ℂ).re = n := by rw [← of_real_int_cast, of_real_re]
+#align complex.int_cast_re Complex.intCast_re
 -/
 
-#print Complex.int_cast_im /-
+#print Complex.intCast_im /-
 @[simp, norm_cast]
-theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast, of_real_im]
-#align complex.int_cast_im Complex.int_cast_im
+theorem intCast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast, of_real_im]
+#align complex.int_cast_im Complex.intCast_im
 -/
 
-#print Complex.ofReal_rat_cast /-
+#print Complex.ofReal_ratCast /-
 @[simp, norm_cast]
-theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_ratCast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
   map_ratCast ofReal n
-#align complex.of_real_rat_cast Complex.ofReal_rat_cast
+#align complex.of_real_rat_cast Complex.ofReal_ratCast
 -/
 
-#print Complex.rat_cast_re /-
+#print Complex.ratCast_re /-
 @[simp, norm_cast]
-theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
-#align complex.rat_cast_re Complex.rat_cast_re
+theorem ratCast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
+#align complex.rat_cast_re Complex.ratCast_re
 -/
 
-#print Complex.rat_cast_im /-
+#print Complex.ratCast_im /-
 @[simp, norm_cast]
-theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
-#align complex.rat_cast_im Complex.rat_cast_im
+theorem ratCast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
+#align complex.rat_cast_im Complex.ratCast_im
 -/
 
 /-! ### Characteristic zero -/
 
 
-#print Complex.charZero /-
-instance charZero : CharZero ℂ :=
+#print Complex.instCharZero /-
+instance instCharZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
-#align complex.char_zero_complex Complex.charZero
+#align complex.char_zero_complex Complex.instCharZero
 -/
 
 #print Complex.re_eq_add_conj /-

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

@@ -1403,7 +1403,7 @@ scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
 protected def starOrderedRing : StarOrderedRing ℂ :=
-  StarOrderedRing.ofNonnegIff' (fun _ _ => add_le_add_left) fun r =>
+  StarOrderedRing.of_nonneg_iff' (fun _ _ => add_le_add_left) fun r =>
     by
     refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
     · have h₁ : 0 ≤ r.re := by rw [le_def] at hr; exact hr.1

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

@@ -1553,14 +1553,14 @@ variable {α : Type _} (s : Finset α)
 #print Complex.ofReal_prod /-
 @[simp, norm_cast]
 theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
-  RingHom.map_prod ofReal _ _
+  map_prod ofReal _ _
 #align complex.of_real_prod Complex.ofReal_prod
 -/
 
 #print Complex.ofReal_sum /-
 @[simp, norm_cast]
 theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
-  RingHom.map_sum ofReal _ _
+  map_sum ofReal _ _
 #align complex.of_real_sum Complex.ofReal_sum
 -/
 

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

@@ -248,33 +248,25 @@ theorem add_im (z w : ℂ) : (z + w).im = z.im + w.im :=
 #align complex.add_im Complex.add_im
 -/
 
-#print Complex.bit0_re /-
 @[simp]
 theorem bit0_re (z : ℂ) : (bit0 z).re = bit0 z.re :=
   rfl
 #align complex.bit0_re Complex.bit0_re
--/
 
-#print Complex.bit1_re /-
 @[simp]
 theorem bit1_re (z : ℂ) : (bit1 z).re = bit1 z.re :=
   rfl
 #align complex.bit1_re Complex.bit1_re
--/
 
-#print Complex.bit0_im /-
 @[simp]
 theorem bit0_im (z : ℂ) : (bit0 z).im = bit0 z.im :=
   Eq.refl _
 #align complex.bit0_im Complex.bit0_im
--/
 
-#print Complex.bit1_im /-
 @[simp]
 theorem bit1_im (z : ℂ) : (bit1 z).im = bit0 z.im :=
   add_zero _
 #align complex.bit1_im Complex.bit1_im
--/
 
 #print Complex.ofReal_add /-
 @[simp, norm_cast]
@@ -283,19 +275,15 @@ theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
 #align complex.of_real_add Complex.ofReal_add
 -/
 
-#print Complex.ofReal_bit0 /-
 @[simp, norm_cast]
-theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
+theorem of_real_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
   ext_iff.2 <| by simp [bit0]
-#align complex.of_real_bit0 Complex.ofReal_bit0
--/
+#align complex.of_real_bit0 Complex.of_real_bit0
 
-#print Complex.ofReal_bit1 /-
 @[simp, norm_cast]
-theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
+theorem of_real_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
   ext_iff.2 <| by simp [bit1]
-#align complex.of_real_bit1 Complex.ofReal_bit1
--/
+#align complex.of_real_bit1 Complex.of_real_bit1
 
 instance : Neg ℂ :=
   ⟨fun z => ⟨-z.re, -z.im⟩⟩
@@ -589,17 +577,13 @@ theorem conj_I : conj I = -I :=
 #align complex.conj_I Complex.conj_I
 -/
 
-#print Complex.conj_bit0 /-
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit0 Complex.conj_bit0
--/
 
-#print Complex.conj_bit1 /-
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit1 Complex.conj_bit1
--/
 
 #print Complex.conj_neg_I /-
 @[simp]
@@ -824,7 +808,7 @@ theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
 #print Complex.ofReal_pow /-
 @[simp, norm_cast]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
-  induction n <;> simp [*, of_real_mul, pow_succ]
+  induction n <;> simp [*, of_real_mul, pow_succ']
 #align complex.of_real_pow Complex.ofReal_pow
 -/
 
@@ -1039,7 +1023,7 @@ instance charZero : CharZero ℂ :=
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   simp only [add_conj, of_real_mul, of_real_one, of_real_bit0,
-    mul_div_cancel_left (z.re : ℂ) two_ne_zero]
+    mul_div_cancel_left₀ (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 -/
 
@@ -1047,7 +1031,7 @@ theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   simp only [sub_conj, of_real_mul, of_real_one, of_real_bit0, mul_right_comm,
-    mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
+    mul_div_cancel_left₀ _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 -/
 
@@ -1152,7 +1136,7 @@ theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
 #print Complex.sq_abs_sub_sq_re /-
 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
-  rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel']
+  rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel_left]
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
 -/
 

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

@@ -1031,7 +1031,7 @@ theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast,
 #print Complex.charZero /-
 instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
-    rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h 
+    rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
 #align complex.char_zero_complex Complex.charZero
 -/
 
@@ -1422,8 +1422,8 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
   StarOrderedRing.ofNonnegIff' (fun _ _ => add_le_add_left) fun r =>
     by
     refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-    · have h₁ : 0 ≤ r.re := by rw [le_def] at hr ; exact hr.1
-      have h₂ : r.im = 0 := by rw [le_def] at hr ; exact hr.2.symm
+    · have h₁ : 0 ≤ r.re := by rw [le_def] at hr; exact hr.1
+      have h₂ : r.im = 0 := by rw [le_def] at hr; exact hr.2.symm
       ext
       ·
         simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,
@@ -1495,7 +1495,7 @@ theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) :=
     apply lt_of_le_of_lt (abs_le_abs_re_add_abs_im _)
     dsimp [lim_aux] at *
     have := add_lt_add H₁ H₂
-    rwa [add_halves] at this 
+    rwa [add_halves] at this
 #align complex.equiv_lim_aux Complex.equiv_limAux
 -/
 

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

@@ -1303,10 +1303,10 @@ theorem abs_natCast (n : ℕ) : abs (n : ℂ) = n := by
 #align complex.abs_cast_nat Complex.abs_natCast
 -/
 
-#print Complex.int_cast_abs /-
+#print Complex.abs_intCast /-
 @[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : ↑|n| = abs n := by rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
-#align complex.int_cast_abs Complex.int_cast_abs
+theorem abs_intCast (n : ℤ) : ↑|n| = abs n := by rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
+#align complex.int_cast_abs Complex.abs_intCast
 -/
 
 #print Complex.normSq_eq_abs /-

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

@@ -1442,7 +1442,7 @@ end ComplexOrder
 /-! ### Cauchy sequences -/
 
 
-local notation "abs'" => Abs.abs
+local notation "abs'" => abs
 
 #print Complex.isCauSeq_re /-
 theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>

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

@@ -348,19 +348,19 @@ theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
 #align complex.of_real_mul Complex.ofReal_mul
 -/
 
-#print Complex.ofReal_mul_re /-
-theorem ofReal_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
-#align complex.of_real_mul_re Complex.ofReal_mul_re
+#print Complex.re_ofReal_mul /-
+theorem re_ofReal_mul (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
+#align complex.of_real_mul_re Complex.re_ofReal_mul
 -/
 
-#print Complex.ofReal_mul_im /-
-theorem ofReal_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
-#align complex.of_real_mul_im Complex.ofReal_mul_im
+#print Complex.im_ofReal_mul /-
+theorem im_ofReal_mul (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
+#align complex.of_real_mul_im Complex.im_ofReal_mul
 -/
 
 #print Complex.ofReal_mul' /-
 theorem ofReal_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
-  ext (ofReal_mul_re _ _) (ofReal_mul_im _ _)
+  ext (re_ofReal_mul _ _) (im_ofReal_mul _ _)
 #align complex.of_real_mul' Complex.ofReal_mul'
 -/
 

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

@@ -704,7 +704,7 @@ theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 
 #print Complex.normSq_nonneg /-
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
-  add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
+  add_nonneg (hMul_self_nonneg _) (hMul_self_nonneg _)
 #align complex.norm_sq_nonneg Complex.normSq_nonneg
 -/
 
@@ -758,13 +758,13 @@ theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z *
 
 #print Complex.re_sq_le_normSq /-
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
-  le_add_of_nonneg_right (mul_self_nonneg _)
+  le_add_of_nonneg_right (hMul_self_nonneg _)
 #align complex.re_sq_le_norm_sq Complex.re_sq_le_normSq
 -/
 
 #print Complex.im_sq_le_normSq /-
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
-  le_add_of_nonneg_left (mul_self_nonneg _)
+  le_add_of_nonneg_left (hMul_self_nonneg _)
 #align complex.im_sq_le_norm_sq Complex.im_sq_le_normSq
 -/
 
@@ -1216,7 +1216,7 @@ theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
 
 #print Complex.abs_re_le_abs /-
 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
-  Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq]; exact le_add_of_nonneg_right (mul_self_nonneg _)
+  Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq]; exact le_add_of_nonneg_right (hMul_self_nonneg _)
 #align complex.abs_re_le_abs Complex.abs_re_le_abs
 -/
 

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

@@ -1294,11 +1294,13 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 -/
 
-#print Complex.abs_cast_nat /-
+/- warning: complex.abs_cast_nat clashes with complex.abs_of_nat -> Complex.abs_natCast
+Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_natCastₓ'. -/
+#print Complex.abs_natCast /-
 @[simp, norm_cast]
-theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
+theorem abs_natCast (n : ℕ) : abs (n : ℂ) = n := by
   rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
-#align complex.abs_cast_nat Complex.abs_cast_nat
+#align complex.abs_cast_nat Complex.abs_natCast
 -/
 
 #print Complex.int_cast_abs /-

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

@@ -1394,10 +1394,10 @@ theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
 #align complex.not_lt_zero_iff Complex.not_lt_zero_iff
 -/
 
-#print Complex.eq_re_ofReal_le /-
-theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by ext; rfl;
+#print Complex.eq_re_of_ofReal_le /-
+theorem eq_re_of_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by ext; rfl;
   simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
-#align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
+#align complex.eq_re_of_real_le Complex.eq_re_of_ofReal_le
 -/
 
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.

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

@@ -1129,12 +1129,12 @@ theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 -/
 
-#print Complex.abs_of_nat /-
-theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
+#print Complex.abs_natCast /-
+theorem abs_natCast (n : ℕ) : Complex.abs n = n :=
   calc
     Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
     _ = _ := abs_of_nonneg (Nat.cast_nonneg n)
-#align complex.abs_of_nat Complex.abs_of_nat
+#align complex.abs_of_nat Complex.abs_natCast
 -/
 
 #print Complex.mul_self_abs /-

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

@@ -3,7 +3,7 @@ Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 -/
-import Mathbin.Data.Real.Sqrt
+import Data.Real.Sqrt
 
 #align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
 

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

@@ -559,7 +559,7 @@ notation `conj` in the locale `complex_conjugate`. -/
 instance : StarRing ℂ where
   unit z := ⟨z.re, -z.im⟩
   star_involutive x := by simp only [eta, neg_neg]
-  star_mul a b := by ext <;> simp [add_comm] <;> ring
+  star_hMul a b := by ext <;> simp [add_comm] <;> ring
   star_add a b := by ext <;> simp [add_comm]
 
 #print Complex.conj_re /-
@@ -746,7 +746,7 @@ theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 
 #print Complex.normSq_mul /-
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
-  normSq.map_mul z w
+  normSq.map_hMul z w
 #align complex.norm_sq_mul Complex.normSq_mul
 -/
 

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

@@ -1400,7 +1400,6 @@ theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
 #align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
 -/
 
-#print Complex.strictOrderedCommRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
 -/
 protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
@@ -1411,11 +1410,9 @@ protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
     mul_pos := fun z w hz hw => by
       simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1] }
 #align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
--/
 
 scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 
-#print Complex.starOrderedRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a star ordered ring.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
@@ -1435,7 +1432,6 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
     · obtain ⟨s, rfl⟩ := h
       simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def]
 #align complex.star_ordered_ring Complex.starOrderedRing
--/
 
 scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Real.Sqrt
 
+#align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # The complex numbers
 

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

@@ -1269,7 +1269,7 @@ theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
 -/
 
 #print Complex.abs_le_sqrt_two_mul_max /-
-theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
+theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max |z.re| |z.im| :=
   by
   cases' z with x y
   simp only [abs_apply, norm_sq_mk, ← sq]
@@ -1278,7 +1278,7 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
   calc
     Real.sqrt (x ^ 2 + y ^ 2) ≤ Real.sqrt (y ^ 2 + y ^ 2) :=
       Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
-    _ = Real.sqrt 2 * max (|x|) (|y|) := by
+    _ = Real.sqrt 2 * max |x| |y| := by
       rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 -/
@@ -1306,8 +1306,7 @@ theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
 
 #print Complex.int_cast_abs /-
 @[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
-  rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
+theorem int_cast_abs (n : ℤ) : ↑|n| = abs n := by rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
 #align complex.int_cast_abs Complex.int_cast_abs
 -/
 

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

@@ -37,7 +37,6 @@ structure Complex : Type where
 #align complex Complex
 -/
 
--- mathport name: exprℂ
 notation "ℂ" => Complex
 
 namespace Complex
@@ -112,25 +111,35 @@ theorem ofReal_re (r : ℝ) : (r : ℂ).re = r :=
 #align complex.of_real_re Complex.ofReal_re
 -/
 
+#print Complex.ofReal_im /-
 @[simp, norm_cast]
 theorem ofReal_im (r : ℝ) : (r : ℂ).im = 0 :=
   rfl
 #align complex.of_real_im Complex.ofReal_im
+-/
 
+#print Complex.ofReal_def /-
 theorem ofReal_def (r : ℝ) : (r : ℂ) = ⟨r, 0⟩ :=
   rfl
 #align complex.of_real_def Complex.ofReal_def
+-/
 
+#print Complex.ofReal_inj /-
 @[simp, norm_cast]
 theorem ofReal_inj {z w : ℝ} : (z : ℂ) = w ↔ z = w :=
   ⟨congr_arg re, congr_arg _⟩
 #align complex.of_real_inj Complex.ofReal_inj
+-/
 
+#print Complex.ofReal_injective /-
 theorem ofReal_injective : Function.Injective (coe : ℝ → ℂ) := fun z w => congr_arg re
 #align complex.of_real_injective Complex.ofReal_injective
+-/
 
+#print Complex.canLift /-
 instance canLift : CanLift ℂ ℝ coe fun z => z.im = 0 where prf z hz := ⟨z.re, ext rfl hz.symm⟩
 #align complex.can_lift Complex.canLift
+-/
 
 #print Complex.Set.reProdIm /-
 /-- The product of a set on the real axis and a set on the imaginary axis of the complex plane,
@@ -140,7 +149,6 @@ def Complex.Set.reProdIm (s t : Set ℝ) : Set ℂ :=
 #align set.re_prod_im Complex.Set.reProdIm
 -/
 
--- mathport name: «expr ×ℂ »
 infixl:72 " ×ℂ " => Complex.Set.reProdIm
 
 #print Complex.mem_reProdIm /-
@@ -155,122 +163,166 @@ instance : Zero ℂ :=
 instance : Inhabited ℂ :=
   ⟨0⟩
 
+#print Complex.zero_re /-
 @[simp]
 theorem zero_re : (0 : ℂ).re = 0 :=
   rfl
 #align complex.zero_re Complex.zero_re
+-/
 
+#print Complex.zero_im /-
 @[simp]
 theorem zero_im : (0 : ℂ).im = 0 :=
   rfl
 #align complex.zero_im Complex.zero_im
+-/
 
+#print Complex.ofReal_zero /-
 @[simp, norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : ℂ) = 0 :=
   rfl
 #align complex.of_real_zero Complex.ofReal_zero
+-/
 
+#print Complex.ofReal_eq_zero /-
 @[simp]
 theorem ofReal_eq_zero {z : ℝ} : (z : ℂ) = 0 ↔ z = 0 :=
   ofReal_inj
 #align complex.of_real_eq_zero Complex.ofReal_eq_zero
+-/
 
+#print Complex.ofReal_ne_zero /-
 theorem ofReal_ne_zero {z : ℝ} : (z : ℂ) ≠ 0 ↔ z ≠ 0 :=
   not_congr ofReal_eq_zero
 #align complex.of_real_ne_zero Complex.ofReal_ne_zero
+-/
 
 instance : One ℂ :=
   ⟨(1 : ℝ)⟩
 
+#print Complex.one_re /-
 @[simp]
 theorem one_re : (1 : ℂ).re = 1 :=
   rfl
 #align complex.one_re Complex.one_re
+-/
 
+#print Complex.one_im /-
 @[simp]
 theorem one_im : (1 : ℂ).im = 0 :=
   rfl
 #align complex.one_im Complex.one_im
+-/
 
+#print Complex.ofReal_one /-
 @[simp, norm_cast]
 theorem ofReal_one : ((1 : ℝ) : ℂ) = 1 :=
   rfl
 #align complex.of_real_one Complex.ofReal_one
+-/
 
+#print Complex.ofReal_eq_one /-
 @[simp]
 theorem ofReal_eq_one {z : ℝ} : (z : ℂ) = 1 ↔ z = 1 :=
   ofReal_inj
 #align complex.of_real_eq_one Complex.ofReal_eq_one
+-/
 
+#print Complex.ofReal_ne_one /-
 theorem ofReal_ne_one {z : ℝ} : (z : ℂ) ≠ 1 ↔ z ≠ 1 :=
   not_congr ofReal_eq_one
 #align complex.of_real_ne_one Complex.ofReal_ne_one
+-/
 
 instance : Add ℂ :=
   ⟨fun z w => ⟨z.re + w.re, z.im + w.im⟩⟩
 
+#print Complex.add_re /-
 @[simp]
 theorem add_re (z w : ℂ) : (z + w).re = z.re + w.re :=
   rfl
 #align complex.add_re Complex.add_re
+-/
 
+#print Complex.add_im /-
 @[simp]
 theorem add_im (z w : ℂ) : (z + w).im = z.im + w.im :=
   rfl
 #align complex.add_im Complex.add_im
+-/
 
+#print Complex.bit0_re /-
 @[simp]
 theorem bit0_re (z : ℂ) : (bit0 z).re = bit0 z.re :=
   rfl
 #align complex.bit0_re Complex.bit0_re
+-/
 
+#print Complex.bit1_re /-
 @[simp]
 theorem bit1_re (z : ℂ) : (bit1 z).re = bit1 z.re :=
   rfl
 #align complex.bit1_re Complex.bit1_re
+-/
 
+#print Complex.bit0_im /-
 @[simp]
 theorem bit0_im (z : ℂ) : (bit0 z).im = bit0 z.im :=
   Eq.refl _
 #align complex.bit0_im Complex.bit0_im
+-/
 
+#print Complex.bit1_im /-
 @[simp]
 theorem bit1_im (z : ℂ) : (bit1 z).im = bit0 z.im :=
   add_zero _
 #align complex.bit1_im Complex.bit1_im
+-/
 
+#print Complex.ofReal_add /-
 @[simp, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
   ext_iff.2 <| by simp
 #align complex.of_real_add Complex.ofReal_add
+-/
 
+#print Complex.ofReal_bit0 /-
 @[simp, norm_cast]
 theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
   ext_iff.2 <| by simp [bit0]
 #align complex.of_real_bit0 Complex.ofReal_bit0
+-/
 
+#print Complex.ofReal_bit1 /-
 @[simp, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
   ext_iff.2 <| by simp [bit1]
 #align complex.of_real_bit1 Complex.ofReal_bit1
+-/
 
 instance : Neg ℂ :=
   ⟨fun z => ⟨-z.re, -z.im⟩⟩
 
+#print Complex.neg_re /-
 @[simp]
 theorem neg_re (z : ℂ) : (-z).re = -z.re :=
   rfl
 #align complex.neg_re Complex.neg_re
+-/
 
+#print Complex.neg_im /-
 @[simp]
 theorem neg_im (z : ℂ) : (-z).im = -z.im :=
   rfl
 #align complex.neg_im Complex.neg_im
+-/
 
+#print Complex.ofReal_neg /-
 @[simp, norm_cast]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : ℂ) = -r :=
   ext_iff.2 <| by simp
 #align complex.of_real_neg Complex.ofReal_neg
+-/
 
 instance : Sub ℂ :=
   ⟨fun z w => ⟨z.re - w.re, z.im - w.im⟩⟩
@@ -278,30 +330,42 @@ instance : Sub ℂ :=
 instance : Mul ℂ :=
   ⟨fun z w => ⟨z.re * w.re - z.im * w.im, z.re * w.im + z.im * w.re⟩⟩
 
+#print Complex.mul_re /-
 @[simp]
 theorem mul_re (z w : ℂ) : (z * w).re = z.re * w.re - z.im * w.im :=
   rfl
 #align complex.mul_re Complex.mul_re
+-/
 
+#print Complex.mul_im /-
 @[simp]
 theorem mul_im (z w : ℂ) : (z * w).im = z.re * w.im + z.im * w.re :=
   rfl
 #align complex.mul_im Complex.mul_im
+-/
 
+#print Complex.ofReal_mul /-
 @[simp, norm_cast]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
   ext_iff.2 <| by simp
 #align complex.of_real_mul Complex.ofReal_mul
+-/
 
+#print Complex.ofReal_mul_re /-
 theorem ofReal_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
 #align complex.of_real_mul_re Complex.ofReal_mul_re
+-/
 
+#print Complex.ofReal_mul_im /-
 theorem ofReal_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
 #align complex.of_real_mul_im Complex.ofReal_mul_im
+-/
 
+#print Complex.ofReal_mul' /-
 theorem ofReal_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
   ext (ofReal_mul_re _ _) (ofReal_mul_im _ _)
 #align complex.of_real_mul' Complex.ofReal_mul'
+-/
 
 /-! ### The imaginary unit, `I` -/
 
@@ -313,49 +377,71 @@ def I : ℂ :=
 #align complex.I Complex.I
 -/
 
+#print Complex.I_re /-
 @[simp]
 theorem I_re : I.re = 0 :=
   rfl
 #align complex.I_re Complex.I_re
+-/
 
+#print Complex.I_im /-
 @[simp]
 theorem I_im : I.im = 1 :=
   rfl
 #align complex.I_im Complex.I_im
+-/
 
+#print Complex.I_mul_I /-
 @[simp]
 theorem I_mul_I : I * I = -1 :=
   ext_iff.2 <| by simp
 #align complex.I_mul_I Complex.I_mul_I
+-/
 
+#print Complex.I_mul /-
 theorem I_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
   ext_iff.2 <| by simp
 #align complex.I_mul Complex.I_mul
+-/
 
+#print Complex.I_ne_zero /-
 theorem I_ne_zero : (I : ℂ) ≠ 0 :=
   mt (congr_arg im) zero_ne_one.symm
 #align complex.I_ne_zero Complex.I_ne_zero
+-/
 
+#print Complex.mk_eq_add_mul_I /-
 theorem mk_eq_add_mul_I (a b : ℝ) : Complex.mk a b = a + b * I :=
   ext_iff.2 <| by simp
 #align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_I
+-/
 
+#print Complex.re_add_im /-
 @[simp]
 theorem re_add_im (z : ℂ) : (z.re : ℂ) + z.im * I = z :=
   ext_iff.2 <| by simp
 #align complex.re_add_im Complex.re_add_im
+-/
 
+#print Complex.mul_I_re /-
 theorem mul_I_re (z : ℂ) : (z * I).re = -z.im := by simp
 #align complex.mul_I_re Complex.mul_I_re
+-/
 
+#print Complex.mul_I_im /-
 theorem mul_I_im (z : ℂ) : (z * I).im = z.re := by simp
 #align complex.mul_I_im Complex.mul_I_im
+-/
 
+#print Complex.I_mul_re /-
 theorem I_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
 #align complex.I_mul_re Complex.I_mul_re
+-/
 
+#print Complex.I_mul_im /-
 theorem I_mul_im (z : ℂ) : (I * z).im = z.re := by simp
 #align complex.I_mul_im Complex.I_mul_im
+-/
 
 #print Complex.equivRealProd_symm_apply /-
 @[simp]
@@ -423,37 +509,49 @@ instance : Ring ℂ := by infer_instance
 instance : CommSemiring ℂ :=
   inferInstance
 
+#print Complex.reAddGroupHom /-
 /-- The "real part" map, considered as an additive group homomorphism. -/
 def reAddGroupHom : ℂ →+ ℝ where
   toFun := re
   map_zero' := zero_re
   map_add' := add_re
 #align complex.re_add_group_hom Complex.reAddGroupHom
+-/
 
+#print Complex.coe_reAddGroupHom /-
 @[simp]
 theorem coe_reAddGroupHom : (reAddGroupHom : ℂ → ℝ) = re :=
   rfl
 #align complex.coe_re_add_group_hom Complex.coe_reAddGroupHom
+-/
 
+#print Complex.imAddGroupHom /-
 /-- The "imaginary part" map, considered as an additive group homomorphism. -/
 def imAddGroupHom : ℂ →+ ℝ where
   toFun := im
   map_zero' := zero_im
   map_add' := add_im
 #align complex.im_add_group_hom Complex.imAddGroupHom
+-/
 
+#print Complex.coe_imAddGroupHom /-
 @[simp]
 theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
   rfl
 #align complex.coe_im_add_group_hom Complex.coe_imAddGroupHom
+-/
 
+#print Complex.I_pow_bit0 /-
 @[simp]
 theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
 #align complex.I_pow_bit0 Complex.I_pow_bit0
+-/
 
+#print Complex.I_pow_bit1 /-
 @[simp]
 theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
 #align complex.I_pow_bit1 Complex.I_pow_bit1
+-/
 
 /-! ### Complex conjugation -/
 
@@ -467,58 +565,80 @@ instance : StarRing ℂ where
   star_mul a b := by ext <;> simp [add_comm] <;> ring
   star_add a b := by ext <;> simp [add_comm]
 
+#print Complex.conj_re /-
 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
   rfl
 #align complex.conj_re Complex.conj_re
+-/
 
+#print Complex.conj_im /-
 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
   rfl
 #align complex.conj_im Complex.conj_im
+-/
 
+#print Complex.conj_ofReal /-
 theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
 #align complex.conj_of_real Complex.conj_ofReal
+-/
 
+#print Complex.conj_I /-
 @[simp]
 theorem conj_I : conj I = -I :=
   ext_iff.2 <| by simp
 #align complex.conj_I Complex.conj_I
+-/
 
+#print Complex.conj_bit0 /-
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit0 Complex.conj_bit0
+-/
 
+#print Complex.conj_bit1 /-
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit1 Complex.conj_bit1
+-/
 
+#print Complex.conj_neg_I /-
 @[simp]
 theorem conj_neg_I : conj (-I) = I :=
   ext_iff.2 <| by simp
 #align complex.conj_neg_I Complex.conj_neg_I
+-/
 
+#print Complex.conj_eq_iff_real /-
 theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_of_real]⟩
 #align complex.conj_eq_iff_real Complex.conj_eq_iff_real
+-/
 
+#print Complex.conj_eq_iff_re /-
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
 #align complex.conj_eq_iff_re Complex.conj_eq_iff_re
+-/
 
+#print Complex.conj_eq_iff_im /-
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
 #align complex.conj_eq_iff_im Complex.conj_eq_iff_im
+-/
 
+#print Complex.star_def /-
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
 @[simp, nolint simp_nf]
 theorem star_def : (Star.star : ℂ → ℂ) = conj :=
   rfl
 #align complex.star_def Complex.star_def
+-/
 
 /-! ### Norm squared -/
 
@@ -534,94 +654,134 @@ def normSq : ℂ →*₀ ℝ where
 #align complex.norm_sq Complex.normSq
 -/
 
+#print Complex.normSq_apply /-
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
 #align complex.norm_sq_apply Complex.normSq_apply
+-/
 
+#print Complex.normSq_ofReal /-
 @[simp]
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
 #align complex.norm_sq_of_real Complex.normSq_ofReal
+-/
 
+#print Complex.normSq_mk /-
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
   rfl
 #align complex.norm_sq_mk Complex.normSq_mk
+-/
 
+#print Complex.normSq_add_mul_I /-
 theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
 #align complex.norm_sq_add_mul_I Complex.normSq_add_mul_I
+-/
 
+#print Complex.normSq_eq_conj_mul_self /-
 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
 #align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_self
+-/
 
+#print Complex.normSq_zero /-
 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
   normSq.map_zero
 #align complex.norm_sq_zero Complex.normSq_zero
+-/
 
+#print Complex.normSq_one /-
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
+-/
 
+#print Complex.normSq_I /-
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 #align complex.norm_sq_I Complex.normSq_I
+-/
 
+#print Complex.normSq_nonneg /-
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align complex.norm_sq_nonneg Complex.normSq_nonneg
+-/
 
+#print Complex.range_normSq /-
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
   Subset.antisymm (range_subset_iff.2 normSq_nonneg) fun x hx =>
     ⟨Real.sqrt x, by rw [norm_sq_of_real, Real.mul_self_sqrt hx]⟩
 #align complex.range_norm_sq Complex.range_normSq
+-/
 
+#print Complex.normSq_eq_zero /-
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
     ext (eq_zero_of_mul_self_add_mul_self_eq_zero h)
       (eq_zero_of_mul_self_add_mul_self_eq_zero <| (add_comm _ _).trans h),
     fun h => h.symm ▸ normSq_zero⟩
 #align complex.norm_sq_eq_zero Complex.normSq_eq_zero
+-/
 
+#print Complex.normSq_pos /-
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
   (normSq_nonneg z).lt_iff_ne.trans <| not_congr (eq_comm.trans normSq_eq_zero)
 #align complex.norm_sq_pos Complex.normSq_pos
+-/
 
+#print Complex.normSq_neg /-
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_neg Complex.normSq_neg
+-/
 
+#print Complex.normSq_conj /-
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_conj Complex.normSq_conj
+-/
 
+#print Complex.normSq_mul /-
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align complex.norm_sq_mul Complex.normSq_mul
+-/
 
+#print Complex.normSq_add /-
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
 #align complex.norm_sq_add Complex.normSq_add
+-/
 
+#print Complex.re_sq_le_normSq /-
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.re_sq_le_norm_sq Complex.re_sq_le_normSq
+-/
 
+#print Complex.im_sq_le_normSq /-
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align complex.im_sq_le_norm_sq Complex.im_sq_le_normSq
+-/
 
+#print Complex.mul_conj /-
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
 #align complex.mul_conj Complex.mul_conj
+-/
 
+#print Complex.add_conj /-
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
 #align complex.add_conj Complex.add_conj
+-/
 
 #print Complex.ofReal /-
 /-- The coercion `ℝ → ℂ` as a `ring_hom`. -/
@@ -630,44 +790,60 @@ def ofReal : ℝ →+* ℂ :=
 #align complex.of_real Complex.ofReal
 -/
 
+#print Complex.ofReal_eq_coe /-
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
   rfl
 #align complex.of_real_eq_coe Complex.ofReal_eq_coe
+-/
 
+#print Complex.I_sq /-
 @[simp]
 theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
 #align complex.I_sq Complex.I_sq
+-/
 
+#print Complex.sub_re /-
 @[simp]
 theorem sub_re (z w : ℂ) : (z - w).re = z.re - w.re :=
   rfl
 #align complex.sub_re Complex.sub_re
+-/
 
+#print Complex.sub_im /-
 @[simp]
 theorem sub_im (z w : ℂ) : (z - w).im = z.im - w.im :=
   rfl
 #align complex.sub_im Complex.sub_im
+-/
 
+#print Complex.ofReal_sub /-
 @[simp, norm_cast]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
   ext_iff.2 <| by simp
 #align complex.of_real_sub Complex.ofReal_sub
+-/
 
+#print Complex.ofReal_pow /-
 @[simp, norm_cast]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
   induction n <;> simp [*, of_real_mul, pow_succ]
 #align complex.of_real_pow Complex.ofReal_pow
+-/
 
+#print Complex.sub_conj /-
 theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
 #align complex.sub_conj Complex.sub_conj
+-/
 
+#print Complex.normSq_sub /-
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
   rw [sub_eq_add_neg, norm_sq_add]
   simp only [RingHom.map_neg, mul_neg, neg_re, Tactic.Ring.add_neg_eq_sub, norm_sq_neg]
 #align complex.norm_sq_sub Complex.normSq_sub
+-/
 
 /-! ### Inversion -/
 
@@ -675,30 +851,42 @@ theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z *
 noncomputable instance : Inv ℂ :=
   ⟨fun z => conj z * ((normSq z)⁻¹ : ℝ)⟩
 
+#print Complex.inv_def /-
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
 #align complex.inv_def Complex.inv_def
+-/
 
+#print Complex.inv_re /-
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
 #align complex.inv_re Complex.inv_re
+-/
 
+#print Complex.inv_im /-
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
 #align complex.inv_im Complex.inv_im
+-/
 
+#print Complex.ofReal_inv /-
 @[simp, norm_cast]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : ℂ) = r⁻¹ :=
   ext_iff.2 <| by simp
 #align complex.of_real_inv Complex.ofReal_inv
+-/
 
+#print Complex.inv_zero /-
 protected theorem inv_zero : (0⁻¹ : ℂ) = 0 := by rw [← of_real_zero, ← of_real_inv, inv_zero]
 #align complex.inv_zero Complex.inv_zero
+-/
 
+#print Complex.mul_inv_cancel /-
 protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
   rw [inv_def, ← mul_assoc, mul_conj, ← of_real_mul, mul_inv_cancel (mt norm_sq_eq_zero.1 h),
     of_real_one]
 #align complex.mul_inv_cancel Complex.mul_inv_cancel
+-/
 
 /-! ### Field instance and lemmas -/
 
@@ -709,123 +897,168 @@ noncomputable instance : Field ℂ :=
     mul_inv_cancel := @Complex.mul_inv_cancel
     inv_zero := Complex.inv_zero }
 
+#print Complex.I_zpow_bit0 /-
 @[simp]
 theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
 #align complex.I_zpow_bit0 Complex.I_zpow_bit0
+-/
 
+#print Complex.I_zpow_bit1 /-
 @[simp]
 theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
 #align complex.I_zpow_bit1 Complex.I_zpow_bit1
+-/
 
+#print Complex.div_re /-
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
 #align complex.div_re Complex.div_re
+-/
 
+#print Complex.div_im /-
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
 #align complex.div_im Complex.div_im
+-/
 
+#print Complex.conj_inv /-
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align complex.conj_inv Complex.conj_inv
+-/
 
+#print Complex.ofReal_div /-
 @[simp, norm_cast]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : ℂ) = r / s :=
   map_div₀ ofReal r s
 #align complex.of_real_div Complex.ofReal_div
+-/
 
+#print Complex.ofReal_zpow /-
 @[simp, norm_cast]
 theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : ℂ) = (r : ℂ) ^ n :=
   map_zpow₀ ofReal r n
 #align complex.of_real_zpow Complex.ofReal_zpow
+-/
 
+#print Complex.div_I /-
 @[simp]
 theorem div_I (z : ℂ) : z / I = -(z * I) :=
   (div_eq_iff_mul_eq I_ne_zero).2 <| by simp [mul_assoc]
 #align complex.div_I Complex.div_I
+-/
 
+#print Complex.inv_I /-
 @[simp]
 theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
 #align complex.inv_I Complex.inv_I
+-/
 
+#print Complex.normSq_inv /-
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
 #align complex.norm_sq_inv Complex.normSq_inv
+-/
 
+#print Complex.normSq_div /-
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
 #align complex.norm_sq_div Complex.normSq_div
+-/
 
 /-! ### Cast lemmas -/
 
 
+#print Complex.ofReal_nat_cast /-
 @[simp, norm_cast]
 theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
   map_natCast ofReal n
 #align complex.of_real_nat_cast Complex.ofReal_nat_cast
+-/
 
+#print Complex.nat_cast_re /-
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
 #align complex.nat_cast_re Complex.nat_cast_re
+-/
 
+#print Complex.nat_cast_im /-
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
 #align complex.nat_cast_im Complex.nat_cast_im
+-/
 
+#print Complex.ofReal_int_cast /-
 @[simp, norm_cast]
 theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
   map_intCast ofReal n
 #align complex.of_real_int_cast Complex.ofReal_int_cast
+-/
 
+#print Complex.int_cast_re /-
 @[simp, norm_cast]
 theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← of_real_int_cast, of_real_re]
 #align complex.int_cast_re Complex.int_cast_re
+-/
 
+#print Complex.int_cast_im /-
 @[simp, norm_cast]
 theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast, of_real_im]
 #align complex.int_cast_im Complex.int_cast_im
+-/
 
+#print Complex.ofReal_rat_cast /-
 @[simp, norm_cast]
 theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
   map_ratCast ofReal n
 #align complex.of_real_rat_cast Complex.ofReal_rat_cast
+-/
 
+#print Complex.rat_cast_re /-
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
 #align complex.rat_cast_re Complex.rat_cast_re
+-/
 
+#print Complex.rat_cast_im /-
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align complex.rat_cast_im Complex.rat_cast_im
+-/
 
 /-! ### Characteristic zero -/
 
 
+#print Complex.charZero /-
 instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h 
 #align complex.char_zero_complex Complex.charZero
+-/
 
+#print Complex.re_eq_add_conj /-
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   simp only [add_conj, of_real_mul, of_real_one, of_real_bit0,
     mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
+-/
 
+#print Complex.im_eq_sub_conj /-
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   simp only [sub_conj, of_real_mul, of_real_one, of_real_bit0, mul_right_comm,
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
+-/
 
 /-! ### Absolute value -/
 
 
 namespace AbsTheory
 
--- mathport name: abs
 -- We develop enough theory to bundle `abs` into an `absolute_value` before making things public;
 -- this is so there's not two versions of it hanging around.
 local notation "abs" z => (normSq z).sqrt
@@ -836,8 +1069,10 @@ private theorem mul_self_abs (z : ℂ) : ((abs z) * abs z) = normSq z :=
 private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
   Real.sqrt_nonneg _
 
+#print Complex.AbsTheory.abs_conj /-
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
+-/
 
 private theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   by
@@ -872,119 +1107,168 @@ noncomputable def Complex.abs : AbsoluteValue ℂ ℝ
 
 end AbsTheory
 
+#print Complex.abs_def /-
 theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
 #align complex.abs_def Complex.abs_def
+-/
 
+#print Complex.abs_apply /-
 theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
 #align complex.abs_apply Complex.abs_apply
+-/
 
+#print Complex.abs_ofReal /-
 @[simp, norm_cast]
 theorem abs_ofReal (r : ℝ) : abs r = |r| := by
   simp [abs, norm_sq_of_real, Real.sqrt_mul_self_eq_abs]
 #align complex.abs_of_real Complex.abs_ofReal
+-/
 
+#print Complex.abs_of_nonneg /-
 theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
   (abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
+-/
 
+#print Complex.abs_of_nat /-
 theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
     Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
     _ = _ := abs_of_nonneg (Nat.cast_nonneg n)
 #align complex.abs_of_nat Complex.abs_of_nat
+-/
 
+#print Complex.mul_self_abs /-
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
 #align complex.mul_self_abs Complex.mul_self_abs
+-/
 
+#print Complex.sq_abs /-
 theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
 #align complex.sq_abs Complex.sq_abs
+-/
 
+#print Complex.sq_abs_sub_sq_re /-
 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
   rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel']
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
+-/
 
+#print Complex.sq_abs_sub_sq_im /-
 @[simp]
 theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
   rw [← sq_abs_sub_sq_re, sub_sub_cancel]
 #align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
+-/
 
+#print Complex.abs_I /-
 @[simp]
 theorem abs_I : abs I = 1 := by simp [abs]
 #align complex.abs_I Complex.abs_I
+-/
 
+#print Complex.abs_two /-
 @[simp]
 theorem abs_two : abs 2 = 2 :=
   calc
     abs 2 = abs (2 : ℝ) := by rw [of_real_bit0, of_real_one]
     _ = (2 : ℝ) := abs_of_nonneg (by norm_num)
 #align complex.abs_two Complex.abs_two
+-/
 
+#print Complex.range_abs /-
 @[simp]
 theorem range_abs : range abs = Ici 0 :=
   Subset.antisymm (range_subset_iff.2 abs.NonNeg) fun x hx => ⟨x, abs_of_nonneg hx⟩
 #align complex.range_abs Complex.range_abs
+-/
 
+#print Complex.abs_conj /-
 @[simp]
 theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
+-/
 
+#print Complex.abs_prod /-
 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
     abs (s.Prod f) = s.Prod fun i => abs (f i) :=
   map_prod abs _ _
 #align complex.abs_prod Complex.abs_prod
+-/
 
+#print Complex.abs_pow /-
 @[simp]
 theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
   map_pow abs z n
 #align complex.abs_pow Complex.abs_pow
+-/
 
+#print Complex.abs_zpow /-
 @[simp]
 theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
   map_zpow₀ abs z n
 #align complex.abs_zpow Complex.abs_zpow
+-/
 
+#print Complex.abs_re_le_abs /-
 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq]; exact le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.abs_re_le_abs Complex.abs_re_le_abs
+-/
 
+#print Complex.abs_im_le_abs /-
 theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
   Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq, ← sq]; exact le_add_of_nonneg_left (sq_nonneg _)
 #align complex.abs_im_le_abs Complex.abs_im_le_abs
+-/
 
+#print Complex.re_le_abs /-
 theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
 #align complex.re_le_abs Complex.re_le_abs
+-/
 
+#print Complex.im_le_abs /-
 theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
 #align complex.im_le_abs Complex.im_le_abs
+-/
 
+#print Complex.abs_re_lt_abs /-
 @[simp]
 theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
   rw [abs, AbsoluteValue.coe_mk, MulHom.coe_mk, Real.lt_sqrt (abs_nonneg _), norm_sq_apply,
     _root_.sq_abs, ← sq, lt_add_iff_pos_right, mul_self_pos]
 #align complex.abs_re_lt_abs Complex.abs_re_lt_abs
+-/
 
+#print Complex.abs_im_lt_abs /-
 @[simp]
 theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa using @abs_re_lt_abs (z * I)
 #align complex.abs_im_lt_abs Complex.abs_im_lt_abs
+-/
 
+#print Complex.abs_abs /-
 @[simp]
 theorem abs_abs (z : ℂ) : |abs z| = abs z :=
   abs_of_nonneg (abs.NonNeg _)
 #align complex.abs_abs Complex.abs_abs
+-/
 
+#print Complex.abs_le_abs_re_add_abs_im /-
 theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
 #align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
+-/
 
+#print Complex.abs_le_sqrt_two_mul_max /-
 theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
   by
   cases' z with x y
@@ -997,30 +1281,41 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
     _ = Real.sqrt 2 * max (|x|) (|y|) := by
       rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
+-/
 
+#print Complex.abs_re_div_abs_le_one /-
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_re_le_abs]
 #align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_one
+-/
 
+#print Complex.abs_im_div_abs_le_one /-
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
+-/
 
+#print Complex.abs_cast_nat /-
 @[simp, norm_cast]
 theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
   rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
 #align complex.abs_cast_nat Complex.abs_cast_nat
+-/
 
+#print Complex.int_cast_abs /-
 @[simp, norm_cast]
 theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
   rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
 #align complex.int_cast_abs Complex.int_cast_abs
+-/
 
+#print Complex.normSq_eq_abs /-
 theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
 #align complex.norm_sq_eq_abs Complex.normSq_eq_abs
+-/
 
 #print Complex.partialOrder /-
 /-- We put a partial order on ℂ so that `z ≤ w` exactly if `w - z` is real and nonnegative.
@@ -1041,51 +1336,73 @@ section ComplexOrder
 
 scoped[ComplexOrder] attribute [instance] Complex.partialOrder
 
+#print Complex.le_def /-
 theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
   Iff.rfl
 #align complex.le_def Complex.le_def
+-/
 
+#print Complex.lt_def /-
 theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
   Iff.rfl
 #align complex.lt_def Complex.lt_def
+-/
 
+#print Complex.real_le_real /-
 @[simp, norm_cast]
 theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
 #align complex.real_le_real Complex.real_le_real
+-/
 
+#print Complex.real_lt_real /-
 @[simp, norm_cast]
 theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
 #align complex.real_lt_real Complex.real_lt_real
+-/
 
+#print Complex.zero_le_real /-
 @[simp, norm_cast]
 theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
   real_le_real
 #align complex.zero_le_real Complex.zero_le_real
+-/
 
+#print Complex.zero_lt_real /-
 @[simp, norm_cast]
 theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
   real_lt_real
 #align complex.zero_lt_real Complex.zero_lt_real
+-/
 
+#print Complex.not_le_iff /-
 theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
   rw [le_def, not_and_or, not_le]
 #align complex.not_le_iff Complex.not_le_iff
+-/
 
+#print Complex.not_lt_iff /-
 theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
   rw [lt_def, not_and_or, not_lt]
 #align complex.not_lt_iff Complex.not_lt_iff
+-/
 
+#print Complex.not_le_zero_iff /-
 theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
   not_le_iff
 #align complex.not_le_zero_iff Complex.not_le_zero_iff
+-/
 
+#print Complex.not_lt_zero_iff /-
 theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
   not_lt_iff
 #align complex.not_lt_zero_iff Complex.not_lt_zero_iff
+-/
 
+#print Complex.eq_re_ofReal_le /-
 theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by ext; rfl;
   simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
 #align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
+-/
 
 #print Complex.strictOrderedCommRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
@@ -1131,39 +1448,51 @@ end ComplexOrder
 /-! ### Cauchy sequences -/
 
 
--- mathport name: exprabs'
 local notation "abs'" => Abs.abs
 
+#print Complex.isCauSeq_re /-
 theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_re Complex.isCauSeq_re
+-/
 
+#print Complex.isCauSeq_im /-
 theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_im Complex.isCauSeq_im
+-/
 
+#print Complex.cauSeqRe /-
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_re f⟩
 #align complex.cau_seq_re Complex.cauSeqRe
+-/
 
+#print Complex.cauSeqIm /-
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_im f⟩
 #align complex.cau_seq_im Complex.cauSeqIm
+-/
 
+#print Complex.isCauSeq_abs /-
 theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.is_cau_seq_abs Complex.isCauSeq_abs
+-/
 
+#print Complex.limAux /-
 /-- The limit of a Cauchy sequence of complex numbers. -/
 noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
   ⟨CauSeq.lim (cauSeqRe f), CauSeq.lim (cauSeqIm f)⟩
 #align complex.lim_aux Complex.limAux
+-/
 
+#print Complex.equiv_limAux /-
 theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
         (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
@@ -1174,12 +1503,14 @@ theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) :=
     have := add_lt_add H₁ H₂
     rwa [add_halves] at this 
 #align complex.equiv_lim_aux Complex.equiv_limAux
+-/
 
 instance : CauSeq.IsComplete ℂ abs :=
   ⟨fun f => ⟨limAux f, equiv_limAux f⟩⟩
 
 open CauSeq
 
+#print Complex.lim_eq_lim_im_add_lim_re /-
 theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
     limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
   lim_eq_of_equiv_const <|
@@ -1189,52 +1520,71 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
         CauSeq.ext fun _ =>
           Complex.ext (by simp [lim_aux, cau_seq_re]) (by simp [lim_aux, cau_seq_im])
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
+-/
 
+#print Complex.lim_re /-
 theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_re Complex.lim_re
+-/
 
+#print Complex.lim_im /-
 theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_im Complex.lim_im
+-/
 
+#print Complex.isCauSeq_conj /-
 theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by rw [← RingHom.map_sub, abs_conj] <;> exact hi j hj⟩
 #align complex.is_cau_seq_conj Complex.isCauSeq_conj
+-/
 
+#print Complex.cauSeqConj /-
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
 noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
   ⟨_, isCauSeq_conj f⟩
 #align complex.cau_seq_conj Complex.cauSeqConj
+-/
 
+#print Complex.lim_conj /-
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])
     (by simp [cau_seq_conj, (lim_im _).symm, cau_seq_im, (lim_neg _).symm] <;> rfl)
 #align complex.lim_conj Complex.lim_conj
+-/
 
+#print Complex.cauSeqAbs /-
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_abs f.2⟩
 #align complex.cau_seq_abs Complex.cauSeqAbs
+-/
 
+#print Complex.lim_abs /-
 theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f) :=
   lim_eq_of_equiv_const fun ε ε0 =>
     let ⟨i, hi⟩ := equiv_lim f ε ε0
     ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.lim_abs Complex.lim_abs
+-/
 
 variable {α : Type _} (s : Finset α)
 
+#print Complex.ofReal_prod /-
 @[simp, norm_cast]
 theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
   RingHom.map_prod ofReal _ _
 #align complex.of_real_prod Complex.ofReal_prod
+-/
 
+#print Complex.ofReal_sum /-
 @[simp, norm_cast]
 theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
   RingHom.map_sum ofReal _ _
 #align complex.of_real_sum Complex.ofReal_sum
+-/
 
 #print Complex.re_sum /-
 @[simp]

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

@@ -893,7 +893,6 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
     Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
     _ = _ := abs_of_nonneg (Nat.cast_nonneg n)
-    
 #align complex.abs_of_nat Complex.abs_of_nat
 
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
@@ -923,7 +922,6 @@ theorem abs_two : abs 2 = 2 :=
   calc
     abs 2 = abs (2 : ℝ) := by rw [of_real_bit0, of_real_one]
     _ = (2 : ℝ) := abs_of_nonneg (by norm_num)
-    
 #align complex.abs_two Complex.abs_two
 
 @[simp]
@@ -998,7 +996,6 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
       Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
     _ = Real.sqrt 2 * max (|x|) (|y|) := by
       rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
-    
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
@@ -1191,7 +1188,6 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
       _ = CauSeq.const abs (↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I) :=
         CauSeq.ext fun _ =>
           Complex.ext (by simp [lim_aux, cau_seq_re]) (by simp [lim_aux, cau_seq_im])
-      
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
 
 theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
+! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1110,21 +1110,20 @@ scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
 protected def starOrderedRing : StarOrderedRing ℂ :=
-  { Complex.strictOrderedCommRing with
-    nonneg_iff := fun r =>
-      by
-      refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-      · have h₁ : 0 ≤ r.re := by rw [le_def] at hr ; exact hr.1
-        have h₂ : r.im = 0 := by rw [le_def] at hr ; exact hr.2.symm
-        ext
-        ·
-          simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,
-            MulZeroClass.mul_zero, ← Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
-        ·
-          simp only [h₂, add_zero, of_real_im, star_def, MulZeroClass.zero_mul, conj_im, mul_im,
-            MulZeroClass.mul_zero, neg_zero]
-      · obtain ⟨s, rfl⟩ := h
-        simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def] }
+  StarOrderedRing.ofNonnegIff' (fun _ _ => add_le_add_left) fun r =>
+    by
+    refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
+    · have h₁ : 0 ≤ r.re := by rw [le_def] at hr ; exact hr.1
+      have h₂ : r.im = 0 := by rw [le_def] at hr ; exact hr.2.symm
+      ext
+      ·
+        simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,
+          MulZeroClass.mul_zero, ← Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
+      ·
+        simp only [h₂, add_zero, of_real_im, star_def, MulZeroClass.zero_mul, conj_im, mul_im,
+          MulZeroClass.mul_zero, neg_zero]
+    · obtain ⟨s, rfl⟩ := h
+      simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def]
 #align complex.star_ordered_ring Complex.starOrderedRing
 -/
 

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

@@ -380,7 +380,11 @@ instance : AddCommGroup ℂ := by
                   sub := Sub.sub
                   nsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
                   zsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩ } <;> intros <;>
-            try rfl <;> apply ext_iff.2 <;> constructor <;> simp <;> · first |ring1|ring_nf
+            try rfl <;> apply ext_iff.2 <;> constructor <;> simp <;>
+    ·
+      first
+      | ring1
+      | ring_nf
 
 instance : AddGroupWithOne ℂ :=
   { Complex.addCommGroup with
@@ -405,7 +409,10 @@ instance : CommRing ℂ := by
           apply ext_iff.2 <;>
         constructor <;>
       simp <;>
-    · first |ring1|ring_nf
+    ·
+      first
+      | ring1
+      | ring_nf
 
 /-- This shortcut instance ensures we do not find `ring` via the noncomputable `complex.field`
 instance. -/
@@ -798,7 +805,7 @@ theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast,
 
 instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
-    rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
+    rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h 
 #align complex.char_zero_complex Complex.charZero
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
@@ -1107,8 +1114,8 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
     nonneg_iff := fun r =>
       by
       refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-      · have h₁ : 0 ≤ r.re := by rw [le_def] at hr; exact hr.1
-        have h₂ : r.im = 0 := by rw [le_def] at hr; exact hr.2.symm
+      · have h₁ : 0 ≤ r.re := by rw [le_def] at hr ; exact hr.1
+        have h₂ : r.im = 0 := by rw [le_def] at hr ; exact hr.2.symm
         ext
         ·
           simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,
@@ -1169,7 +1176,7 @@ theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) :=
     apply lt_of_le_of_lt (abs_le_abs_re_add_abs_im _)
     dsimp [lim_aux] at *
     have := add_lt_add H₁ H₂
-    rwa [add_halves] at this
+    rwa [add_halves] at this 
 #align complex.equiv_lim_aux Complex.equiv_limAux
 
 instance : CauSeq.IsComplete ℂ abs :=

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

@@ -22,7 +22,7 @@ of characteristic zero. The result that the complex numbers are algebraically cl
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 open Set Function
 
@@ -42,7 +42,7 @@ notation "ℂ" => Complex
 
 namespace Complex
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 noncomputable instance : DecidableEq ℂ :=
   Classical.decEq _

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

@@ -112,53 +112,23 @@ theorem ofReal_re (r : ℝ) : (r : ℂ).re = r :=
 #align complex.of_real_re Complex.ofReal_re
 -/
 
-/- warning: complex.of_real_im -> Complex.ofReal_im is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  forall (r : Real), Eq.{1} Real (Complex.im (Complex.ofReal' r)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_im Complex.ofReal_imₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_im (r : ℝ) : (r : ℂ).im = 0 :=
   rfl
 #align complex.of_real_im Complex.ofReal_im
 
-/- warning: complex.of_real_def -> Complex.ofReal_def is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) (Complex.mk r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall (r : Real), Eq.{1} Complex (Complex.ofReal' r) (Complex.mk r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_def Complex.ofReal_defₓ'. -/
 theorem ofReal_def (r : ℝ) : (r : ℂ) = ⟨r, 0⟩ :=
   rfl
 #align complex.of_real_def Complex.ofReal_def
 
-/- warning: complex.of_real_inj -> Complex.ofReal_inj is a dubious translation:
-lean 3 declaration is
-  forall {z : Real} {w : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) w)) (Eq.{1} Real z w)
-but is expected to have type
-  forall {z : Real} {w : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (Complex.ofReal' w)) (Eq.{1} Real z w)
-Case conversion may be inaccurate. Consider using '#align complex.of_real_inj Complex.ofReal_injₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_inj {z w : ℝ} : (z : ℂ) = w ↔ z = w :=
   ⟨congr_arg re, congr_arg _⟩
 #align complex.of_real_inj Complex.ofReal_inj
 
-/- warning: complex.of_real_injective -> Complex.ofReal_injective is a dubious translation:
-lean 3 declaration is
-  Function.Injective.{1, 1} Real Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
-but is expected to have type
-  Function.Injective.{1, 1} Real Complex Complex.ofReal'
-Case conversion may be inaccurate. Consider using '#align complex.of_real_injective Complex.ofReal_injectiveₓ'. -/
 theorem ofReal_injective : Function.Injective (coe : ℝ → ℂ) := fun z w => congr_arg re
 #align complex.of_real_injective Complex.ofReal_injective
 
-/- warning: complex.can_lift -> Complex.canLift is a dubious translation:
-lean 3 declaration is
-  CanLift.{1, 1} Complex Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe)))) (fun (z : Complex) => Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  CanLift.{1, 1} Complex Real Complex.ofReal' (fun (z : Complex) => Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align complex.can_lift Complex.canLiftₓ'. -/
 instance canLift : CanLift ℂ ℝ coe fun z => z.im = 0 where prf z hz := ⟨z.re, ext rfl hz.symm⟩
 #align complex.can_lift Complex.canLift
 
@@ -185,56 +155,26 @@ instance : Zero ℂ :=
 instance : Inhabited ℂ :=
   ⟨0⟩
 
-/- warning: complex.zero_re -> Complex.zero_re is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.zero_re Complex.zero_reₓ'. -/
 @[simp]
 theorem zero_re : (0 : ℂ).re = 0 :=
   rfl
 #align complex.zero_re Complex.zero_re
 
-/- warning: complex.zero_im -> Complex.zero_im is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.zero_im Complex.zero_imₓ'. -/
 @[simp]
 theorem zero_im : (0 : ℂ).im = 0 :=
   rfl
 #align complex.zero_im Complex.zero_im
 
-/- warning: complex.of_real_zero -> Complex.ofReal_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
-but is expected to have type
-  Eq.{1} Complex (Complex.ofReal' (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_zero Complex.ofReal_zeroₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_zero : ((0 : ℝ) : ℂ) = 0 :=
   rfl
 #align complex.of_real_zero Complex.ofReal_zero
 
-/- warning: complex.of_real_eq_zero -> Complex.ofReal_eq_zero is a dubious translation:
-lean 3 declaration is
-  forall {z : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {z : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_zero Complex.ofReal_eq_zeroₓ'. -/
 @[simp]
 theorem ofReal_eq_zero {z : ℝ} : (z : ℂ) = 0 ↔ z = 0 :=
   ofReal_inj
 #align complex.of_real_eq_zero Complex.ofReal_eq_zero
 
-/- warning: complex.of_real_ne_zero -> Complex.ofReal_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {z : Real}, Iff (Ne.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {z : Real}, Iff (Ne.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_ne_zero Complex.ofReal_ne_zeroₓ'. -/
 theorem ofReal_ne_zero {z : ℝ} : (z : ℂ) ≠ 0 ↔ z ≠ 0 :=
   not_congr ofReal_eq_zero
 #align complex.of_real_ne_zero Complex.ofReal_ne_zero
@@ -242,56 +182,26 @@ theorem ofReal_ne_zero {z : ℝ} : (z : ℂ) ≠ 0 ↔ z ≠ 0 :=
 instance : One ℂ :=
   ⟨(1 : ℝ)⟩
 
-/- warning: complex.one_re -> Complex.one_re is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
-  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align complex.one_re Complex.one_reₓ'. -/
 @[simp]
 theorem one_re : (1 : ℂ).re = 1 :=
   rfl
 #align complex.one_re Complex.one_re
 
-/- warning: complex.one_im -> Complex.one_im is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.one_im Complex.one_imₓ'. -/
 @[simp]
 theorem one_im : (1 : ℂ).im = 0 :=
   rfl
 #align complex.one_im Complex.one_im
 
-/- warning: complex.of_real_one -> Complex.ofReal_one is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
-but is expected to have type
-  Eq.{1} Complex (Complex.ofReal' (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_one Complex.ofReal_oneₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_one : ((1 : ℝ) : ℂ) = 1 :=
   rfl
 #align complex.of_real_one Complex.ofReal_one
 
-/- warning: complex.of_real_eq_one -> Complex.ofReal_eq_one is a dubious translation:
-lean 3 declaration is
-  forall {z : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  forall {z : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_one Complex.ofReal_eq_oneₓ'. -/
 @[simp]
 theorem ofReal_eq_one {z : ℝ} : (z : ℂ) = 1 ↔ z = 1 :=
   ofReal_inj
 #align complex.of_real_eq_one Complex.ofReal_eq_one
 
-/- warning: complex.of_real_ne_one -> Complex.ofReal_ne_one is a dubious translation:
-lean 3 declaration is
-  forall {z : Real}, Iff (Ne.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
-but is expected to have type
-  forall {z : Real}, Iff (Ne.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_ne_one Complex.ofReal_ne_oneₓ'. -/
 theorem ofReal_ne_one {z : ℝ} : (z : ℂ) ≠ 1 ↔ z ≠ 1 :=
   not_congr ofReal_eq_one
 #align complex.of_real_ne_one Complex.ofReal_ne_one
@@ -299,100 +209,46 @@ theorem ofReal_ne_one {z : ℝ} : (z : ℂ) ≠ 1 ↔ z ≠ 1 :=
 instance : Add ℂ :=
   ⟨fun z w => ⟨z.re + w.re, z.im + w.im⟩⟩
 
-/- warning: complex.add_re -> Complex.add_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Complex.re z) (Complex.re w))
-but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Complex.re z) (Complex.re w))
-Case conversion may be inaccurate. Consider using '#align complex.add_re Complex.add_reₓ'. -/
 @[simp]
 theorem add_re (z w : ℂ) : (z + w).re = z.re + w.re :=
   rfl
 #align complex.add_re Complex.add_re
 
-/- warning: complex.add_im -> Complex.add_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Complex.im z) (Complex.im w))
-but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Complex.im z) (Complex.im w))
-Case conversion may be inaccurate. Consider using '#align complex.add_im Complex.add_imₓ'. -/
 @[simp]
 theorem add_im (z w : ℂ) : (z + w).im = z.im + w.im :=
   rfl
 #align complex.add_im Complex.add_im
 
-/- warning: complex.bit0_re -> Complex.bit0_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.re (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.re z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.bit0_re Complex.bit0_reₓ'. -/
 @[simp]
 theorem bit0_re (z : ℂ) : (bit0 z).re = bit0 z.re :=
   rfl
 #align complex.bit0_re Complex.bit0_re
 
-/- warning: complex.bit1_re -> Complex.bit1_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.re (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Real Real.hasOne Real.hasAdd (Complex.re z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} Real Real.instOneReal Real.instAddReal (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.bit1_re Complex.bit1_reₓ'. -/
 @[simp]
 theorem bit1_re (z : ℂ) : (bit1 z).re = bit1 z.re :=
   rfl
 #align complex.bit1_re Complex.bit1_re
 
-/- warning: complex.bit0_im -> Complex.bit0_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.im (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.im z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.bit0_im Complex.bit0_imₓ'. -/
 @[simp]
 theorem bit0_im (z : ℂ) : (bit0 z).im = bit0 z.im :=
   Eq.refl _
 #align complex.bit0_im Complex.bit0_im
 
-/- warning: complex.bit1_im -> Complex.bit1_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.im (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.im z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.bit1_im Complex.bit1_imₓ'. -/
 @[simp]
 theorem bit1_im (z : ℂ) : (bit1 z).im = bit0 z.im :=
   add_zero _
 #align complex.bit1_im Complex.bit1_im
 
-/- warning: complex.of_real_add -> Complex.ofReal_add is a dubious translation:
-lean 3 declaration is
-  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r s)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
-but is expected to have type
-  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r s)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' r) (Complex.ofReal' s))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_add Complex.ofReal_addₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
   ext_iff.2 <| by simp
 #align complex.of_real_add Complex.ofReal_add
 
-/- warning: complex.of_real_bit0 -> Complex.ofReal_bit0 is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (bit0.{0} Real Real.hasAdd r)) (bit0.{0} Complex Complex.hasAdd ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
-but is expected to have type
-  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (bit0.{0} Real Real.instAddReal r)) (bit0.{0} Complex Complex.instAddComplex (Complex.ofReal' r))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_bit0 Complex.ofReal_bit0ₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
   ext_iff.2 <| by simp [bit0]
 #align complex.of_real_bit0 Complex.ofReal_bit0
 
-/- warning: complex.of_real_bit1 -> Complex.ofReal_bit1 is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (bit1.{0} Real Real.hasOne Real.hasAdd r)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
-but is expected to have type
-  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (bit1.{0} Real Real.instOneReal Real.instAddReal r)) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex (Complex.ofReal' r))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_bit1 Complex.ofReal_bit1ₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
   ext_iff.2 <| by simp [bit1]
@@ -401,34 +257,16 @@ theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
 instance : Neg ℂ :=
   ⟨fun z => ⟨-z.re, -z.im⟩⟩
 
-/- warning: complex.neg_re -> Complex.neg_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.re (Neg.neg.{0} Complex Complex.hasNeg z)) (Neg.neg.{0} Real Real.hasNeg (Complex.re z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (Neg.neg.{0} Complex Complex.instNegComplex z)) (Neg.neg.{0} Real Real.instNegReal (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.neg_re Complex.neg_reₓ'. -/
 @[simp]
 theorem neg_re (z : ℂ) : (-z).re = -z.re :=
   rfl
 #align complex.neg_re Complex.neg_re
 
-/- warning: complex.neg_im -> Complex.neg_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.im (Neg.neg.{0} Complex Complex.hasNeg z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (Neg.neg.{0} Complex Complex.instNegComplex z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.neg_im Complex.neg_imₓ'. -/
 @[simp]
 theorem neg_im (z : ℂ) : (-z).im = -z.im :=
   rfl
 #align complex.neg_im Complex.neg_im
 
-/- warning: complex.of_real_neg -> Complex.ofReal_neg is a dubious translation:
-lean 3 declaration is
-  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Neg.neg.{0} Real Real.hasNeg r)) (Neg.neg.{0} Complex Complex.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
-but is expected to have type
-  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (Neg.neg.{0} Real Real.instNegReal r)) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.ofReal' r))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_neg Complex.ofReal_negₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : ℂ) = -r :=
   ext_iff.2 <| by simp
@@ -440,63 +278,27 @@ instance : Sub ℂ :=
 instance : Mul ℂ :=
   ⟨fun z w => ⟨z.re * w.re - z.im * w.im, z.re * w.im + z.im * w.re⟩⟩
 
-/- warning: complex.mul_re -> Complex.mul_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)))
-but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.mul_re Complex.mul_reₓ'. -/
 @[simp]
 theorem mul_re (z w : ℂ) : (z * w).re = z.re * w.re - z.im * w.im :=
   rfl
 #align complex.mul_re Complex.mul_re
 
-/- warning: complex.mul_im -> Complex.mul_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)))
-but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)))
-Case conversion may be inaccurate. Consider using '#align complex.mul_im Complex.mul_imₓ'. -/
 @[simp]
 theorem mul_im (z w : ℂ) : (z * w).im = z.re * w.im + z.im * w.re :=
   rfl
 #align complex.mul_im Complex.mul_im
 
-/- warning: complex.of_real_mul -> Complex.ofReal_mul is a dubious translation:
-lean 3 declaration is
-  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r s)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
-but is expected to have type
-  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r s)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) (Complex.ofReal' s))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_mul Complex.ofReal_mulₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
   ext_iff.2 <| by simp
 #align complex.of_real_mul Complex.ofReal_mul
 
-/- warning: complex.of_real_mul_re -> Complex.ofReal_mul_re is a dubious translation:
-lean 3 declaration is
-  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.re z))
-but is expected to have type
-  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_mul_re Complex.ofReal_mul_reₓ'. -/
 theorem ofReal_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
 #align complex.of_real_mul_re Complex.ofReal_mul_re
 
-/- warning: complex.of_real_mul_im -> Complex.ofReal_mul_im is a dubious translation:
-lean 3 declaration is
-  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.im z))
-but is expected to have type
-  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_mul_im Complex.ofReal_mul_imₓ'. -/
 theorem ofReal_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
 #align complex.of_real_mul_im Complex.ofReal_mul_im
 
-/- warning: complex.of_real_mul' -> Complex.ofReal_mul' is a dubious translation:
-lean 3 declaration is
-  forall (r : Real) (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) (Complex.mk (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.im z)))
-but is expected to have type
-  forall (r : Real) (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z) (Complex.mk (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.im z)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_mul' Complex.ofReal_mul'ₓ'. -/
 theorem ofReal_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
   ext (ofReal_mul_re _ _) (ofReal_mul_im _ _)
 #align complex.of_real_mul' Complex.ofReal_mul'
@@ -511,113 +313,47 @@ def I : ℂ :=
 #align complex.I Complex.I
 -/
 
-/- warning: complex.I_re -> Complex.I_re is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
-but is expected to have type
-  Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.I_re Complex.I_reₓ'. -/
 @[simp]
 theorem I_re : I.re = 0 :=
   rfl
 #align complex.I_re Complex.I_re
 
-/- warning: complex.I_im -> Complex.I_im is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
-but is expected to have type
-  Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align complex.I_im Complex.I_imₓ'. -/
 @[simp]
 theorem I_im : I.im = 1 :=
   rfl
 #align complex.I_im Complex.I_im
 
-/- warning: complex.I_mul_I -> Complex.I_mul_I is a dubious translation:
-lean 3 declaration is
-  Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
-but is expected to have type
-  Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_I Complex.I_mul_Iₓ'. -/
 @[simp]
 theorem I_mul_I : I * I = -1 :=
   ext_iff.2 <| by simp
 #align complex.I_mul_I Complex.I_mul_I
 
-/- warning: complex.I_mul -> Complex.I_mul is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (Complex.re z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul Complex.I_mulₓ'. -/
 theorem I_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
   ext_iff.2 <| by simp
 #align complex.I_mul Complex.I_mul
 
-/- warning: complex.I_ne_zero -> Complex.I_ne_zero is a dubious translation:
-lean 3 declaration is
-  Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
-but is expected to have type
-  Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
-Case conversion may be inaccurate. Consider using '#align complex.I_ne_zero Complex.I_ne_zeroₓ'. -/
 theorem I_ne_zero : (I : ℂ) ≠ 0 :=
   mt (congr_arg im) zero_ne_one.symm
 #align complex.I_ne_zero Complex.I_ne_zero
 
-/- warning: complex.mk_eq_add_mul_I -> Complex.mk_eq_add_mul_I is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real), Eq.{1} Complex (Complex.mk a b) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) b) Complex.I))
-but is expected to have type
-  forall (a : Real) (b : Real), Eq.{1} Complex (Complex.mk a b) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' a) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' b) Complex.I))
-Case conversion may be inaccurate. Consider using '#align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_Iₓ'. -/
 theorem mk_eq_add_mul_I (a b : ℝ) : Complex.mk a b = a + b * I :=
   ext_iff.2 <| by simp
 #align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_I
 
-/- warning: complex.re_add_im -> Complex.re_add_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re 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) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) Complex.I)) z
-but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (Complex.re z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (Complex.im z)) Complex.I)) z
-Case conversion may be inaccurate. Consider using '#align complex.re_add_im Complex.re_add_imₓ'. -/
 @[simp]
 theorem re_add_im (z : ℂ) : (z.re : ℂ) + z.im * I = z :=
   ext_iff.2 <| by simp
 #align complex.re_add_im Complex.re_add_im
 
-/- warning: complex.mul_I_re -> Complex.mul_I_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z Complex.I)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z Complex.I)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.mul_I_re Complex.mul_I_reₓ'. -/
 theorem mul_I_re (z : ℂ) : (z * I).re = -z.im := by simp
 #align complex.mul_I_re Complex.mul_I_re
 
-/- warning: complex.mul_I_im -> Complex.mul_I_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z Complex.I)) (Complex.re z)
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z Complex.I)) (Complex.re z)
-Case conversion may be inaccurate. Consider using '#align complex.mul_I_im Complex.mul_I_imₓ'. -/
 theorem mul_I_im (z : ℂ) : (z * I).im = z.re := by simp
 #align complex.mul_I_im Complex.mul_I_im
 
-/- warning: complex.I_mul_re -> Complex.I_mul_re is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_re Complex.I_mul_reₓ'. -/
 theorem I_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
 #align complex.I_mul_re Complex.I_mul_re
 
-/- warning: complex.I_mul_im -> Complex.I_mul_im is a dubious translation:
-lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Complex.re z)
-but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Complex.re z)
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_im Complex.I_mul_imₓ'. -/
 theorem I_mul_im (z : ℂ) : (I * z).im = z.re := by simp
 #align complex.I_mul_im Complex.I_mul_im
 
@@ -680,12 +416,6 @@ instance : Ring ℂ := by infer_instance
 instance : CommSemiring ℂ :=
   inferInstance
 
-/- warning: complex.re_add_group_hom -> Complex.reAddGroupHom is a dubious translation:
-lean 3 declaration is
-  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)
-but is expected to have type
-  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)
-Case conversion may be inaccurate. Consider using '#align complex.re_add_group_hom Complex.reAddGroupHomₓ'. -/
 /-- The "real part" map, considered as an additive group homomorphism. -/
 def reAddGroupHom : ℂ →+ ℝ where
   toFun := re
@@ -693,23 +423,11 @@ def reAddGroupHom : ℂ →+ ℝ where
   map_add' := add_re
 #align complex.re_add_group_hom Complex.reAddGroupHom
 
-/- warning: complex.coe_re_add_group_hom -> Complex.coe_reAddGroupHom is a dubious translation:
-lean 3 declaration is
-  Eq.{1} ((fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) Complex.reAddGroupHom) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) Complex.reAddGroupHom) Complex.re
-but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.reAddGroupHom) Complex.re
-Case conversion may be inaccurate. Consider using '#align complex.coe_re_add_group_hom Complex.coe_reAddGroupHomₓ'. -/
 @[simp]
 theorem coe_reAddGroupHom : (reAddGroupHom : ℂ → ℝ) = re :=
   rfl
 #align complex.coe_re_add_group_hom Complex.coe_reAddGroupHom
 
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 /-- The "imaginary part" map, considered as an additive group homomorphism. -/
 def imAddGroupHom : ℂ →+ ℝ where
   toFun := im
@@ -717,33 +435,15 @@ def imAddGroupHom : ℂ →+ ℝ where
   map_add' := add_im
 #align complex.im_add_group_hom Complex.imAddGroupHom
 
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 @[simp]
 theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
   rfl
 #align complex.coe_im_add_group_hom Complex.coe_imAddGroupHom
 
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 @[simp]
 theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
 #align complex.I_pow_bit0 Complex.I_pow_bit0
 
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 @[simp]
 theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
 #align complex.I_pow_bit1 Complex.I_pow_bit1
@@ -760,118 +460,52 @@ instance : StarRing ℂ where
   star_mul a b := by ext <;> simp [add_comm] <;> ring
   star_add a b := by ext <;> simp [add_comm]
 
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 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
   rfl
 #align complex.conj_re Complex.conj_re
 
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 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
   rfl
 #align complex.conj_im Complex.conj_im
 
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 theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
 #align complex.conj_of_real Complex.conj_ofReal
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_I Complex.conj_Iₓ'. -/
 @[simp]
 theorem conj_I : conj I = -I :=
   ext_iff.2 <| by simp
 #align complex.conj_I Complex.conj_I
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_bit0 Complex.conj_bit0ₓ'. -/
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit0 Complex.conj_bit0
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_bit1 Complex.conj_bit1ₓ'. -/
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit1 Complex.conj_bit1
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_neg_I Complex.conj_neg_Iₓ'. -/
 @[simp]
 theorem conj_neg_I : conj (-I) = I :=
   ext_iff.2 <| by simp
 #align complex.conj_neg_I Complex.conj_neg_I
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_real Complex.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_of_real]⟩
 #align complex.conj_eq_iff_real Complex.conj_eq_iff_real
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_re Complex.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
 #align complex.conj_eq_iff_re Complex.conj_eq_iff_re
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_im Complex.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
 #align complex.conj_eq_iff_im Complex.conj_eq_iff_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.star_def Complex.star_defₓ'. -/
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
 @[simp, nolint simp_nf]
@@ -893,117 +527,51 @@ def normSq : ℂ →*₀ ℝ where
 #align complex.norm_sq Complex.normSq
 -/
 
-/- warning: complex.norm_sq_apply -> Complex.normSq_apply is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_apply Complex.normSq_applyₓ'. -/
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
 #align complex.norm_sq_apply Complex.normSq_apply
 
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 @[simp]
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
 #align complex.norm_sq_of_real Complex.normSq_ofReal
 
-/- warning: complex.norm_sq_mk -> Complex.normSq_mk is a dubious translation:
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 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
   rfl
 #align complex.norm_sq_mk Complex.normSq_mk
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_Iₓ'. -/
 theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
 #align complex.norm_sq_add_mul_I Complex.normSq_add_mul_I
 
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 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
 #align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_self
 
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 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
   normSq.map_zero
 #align complex.norm_sq_zero Complex.normSq_zero
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_one Complex.normSq_oneₓ'. -/
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_I Complex.normSq_Iₓ'. -/
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 #align complex.norm_sq_I Complex.normSq_I
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_nonneg Complex.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align complex.norm_sq_nonneg Complex.normSq_nonneg
 
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-Case conversion may be inaccurate. Consider using '#align complex.range_norm_sq Complex.range_normSqₓ'. -/
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
   Subset.antisymm (range_subset_iff.2 normSq_nonneg) fun x hx =>
     ⟨Real.sqrt x, by rw [norm_sq_of_real, Real.mul_self_sqrt hx]⟩
 #align complex.range_norm_sq Complex.range_normSq
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_zero Complex.normSq_eq_zeroₓ'. -/
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
     ext (eq_zero_of_mul_self_add_mul_self_eq_zero h)
@@ -1011,84 +579,39 @@ theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
     fun h => h.symm ▸ normSq_zero⟩
 #align complex.norm_sq_eq_zero Complex.normSq_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_pos Complex.normSq_posₓ'. -/
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
   (normSq_nonneg z).lt_iff_ne.trans <| not_congr (eq_comm.trans normSq_eq_zero)
 #align complex.norm_sq_pos Complex.normSq_pos
 
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Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_neg Complex.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_neg Complex.normSq_neg
 
-/- warning: complex.norm_sq_conj -> Complex.normSq_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_conj Complex.normSq_conj
 
-/- warning: complex.norm_sq_mul -> Complex.normSq_mul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align complex.norm_sq_mul Complex.normSq_mul
 
-/- warning: complex.norm_sq_add -> Complex.normSq_add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
 #align complex.norm_sq_add Complex.normSq_add
 
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-Case conversion may be inaccurate. Consider using '#align complex.re_sq_le_norm_sq Complex.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.re_sq_le_norm_sq Complex.re_sq_le_normSq
 
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-Case conversion may be inaccurate. Consider using '#align complex.im_sq_le_norm_sq Complex.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align complex.im_sq_le_norm_sq Complex.im_sq_le_normSq
 
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(Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
-Case conversion may be inaccurate. Consider using '#align complex.mul_conj Complex.mul_conjₓ'. -/
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
 #align complex.mul_conj Complex.mul_conj
 
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-Case conversion may be inaccurate. Consider using '#align complex.add_conj Complex.add_conjₓ'. -/
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
 #align complex.add_conj Complex.add_conj
@@ -1100,84 +623,39 @@ def ofReal : ℝ →+* ℂ :=
 #align complex.of_real Complex.ofReal
 -/
 
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_coe Complex.ofReal_eq_coeₓ'. -/
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
   rfl
 #align complex.of_real_eq_coe Complex.ofReal_eq_coe
 
-/- warning: complex.I_sq -> Complex.I_sq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.I_sq Complex.I_sqₓ'. -/
 @[simp]
 theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
 #align complex.I_sq Complex.I_sq
 
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-Case conversion may be inaccurate. Consider using '#align complex.sub_re Complex.sub_reₓ'. -/
 @[simp]
 theorem sub_re (z w : ℂ) : (z - w).re = z.re - w.re :=
   rfl
 #align complex.sub_re Complex.sub_re
 
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-Case conversion may be inaccurate. Consider using '#align complex.sub_im Complex.sub_imₓ'. -/
 @[simp]
 theorem sub_im (z w : ℂ) : (z - w).im = z.im - w.im :=
   rfl
 #align complex.sub_im Complex.sub_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_sub Complex.ofReal_subₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
   ext_iff.2 <| by simp
 #align complex.of_real_sub Complex.ofReal_sub
 
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 @[simp, norm_cast]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
   induction n <;> simp [*, of_real_mul, pow_succ]
 #align complex.of_real_pow Complex.ofReal_pow
 
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-Case conversion may be inaccurate. Consider using '#align complex.sub_conj Complex.sub_conjₓ'. -/
 theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
 #align complex.sub_conj Complex.sub_conj
 
-/- warning: complex.norm_sq_sub -> Complex.normSq_sub is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
   rw [sub_eq_add_neg, norm_sq_add]
@@ -1190,62 +668,26 @@ theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z *
 noncomputable instance : Inv ℂ :=
   ⟨fun z => conj z * ((normSq z)⁻¹ : ℝ)⟩
 
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-Case conversion may be inaccurate. Consider using '#align complex.inv_def Complex.inv_defₓ'. -/
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
 #align complex.inv_def Complex.inv_def
 
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-Case conversion may be inaccurate. Consider using '#align complex.inv_re Complex.inv_reₓ'. -/
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
 #align complex.inv_re Complex.inv_re
 
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-Case conversion may be inaccurate. Consider using '#align complex.inv_im Complex.inv_imₓ'. -/
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
 #align complex.inv_im Complex.inv_im
 
-/- warning: complex.of_real_inv -> Complex.ofReal_inv is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_inv Complex.ofReal_invₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : ℂ) = r⁻¹ :=
   ext_iff.2 <| by simp
 #align complex.of_real_inv Complex.ofReal_inv
 
-/- warning: complex.inv_zero -> Complex.inv_zero is a dubious translation:
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-  Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
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-Case conversion may be inaccurate. Consider using '#align complex.inv_zero Complex.inv_zeroₓ'. -/
 protected theorem inv_zero : (0⁻¹ : ℂ) = 0 := by rw [← of_real_zero, ← of_real_inv, inv_zero]
 #align complex.inv_zero Complex.inv_zero
 
-/- warning: complex.mul_inv_cancel -> Complex.mul_inv_cancel is a dubious translation:
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-  forall {z : Complex}, (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (Inv.inv.{0} Complex Complex.hasInv z)) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
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-Case conversion may be inaccurate. Consider using '#align complex.mul_inv_cancel Complex.mul_inv_cancelₓ'. -/
 protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
   rw [inv_def, ← mul_assoc, mul_conj, ← of_real_mul, mul_inv_cancel (mt norm_sq_eq_zero.1 h),
     of_real_one]
@@ -1260,113 +702,50 @@ noncomputable instance : Field ℂ :=
     mul_inv_cancel := @Complex.mul_inv_cancel
     inv_zero := Complex.inv_zero }
 
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-Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit0 Complex.I_zpow_bit0ₓ'. -/
 @[simp]
 theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
 #align complex.I_zpow_bit0 Complex.I_zpow_bit0
 
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-Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit1 Complex.I_zpow_bit1ₓ'. -/
 @[simp]
 theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
 #align complex.I_zpow_bit1 Complex.I_zpow_bit1
 
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-Case conversion may be inaccurate. Consider using '#align complex.div_re Complex.div_reₓ'. -/
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
 #align complex.div_re Complex.div_re
 
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-Case conversion may be inaccurate. Consider using '#align complex.div_im Complex.div_imₓ'. -/
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
 #align complex.div_im Complex.div_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.conj_inv Complex.conj_invₓ'. -/
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align complex.conj_inv Complex.conj_inv
 
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_div Complex.ofReal_divₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : ℂ) = r / s :=
   map_div₀ ofReal r s
 #align complex.of_real_div Complex.ofReal_div
 
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_zpow Complex.ofReal_zpowₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : ℂ) = (r : ℂ) ^ n :=
   map_zpow₀ ofReal r n
 #align complex.of_real_zpow Complex.ofReal_zpow
 
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-Case conversion may be inaccurate. Consider using '#align complex.div_I Complex.div_Iₓ'. -/
 @[simp]
 theorem div_I (z : ℂ) : z / I = -(z * I) :=
   (div_eq_iff_mul_eq I_ne_zero).2 <| by simp [mul_assoc]
 #align complex.div_I Complex.div_I
 
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-Case conversion may be inaccurate. Consider using '#align complex.inv_I Complex.inv_Iₓ'. -/
 @[simp]
 theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
 #align complex.inv_I Complex.inv_I
 
-/- warning: complex.norm_sq_inv -> Complex.normSq_inv is a dubious translation:
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Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_inv Complex.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
 #align complex.norm_sq_inv Complex.normSq_inv
 
-/- warning: complex.norm_sq_div -> Complex.normSq_div is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
@@ -1375,95 +754,41 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 /-! ### Cast lemmas -/
 
 
-/- warning: complex.of_real_nat_cast -> Complex.ofReal_nat_cast is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_nat_cast Complex.ofReal_nat_castₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
   map_natCast ofReal n
 #align complex.of_real_nat_cast Complex.ofReal_nat_cast
 
-/- warning: complex.nat_cast_re -> Complex.nat_cast_re is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complex.nat_cast_re Complex.nat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
 #align complex.nat_cast_re Complex.nat_cast_re
 
-/- warning: complex.nat_cast_im -> Complex.nat_cast_im is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.nat_cast_im Complex.nat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
 #align complex.nat_cast_im Complex.nat_cast_im
 
-/- warning: complex.of_real_int_cast -> Complex.ofReal_int_cast is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.of_real_int_cast Complex.ofReal_int_castₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
   map_intCast ofReal n
 #align complex.of_real_int_cast Complex.ofReal_int_cast
 
-/- warning: complex.int_cast_re -> Complex.int_cast_re is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.int_cast_re Complex.int_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← of_real_int_cast, of_real_re]
 #align complex.int_cast_re Complex.int_cast_re
 
-/- warning: complex.int_cast_im -> Complex.int_cast_im is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.int_cast_im Complex.int_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast, of_real_im]
 #align complex.int_cast_im Complex.int_cast_im
 
-/- warning: complex.of_real_rat_cast -> Complex.ofReal_rat_cast is a dubious translation:
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 @[simp, norm_cast]
 theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
   map_ratCast ofReal n
 #align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
-/- warning: complex.rat_cast_re -> Complex.rat_cast_re is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.rat_cast_re Complex.rat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
 #align complex.rat_cast_re Complex.rat_cast_re
 
-/- warning: complex.rat_cast_im -> Complex.rat_cast_im is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.rat_cast_im Complex.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align complex.rat_cast_im Complex.rat_cast_im
@@ -1471,35 +796,17 @@ theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast,
 /-! ### Characteristic zero -/
 
 
-/- warning: complex.char_zero_complex -> Complex.charZero is a dubious translation:
-lean 3 declaration is
-  CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)
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-  CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)
-Case conversion may be inaccurate. Consider using '#align complex.char_zero_complex Complex.charZeroₓ'. -/
 instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
 #align complex.char_zero_complex Complex.charZero
 
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 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   simp only [add_conj, of_real_mul, of_real_one, of_real_bit0,
     mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 
-/- warning: complex.im_eq_sub_conj -> Complex.im_eq_sub_conj is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.im_eq_sub_conj Complex.im_eq_sub_conjₓ'. -/
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   simp only [sub_conj, of_real_mul, of_real_one, of_real_bit0, mul_right_comm,
@@ -1522,9 +829,6 @@ private theorem mul_self_abs (z : ℂ) : ((abs z) * abs z) = normSq z :=
 private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
   Real.sqrt_nonneg _
 
-/- warning: complex.abs_theory.abs_conj -> Complex.AbsTheory.abs_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
 
@@ -1561,53 +865,23 @@ noncomputable def Complex.abs : AbsoluteValue ℂ ℝ
 
 end AbsTheory
 
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 theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
 #align complex.abs_def Complex.abs_def
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
 theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
 #align complex.abs_apply Complex.abs_apply
 
-/- warning: complex.abs_of_real -> Complex.abs_ofReal is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.abs_of_real Complex.abs_ofRealₓ'. -/
 @[simp, norm_cast]
 theorem abs_ofReal (r : ℝ) : abs r = |r| := by
   simp [abs, norm_sq_of_real, Real.sqrt_mul_self_eq_abs]
 #align complex.abs_of_real Complex.abs_ofReal
 
-/- warning: complex.abs_of_nonneg -> Complex.abs_of_nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.abs_of_nonneg Complex.abs_of_nonnegₓ'. -/
 theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
   (abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 
-/- warning: complex.abs_of_nat -> Complex.abs_of_nat is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
 theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
     Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
@@ -1615,64 +889,28 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
     
 #align complex.abs_of_nat Complex.abs_of_nat
 
-/- warning: complex.mul_self_abs -> Complex.mul_self_abs is a dubious translation:
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(Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
-Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
 #align complex.mul_self_abs Complex.mul_self_abs
 
-/- warning: complex.sq_abs -> Complex.sq_abs is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
 theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
 #align complex.sq_abs Complex.sq_abs
 
-/- warning: complex.sq_abs_sub_sq_re -> Complex.sq_abs_sub_sq_re is a dubious translation:
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 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
   rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel']
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
 
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 @[simp]
 theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
   rw [← sq_abs_sub_sq_re, sub_sub_cancel]
 #align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
 
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 @[simp]
 theorem abs_I : abs I = 1 := by simp [abs]
 #align complex.abs_I Complex.abs_I
 
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 @[simp]
 theorem abs_two : abs 2 = 2 :=
   calc
@@ -1681,151 +919,67 @@ theorem abs_two : abs 2 = 2 :=
     
 #align complex.abs_two Complex.abs_two
 
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 @[simp]
 theorem range_abs : range abs = Ici 0 :=
   Subset.antisymm (range_subset_iff.2 abs.NonNeg) fun x hx => ⟨x, abs_of_nonneg hx⟩
 #align complex.range_abs Complex.range_abs
 
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(CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
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 @[simp]
 theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
 
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 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
     abs (s.Prod f) = s.Prod fun i => abs (f i) :=
   map_prod abs _ _
 #align complex.abs_prod Complex.abs_prod
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_pow Complex.abs_powₓ'. -/
 @[simp]
 theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
   map_pow abs z n
 #align complex.abs_pow Complex.abs_pow
 
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 @[simp]
 theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
   map_zpow₀ abs z n
 #align complex.abs_zpow Complex.abs_zpow
 
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 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq]; exact le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.abs_re_le_abs Complex.abs_re_le_abs
 
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 theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
   Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq, ← sq]; exact le_add_of_nonneg_left (sq_nonneg _)
 #align complex.abs_im_le_abs Complex.abs_im_le_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.re_le_abs Complex.re_le_absₓ'. -/
 theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
 #align complex.re_le_abs Complex.re_le_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.im_le_abs Complex.im_le_absₓ'. -/
 theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
 #align complex.im_le_abs Complex.im_le_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_re_lt_abs Complex.abs_re_lt_absₓ'. -/
 @[simp]
 theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
   rw [abs, AbsoluteValue.coe_mk, MulHom.coe_mk, Real.lt_sqrt (abs_nonneg _), norm_sq_apply,
     _root_.sq_abs, ← sq, lt_add_iff_pos_right, mul_self_pos]
 #align complex.abs_re_lt_abs Complex.abs_re_lt_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_im_lt_abs Complex.abs_im_lt_absₓ'. -/
 @[simp]
 theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa using @abs_re_lt_abs (z * I)
 #align complex.abs_im_lt_abs Complex.abs_im_lt_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_abs Complex.abs_absₓ'. -/
 @[simp]
 theorem abs_abs (z : ℂ) : |abs z| = abs z :=
   abs_of_nonneg (abs.NonNeg _)
 #align complex.abs_abs Complex.abs_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_imₓ'. -/
 theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
 #align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_maxₓ'. -/
 theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
   by
   cases' z with x y
@@ -1840,56 +994,26 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
     
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_oneₓ'. -/
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_re_le_abs]
 #align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_one
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_oneₓ'. -/
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
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-Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
 theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
   rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
 #align complex.abs_cast_nat Complex.abs_cast_nat
 
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 @[simp, norm_cast]
 theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
   rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
 #align complex.int_cast_abs Complex.int_cast_abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
 theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
 #align complex.norm_sq_eq_abs Complex.normSq_eq_abs
@@ -1913,114 +1037,48 @@ section ComplexOrder
 
 scoped[ComplexOrder] attribute [instance] Complex.partialOrder
 
-/- warning: complex.le_def -> Complex.le_def is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.le_def Complex.le_defₓ'. -/
 theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
   Iff.rfl
 #align complex.le_def Complex.le_def
 
-/- warning: complex.lt_def -> Complex.lt_def is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.lt_def Complex.lt_defₓ'. -/
 theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
   Iff.rfl
 #align complex.lt_def Complex.lt_def
 
-/- warning: complex.real_le_real -> Complex.real_le_real is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.real_le_real Complex.real_le_realₓ'. -/
 @[simp, norm_cast]
 theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
 #align complex.real_le_real Complex.real_le_real
 
-/- warning: complex.real_lt_real -> Complex.real_lt_real is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.real_lt_real Complex.real_lt_realₓ'. -/
 @[simp, norm_cast]
 theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
 #align complex.real_lt_real Complex.real_lt_real
 
-/- warning: complex.zero_le_real -> Complex.zero_le_real is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.zero_le_real Complex.zero_le_realₓ'. -/
 @[simp, norm_cast]
 theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
   real_le_real
 #align complex.zero_le_real Complex.zero_le_real
 
-/- warning: complex.zero_lt_real -> Complex.zero_lt_real is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.zero_lt_real Complex.zero_lt_realₓ'. -/
 @[simp, norm_cast]
 theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
   real_lt_real
 #align complex.zero_lt_real Complex.zero_lt_real
 
-/- warning: complex.not_le_iff -> Complex.not_le_iff is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.hasLt (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
-but is expected to have type
-  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.instLTReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.not_le_iff Complex.not_le_iffₓ'. -/
 theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
   rw [le_def, not_and_or, not_le]
 #align complex.not_le_iff Complex.not_le_iff
 
-/- warning: complex.not_lt_iff -> Complex.not_lt_iff is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.hasLe (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
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-  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.instLEReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.not_lt_iff Complex.not_lt_iffₓ'. -/
 theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
   rw [lt_def, not_and_or, not_lt]
 #align complex.not_lt_iff Complex.not_lt_iff
 
-/- warning: complex.not_le_zero_iff -> Complex.not_le_zero_iff is a dubious translation:
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-  forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
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-Case conversion may be inaccurate. Consider using '#align complex.not_le_zero_iff Complex.not_le_zero_iffₓ'. -/
 theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
   not_le_iff
 #align complex.not_le_zero_iff Complex.not_le_zero_iff
 
-/- warning: complex.not_lt_zero_iff -> Complex.not_lt_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
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-Case conversion may be inaccurate. Consider using '#align complex.not_lt_zero_iff Complex.not_lt_zero_iffₓ'. -/
 theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
   not_lt_iff
 #align complex.not_lt_zero_iff Complex.not_lt_zero_iff
 
-/- warning: complex.eq_re_of_real_le -> Complex.eq_re_ofReal_le is a dubious translation:
-lean 3 declaration is
-  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)))
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-  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' r) z) -> (Eq.{1} Complex z (Complex.ofReal' (Complex.re z)))
-Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.eq_re_ofReal_leₓ'. -/
 theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by ext; rfl;
   simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
 #align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
@@ -2073,78 +1131,36 @@ end ComplexOrder
 -- mathport name: exprabs'
 local notation "abs'" => Abs.abs
 
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-Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_re Complex.isCauSeq_reₓ'. -/
 theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_re Complex.isCauSeq_re
 
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-Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_im Complex.isCauSeq_imₓ'. -/
 theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_im Complex.isCauSeq_im
 
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-Case conversion may be inaccurate. Consider using '#align complex.cau_seq_re Complex.cauSeqReₓ'. -/
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_re f⟩
 #align complex.cau_seq_re Complex.cauSeqRe
 
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-Case conversion may be inaccurate. Consider using '#align complex.cau_seq_im Complex.cauSeqImₓ'. -/
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_im f⟩
 #align complex.cau_seq_im Complex.cauSeqIm
 
-/- warning: complex.is_cau_seq_abs -> Complex.isCauSeq_abs is a dubious translation:
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-  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f))
-Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_abs Complex.isCauSeq_absₓ'. -/
 theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.is_cau_seq_abs Complex.isCauSeq_abs
 
-/- warning: complex.lim_aux -> Complex.limAux is a dubious translation:
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-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> Complex
-but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> Complex
-Case conversion may be inaccurate. Consider using '#align complex.lim_aux Complex.limAuxₓ'. -/
 /-- The limit of a Cauchy sequence of complex numbers. -/
 noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
   ⟨CauSeq.lim (cauSeqRe f), CauSeq.lim (cauSeqIm f)⟩
 #align complex.lim_aux Complex.limAux
 
-/- warning: complex.equiv_lim_aux -> Complex.equiv_limAux is a dubious translation:
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Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) (Complex.limAux f))
-Case conversion may be inaccurate. Consider using '#align complex.equiv_lim_aux Complex.equiv_limAuxₓ'. -/
 theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
         (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
@@ -2161,12 +1177,6 @@ instance : CauSeq.IsComplete ℂ abs :=
 
 open CauSeq
 
-/- warning: complex.lim_eq_lim_im_add_lim_re -> Complex.lim_eq_lim_im_add_lim_re is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_reₓ'. -/
 theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
     limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
   lim_eq_of_equiv_const <|
@@ -2178,73 +1188,34 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
       
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
 
-/- warning: complex.lim_re -> Complex.lim_re is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align complex.lim_re Complex.lim_reₓ'. -/
 theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_re Complex.lim_re
 
-/- warning: complex.lim_im -> Complex.lim_im is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align complex.lim_im Complex.lim_imₓ'. -/
 theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_im Complex.lim_im
 
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Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real 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Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
-Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
 theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by rw [← RingHom.map_sub, abs_conj] <;> exact hi j hj⟩
 #align complex.is_cau_seq_conj Complex.isCauSeq_conj
 
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-Case conversion may be inaccurate. Consider using '#align complex.cau_seq_conj Complex.cauSeqConjₓ'. -/
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
 noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
   ⟨_, isCauSeq_conj f⟩
 #align complex.cau_seq_conj Complex.cauSeqConj
 
-/- warning: complex.lim_conj -> Complex.lim_conj is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])
     (by simp [cau_seq_conj, (lim_im _).symm, cau_seq_im, (lim_neg _).symm] <;> rfl)
 #align complex.lim_conj Complex.lim_conj
 
-/- warning: complex.cau_seq_abs -> Complex.cauSeqAbs is a dubious translation:
-lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
-but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
-Case conversion may be inaccurate. Consider using '#align complex.cau_seq_abs Complex.cauSeqAbsₓ'. -/
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_abs f.2⟩
 #align complex.cau_seq_abs Complex.cauSeqAbs
 
-/- warning: complex.lim_abs -> Complex.lim_abs is a dubious translation:
-lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
-but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
-Case conversion may be inaccurate. Consider using '#align complex.lim_abs Complex.lim_absₓ'. -/
 theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f) :=
   lim_eq_of_equiv_const fun ε ε0 =>
     let ⟨i, hi⟩ := equiv_lim f ε ε0
@@ -2253,23 +1224,11 @@ theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f)
 
 variable {α : Type _} (s : Finset α)
 
-/- warning: complex.of_real_prod -> Complex.ofReal_prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (i : α) => f i))) (Finset.prod.{0, u1} Complex α (CommRing.toCommMonoid.{0} Complex Complex.commRing) s (fun (i : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f i)))
-but is expected to have type
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (i : α) => f i))) (Finset.prod.{0, u1} Complex α (CommRing.toCommMonoid.{0} Complex Complex.commRing) s (fun (i : α) => Complex.ofReal' (f i)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_prod Complex.ofReal_prodₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
   RingHom.map_prod ofReal _ _
 #align complex.of_real_prod Complex.ofReal_prod
 
-/- warning: complex.of_real_sum -> Complex.ofReal_sum is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (i : α) => f i))) (Finset.sum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) s (fun (i : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f i)))
-but is expected to have type
-  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (i : α) => f i))) (Finset.sum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) s (fun (i : α) => Complex.ofReal' (f i)))
-Case conversion may be inaccurate. Consider using '#align complex.of_real_sum Complex.ofReal_sumₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
   RingHom.map_sum ofReal _ _

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

@@ -889,9 +889,7 @@ def normSq : ℂ →*₀ ℝ where
   toFun z := z.re * z.re + z.im * z.im
   map_zero' := by simp
   map_one' := by simp
-  map_mul' z w := by
-    dsimp
-    ring
+  map_mul' z w := by dsimp; ring
 #align complex.norm_sq Complex.normSq
 -/
 
@@ -1746,9 +1744,7 @@ but is expected to have type
   forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_le_abs Complex.abs_re_le_absₓ'. -/
 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
-  Real.abs_le_sqrt <| by
-    rw [norm_sq_apply, ← sq]
-    exact le_add_of_nonneg_right (mul_self_nonneg _)
+  Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq]; exact le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.abs_re_le_abs Complex.abs_re_le_abs
 
 /- warning: complex.abs_im_le_abs -> Complex.abs_im_le_abs is a dubious translation:
@@ -1758,9 +1754,7 @@ but is expected to have type
   forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_le_abs Complex.abs_im_le_absₓ'. -/
 theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
-  Real.abs_le_sqrt <| by
-    rw [norm_sq_apply, ← sq, ← sq]
-    exact le_add_of_nonneg_left (sq_nonneg _)
+  Real.abs_le_sqrt <| by rw [norm_sq_apply, ← sq, ← sq]; exact le_add_of_nonneg_left (sq_nonneg _)
 #align complex.abs_im_le_abs Complex.abs_im_le_abs
 
 /- warning: complex.re_le_abs -> Complex.re_le_abs is a dubious translation:
@@ -1837,8 +1831,7 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
   cases' z with x y
   simp only [abs_apply, norm_sq_mk, ← sq]
   wlog hle : |x| ≤ |y|
-  · rw [add_comm, max_comm]
-    exact this _ _ (le_of_not_le hle)
+  · rw [add_comm, max_comm]; exact this _ _ (le_of_not_le hle)
   calc
     Real.sqrt (x ^ 2 + y ^ 2) ≤ Real.sqrt (y ^ 2 + y ^ 2) :=
       Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
@@ -1909,10 +1902,7 @@ protected def partialOrder : PartialOrder ℂ
     where
   le z w := z.re ≤ w.re ∧ z.im = w.im
   lt z w := z.re < w.re ∧ z.im = w.im
-  lt_iff_le_not_le z w := by
-    dsimp
-    rw [lt_iff_le_not_le]
-    tauto
+  lt_iff_le_not_le z w := by dsimp; rw [lt_iff_le_not_le]; tauto
   le_refl x := ⟨le_rfl, rfl⟩
   le_trans x y z h₁ h₂ := ⟨h₁.1.trans h₂.1, h₁.2.trans h₂.2⟩
   le_antisymm z w h₁ h₂ := ext (h₁.1.antisymm h₂.1) h₁.2
@@ -2031,10 +2021,7 @@ lean 3 declaration is
 but is expected to have type
   forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' r) z) -> (Eq.{1} Complex z (Complex.ofReal' (Complex.re z)))
 Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.eq_re_ofReal_leₓ'. -/
-theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
-  by
-  ext
-  rfl
+theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by ext; rfl;
   simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
 #align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
 
@@ -2062,12 +2049,8 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
     nonneg_iff := fun r =>
       by
       refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-      · have h₁ : 0 ≤ r.re := by
-          rw [le_def] at hr
-          exact hr.1
-        have h₂ : r.im = 0 := by
-          rw [le_def] at hr
-          exact hr.2.symm
+      · have h₁ : 0 ≤ r.re := by rw [le_def] at hr; exact hr.1
+        have h₂ : r.im = 0 := by rw [le_def] at hr; exact hr.2.symm
         ext
         ·
           simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,

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

@@ -1035,30 +1035,21 @@ theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_neg Complex.normSq_neg
 
 /- warning: complex.norm_sq_conj -> Complex.normSq_conj is a dubious translation:
-lean 3 declaration is
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(MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_conj Complex.normSq_conj
 
 /- warning: complex.norm_sq_mul -> Complex.normSq_mul is a dubious translation:
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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align complex.norm_sq_mul Complex.normSq_mul
 
 /- warning: complex.norm_sq_add -> Complex.normSq_add is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
@@ -1187,10 +1178,7 @@ theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
 #align complex.sub_conj Complex.sub_conj
 
 /- warning: complex.norm_sq_sub -> Complex.normSq_sub is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
@@ -1379,10 +1367,7 @@ theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
 #align complex.norm_sq_inv Complex.normSq_inv
 
 /- warning: complex.norm_sq_div -> Complex.normSq_div is a dubious translation:
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Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
@@ -1535,17 +1520,12 @@ local notation "abs" z => (normSq z).sqrt
 
 private theorem mul_self_abs (z : ℂ) : ((abs z) * abs z) = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
-#align complex.abs_theory.mul_self_abs complex.abs_theory.mul_self_abs
 
 private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
   Real.sqrt_nonneg _
-#align complex.abs_theory.abs_nonneg' complex.abs_theory.abs_nonneg'
 
 /- warning: complex.abs_theory.abs_conj -> Complex.AbsTheory.abs_conj is a dubious translation:
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(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))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
@@ -1554,15 +1534,12 @@ private theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   by
   rw [mul_self_le_mul_self_iff (abs_nonneg z.re) (abs_nonneg' _), abs_mul_abs_self, mul_self_abs]
   apply re_sq_le_norm_sq
-#align complex.abs_theory.abs_re_le_abs complex.abs_theory.abs_re_le_abs
 
 private theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
-#align complex.abs_theory.re_le_abs complex.abs_theory.re_le_abs
 
 private theorem abs_mul (z w : ℂ) : (abs z * w) = (abs z) * abs w := by
   rw [norm_sq_mul, Real.sqrt_mul (norm_sq_nonneg _)]
-#align complex.abs_theory.abs_mul complex.abs_theory.abs_mul
 
 private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
   (mul_self_le_mul_self_iff (abs_nonneg' (z + w)) (add_nonneg (abs_nonneg' z) (abs_nonneg' w))).2 <|
@@ -1571,7 +1548,6 @@ private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
       add_le_add_iff_left, mul_assoc, mul_le_mul_left (zero_lt_two' ℝ), ←
       Real.sqrt_mul <| norm_sq_nonneg z, ← norm_sq_conj w, ← map_mul]
     exact re_le_abs (z * conj w)
-#align complex.abs_theory.abs_add complex.abs_theory.abs_add
 
 #print Complex.abs /-
 /-- The complex absolute value function, defined as the square root of the norm squared. -/
@@ -2262,10 +2238,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
 #align complex.cau_seq_conj Complex.cauSeqConj
 
 /- warning: complex.lim_conj -> Complex.lim_conj is a dubious translation:
-lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
-but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])

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

@@ -764,7 +764,7 @@ instance : StarRing ℂ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Complex.re z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.re z)
+  forall (z : Complex), Eq.{1} Real (Complex.re (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)) (Complex.re z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_re Complex.conj_reₓ'. -/
 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
@@ -775,7 +775,7 @@ theorem conj_re (z : ℂ) : (conj z).re = z.re :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (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)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_im Complex.conj_imₓ'. -/
 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
@@ -786,7 +786,7 @@ theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (Complex.ofReal' r)) (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) (Complex.ofReal' r)) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.conj_of_real Complex.conj_ofRealₓ'. -/
 theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
@@ -796,7 +796,7 @@ theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) Complex.I) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) Complex.I) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) Complex.I) (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) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.conj_I Complex.conj_Iₓ'. -/
 @[simp]
 theorem conj_I : conj I = -I :=
@@ -807,7 +807,7 @@ theorem conj_I : conj I = -I :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Complex Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit0.{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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (bit0.{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) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit0 Complex.conj_bit0ₓ'. -/
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -817,7 +817,7 @@ theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit1 Complex.conj_bit1ₓ'. -/
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -827,7 +827,7 @@ theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)) Complex.I
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (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) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
 Case conversion may be inaccurate. Consider using '#align complex.conj_neg_I Complex.conj_neg_Iₓ'. -/
 @[simp]
 theorem conj_neg_I : conj (-I) = I :=
@@ -838,7 +838,7 @@ theorem conj_neg_I : conj (-I) = I :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) 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) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_real Complex.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
@@ -849,7 +849,7 @@ theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) 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) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_re Complex.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
@@ -859,7 +859,7 @@ theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) 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) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_im Complex.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
@@ -870,7 +870,7 @@ theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
 lean 3 declaration is
   Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toHasStar.{0} Complex (StarAddMonoid.toHasInvolutiveStar.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing)))))) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.starRing)))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
 but is expected to have type
-  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
+  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
 Case conversion may be inaccurate. Consider using '#align complex.star_def Complex.star_defₓ'. -/
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
@@ -899,7 +899,7 @@ def normSq : ℂ →*₀ ℝ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_apply Complex.normSq_applyₓ'. -/
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
@@ -909,7 +909,7 @@ theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_of_real Complex.normSq_ofRealₓ'. -/
 @[simp]
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
@@ -919,7 +919,7 @@ theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) y y))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mk Complex.normSq_mkₓ'. -/
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
@@ -930,7 +930,7 @@ theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) y (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_Iₓ'. -/
 theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
@@ -940,7 +940,7 @@ theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z)
 but is expected to have type
-  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z)
+  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_selfₓ'. -/
 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
@@ -950,7 +950,7 @@ theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_zero Complex.normSq_zeroₓ'. -/
 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
@@ -961,7 +961,7 @@ theorem normSq_zero : normSq 0 = 0 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_one Complex.normSq_oneₓ'. -/
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
@@ -972,7 +972,7 @@ theorem normSq_one : normSq 1 = 1 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_I Complex.normSq_Iₓ'. -/
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [norm_sq]
@@ -982,7 +982,7 @@ theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_nonneg Complex.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
@@ -992,7 +992,7 @@ theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
 lean 3 declaration is
   Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_norm_sq Complex.range_normSqₓ'. -/
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
@@ -1004,7 +1004,7 @@ theorem range_normSq : range normSq = Ici 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_zero Complex.normSq_eq_zeroₓ'. -/
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
@@ -1017,7 +1017,7 @@ theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_pos Complex.normSq_posₓ'. -/
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
@@ -1028,7 +1028,7 @@ theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Neg.neg.{0} Complex Complex.hasNeg z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_neg Complex.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
@@ -1038,7 +1038,7 @@ theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
@@ -1048,7 +1048,7 @@ theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
@@ -1058,7 +1058,7 @@ theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
@@ -1068,7 +1068,7 @@ theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z *
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.re_sq_le_norm_sq Complex.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
@@ -1078,7 +1078,7 @@ theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.im_sq_le_norm_sq Complex.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
@@ -1088,7 +1088,7 @@ theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) 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)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.mul_conj Complex.mul_conjₓ'. -/
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
@@ -1098,7 +1098,7 @@ theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
+  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)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
 Case conversion may be inaccurate. Consider using '#align complex.add_conj Complex.add_conjₓ'. -/
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
@@ -1115,7 +1115,7 @@ def ofReal : ℝ →+* ℂ :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) Complex.ofReal r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) Complex.ofReal r) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) Complex.ofReal r) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_coe Complex.ofReal_eq_coeₓ'. -/
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
@@ -1180,7 +1180,7 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.im z))) Complex.I)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
+  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.sub_conj Complex.sub_conjₓ'. -/
 theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
@@ -1190,7 +1190,7 @@ theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
@@ -1208,7 +1208,7 @@ noncomputable instance : Inv ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))))
+  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex.instMulComplex) (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) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))))
 Case conversion may be inaccurate. Consider using '#align complex.inv_def Complex.inv_defₓ'. -/
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
@@ -1218,7 +1218,7 @@ theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_re Complex.inv_reₓ'. -/
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
@@ -1228,7 +1228,7 @@ theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, divi
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_im Complex.inv_imₓ'. -/
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
@@ -1298,7 +1298,7 @@ theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1',
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_re Complex.div_reₓ'. -/
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
@@ -1308,7 +1308,7 @@ theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im /
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_im Complex.div_imₓ'. -/
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
@@ -1318,7 +1318,7 @@ theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im /
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Inv.inv.{0} Complex Complex.hasInv x)) (Inv.inv.{0} Complex Complex.hasInv (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) x) Complex.instInvComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) x) Complex.instInvComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
 Case conversion may be inaccurate. Consider using '#align complex.conj_inv Complex.conj_invₓ'. -/
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
@@ -1371,7 +1371,7 @@ theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Inv.inv.{0} Complex Complex.hasInv z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_inv Complex.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -1382,7 +1382,7 @@ theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
@@ -1503,7 +1503,7 @@ instance charZero : CharZero ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align complex.re_eq_add_conj Complex.re_eq_add_conjₓ'. -/
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
@@ -1515,7 +1515,7 @@ theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) Complex.I))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.im_eq_sub_conj Complex.im_eq_sub_conjₓ'. -/
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
@@ -1545,7 +1545,7 @@ private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (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))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
@@ -1591,7 +1591,7 @@ end AbsTheory
 lean 3 declaration is
   Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
 theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
@@ -1601,7 +1601,7 @@ theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
 theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
@@ -1645,7 +1645,7 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
@@ -1655,7 +1655,7 @@ theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
 theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
@@ -1722,7 +1722,7 @@ theorem range_abs : range abs = Ici 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
 theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
@@ -1919,7 +1919,7 @@ theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
 theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
@@ -2243,7 +2243,7 @@ theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => 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) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
 theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
@@ -2265,7 +2265,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])

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

@@ -1949,7 +1949,7 @@ scoped[ComplexOrder] attribute [instance] Complex.partialOrder
 
 /- warning: complex.le_def -> Complex.le_def is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.hasLe (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+  forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.hasLe (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.instLEReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 Case conversion may be inaccurate. Consider using '#align complex.le_def Complex.le_defₓ'. -/
@@ -1959,7 +1959,7 @@ theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
 
 /- warning: complex.lt_def -> Complex.lt_def is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.hasLt (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+  forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.hasLt (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.instLTReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 Case conversion may be inaccurate. Consider using '#align complex.lt_def Complex.lt_defₓ'. -/
@@ -1969,7 +1969,7 @@ theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
 
 /- warning: complex.real_le_real -> Complex.real_le_real is a dubious translation:
 lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LE.le.{0} Real Real.hasLe x y)
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LE.le.{0} Real Real.hasLe x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LE.le.{0} Real Real.instLEReal x y)
 Case conversion may be inaccurate. Consider using '#align complex.real_le_real Complex.real_le_realₓ'. -/
@@ -1979,7 +1979,7 @@ theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by sim
 
 /- warning: complex.real_lt_real -> Complex.real_lt_real is a dubious translation:
 lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LT.lt.{0} Real Real.hasLt x y)
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LT.lt.{0} Real Real.hasLt x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LT.lt.{0} Real Real.instLTReal x y)
 Case conversion may be inaccurate. Consider using '#align complex.real_lt_real Complex.real_lt_realₓ'. -/
@@ -1989,7 +1989,7 @@ theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [l
 
 /- warning: complex.zero_le_real -> Complex.zero_le_real is a dubious translation:
 lean 3 declaration is
-  forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+  forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
 Case conversion may be inaccurate. Consider using '#align complex.zero_le_real Complex.zero_le_realₓ'. -/
@@ -2000,7 +2000,7 @@ theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
 
 /- warning: complex.zero_lt_real -> Complex.zero_lt_real is a dubious translation:
 lean 3 declaration is
-  forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+  forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
 Case conversion may be inaccurate. Consider using '#align complex.zero_lt_real Complex.zero_lt_realₓ'. -/
@@ -2011,7 +2011,7 @@ theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
 
 /- warning: complex.not_le_iff -> Complex.not_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.hasLt (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.hasLt (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.instLTReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 Case conversion may be inaccurate. Consider using '#align complex.not_le_iff Complex.not_le_iffₓ'. -/
@@ -2021,7 +2021,7 @@ theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im :=
 
 /- warning: complex.not_lt_iff -> Complex.not_lt_iff is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.hasLe (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.hasLe (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.instLEReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 Case conversion may be inaccurate. Consider using '#align complex.not_lt_iff Complex.not_lt_iffₓ'. -/
@@ -2031,7 +2031,7 @@ theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im :=
 
 /- warning: complex.not_le_zero_iff -> Complex.not_le_zero_iff is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+  forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
 but is expected to have type
   forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
 Case conversion may be inaccurate. Consider using '#align complex.not_le_zero_iff Complex.not_le_zero_iffₓ'. -/
@@ -2041,7 +2041,7 @@ theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
 
 /- warning: complex.not_lt_zero_iff -> Complex.not_lt_zero_iff is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+  forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toHasLt.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
 but is expected to have type
   forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
 Case conversion may be inaccurate. Consider using '#align complex.not_lt_zero_iff Complex.not_lt_zero_iffₓ'. -/
@@ -2051,7 +2051,7 @@ theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
 
 /- warning: complex.eq_re_of_real_le -> Complex.eq_re_ofReal_le is a dubious translation:
 lean 3 declaration is
-  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)))
+  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toHasLe.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)))
 but is expected to have type
   forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' r) z) -> (Eq.{1} Complex z (Complex.ofReal' (Complex.re z)))
 Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.eq_re_ofReal_leₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -764,7 +764,7 @@ instance : StarRing ℂ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Complex.re z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.re z)
+  forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.re z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_re Complex.conj_reₓ'. -/
 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
@@ -775,7 +775,7 @@ theorem conj_re (z : ℂ) : (conj z).re = z.re :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_im Complex.conj_imₓ'. -/
 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
@@ -786,7 +786,7 @@ theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.conj_of_real Complex.conj_ofRealₓ'. -/
 theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
@@ -796,7 +796,7 @@ theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) Complex.I) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) Complex.I) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) Complex.I) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.conj_I Complex.conj_Iₓ'. -/
 @[simp]
 theorem conj_I : conj I = -I :=
@@ -807,7 +807,7 @@ theorem conj_I : conj I = -I :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Complex Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit0.{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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit0.{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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit0 Complex.conj_bit0ₓ'. -/
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -817,7 +817,7 @@ theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit1 Complex.conj_bit1ₓ'. -/
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -827,7 +827,7 @@ theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)) Complex.I
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
 Case conversion may be inaccurate. Consider using '#align complex.conj_neg_I Complex.conj_neg_Iₓ'. -/
 @[simp]
 theorem conj_neg_I : conj (-I) = I :=
@@ -838,7 +838,7 @@ theorem conj_neg_I : conj (-I) = I :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_real Complex.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
@@ -849,7 +849,7 @@ theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_re Complex.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
@@ -859,7 +859,7 @@ theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_im Complex.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
@@ -870,7 +870,7 @@ theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
 lean 3 declaration is
   Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toHasStar.{0} Complex (StarAddMonoid.toHasInvolutiveStar.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing)))))) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.starRing)))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
 but is expected to have type
-  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing)))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))
+  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalCommSemiring.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalCommSemiring.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing)))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing))
 Case conversion may be inaccurate. Consider using '#align complex.star_def Complex.star_defₓ'. -/
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
@@ -899,7 +899,7 @@ def normSq : ℂ →*₀ ℝ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_apply Complex.normSq_applyₓ'. -/
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
@@ -909,7 +909,7 @@ theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_of_real Complex.normSq_ofRealₓ'. -/
 @[simp]
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
@@ -919,7 +919,7 @@ theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) y y))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mk Complex.normSq_mkₓ'. -/
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
@@ -930,7 +930,7 @@ theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) y (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_Iₓ'. -/
 theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
@@ -940,7 +940,7 @@ theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z)
 but is expected to have type
-  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z)
+  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_selfₓ'. -/
 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
@@ -950,7 +950,7 @@ theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_zero Complex.normSq_zeroₓ'. -/
 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
@@ -961,7 +961,7 @@ theorem normSq_zero : normSq 0 = 0 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_one Complex.normSq_oneₓ'. -/
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
@@ -972,7 +972,7 @@ theorem normSq_one : normSq 1 = 1 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_I Complex.normSq_Iₓ'. -/
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [norm_sq]
@@ -982,7 +982,7 @@ theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_nonneg Complex.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
@@ -992,7 +992,7 @@ theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
 lean 3 declaration is
   Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_norm_sq Complex.range_normSqₓ'. -/
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
@@ -1004,7 +1004,7 @@ theorem range_normSq : range normSq = Ici 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_zero Complex.normSq_eq_zeroₓ'. -/
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
@@ -1017,7 +1017,7 @@ theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_pos Complex.normSq_posₓ'. -/
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
@@ -1028,7 +1028,7 @@ theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Neg.neg.{0} Complex Complex.hasNeg z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_neg Complex.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
@@ -1038,7 +1038,7 @@ theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
@@ -1048,7 +1048,7 @@ theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
@@ -1058,7 +1058,7 @@ theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
@@ -1068,7 +1068,7 @@ theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z *
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.re_sq_le_norm_sq Complex.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
@@ -1078,7 +1078,7 @@ theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.im_sq_le_norm_sq Complex.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
@@ -1088,7 +1088,7 @@ theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.mul_conj Complex.mul_conjₓ'. -/
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
@@ -1098,7 +1098,7 @@ theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
 Case conversion may be inaccurate. Consider using '#align complex.add_conj Complex.add_conjₓ'. -/
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
@@ -1115,7 +1115,7 @@ def ofReal : ℝ →+* ℂ :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) Complex.ofReal r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))))) Complex.ofReal r) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real Real.semiring) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) Complex.ofReal r) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_coe Complex.ofReal_eq_coeₓ'. -/
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
@@ -1180,7 +1180,7 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.im z))) Complex.I)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
+  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.sub_conj Complex.sub_conjₓ'. -/
 theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
@@ -1190,7 +1190,7 @@ theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
@@ -1208,7 +1208,7 @@ noncomputable instance : Inv ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))))
+  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))))
 Case conversion may be inaccurate. Consider using '#align complex.inv_def Complex.inv_defₓ'. -/
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
@@ -1218,7 +1218,7 @@ theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_re Complex.inv_reₓ'. -/
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
@@ -1228,7 +1228,7 @@ theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, divi
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_im Complex.inv_imₓ'. -/
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
@@ -1288,7 +1288,7 @@ theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mu
 lean 3 declaration is
   forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) Complex.I (bit1.{0} Int Int.hasOne Int.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
 but is expected to have type
-  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
+  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit1.{0} Int (Semiring.toOne.{0} Int Int.instSemiringInt) Int.instAddInt n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit1 Complex.I_zpow_bit1ₓ'. -/
 @[simp]
 theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
@@ -1298,7 +1298,7 @@ theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1',
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_re Complex.div_reₓ'. -/
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
@@ -1308,7 +1308,7 @@ theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im /
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_im Complex.div_imₓ'. -/
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
@@ -1318,7 +1318,7 @@ theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im /
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Inv.inv.{0} Complex Complex.hasInv x)) (Inv.inv.{0} Complex Complex.hasInv (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) x) Complex.instInvComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) x))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) x) Complex.instInvComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) x))
 Case conversion may be inaccurate. Consider using '#align complex.conj_inv Complex.conj_invₓ'. -/
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
@@ -1371,7 +1371,7 @@ theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Inv.inv.{0} Complex Complex.hasInv z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_inv Complex.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -1382,7 +1382,7 @@ theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
@@ -1396,7 +1396,7 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} Complex (Complex.ofReal' (Nat.cast.{0} Real Real.natCast n)) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)
+  forall (n : Nat), Eq.{1} Complex (Complex.ofReal' (Nat.cast.{0} Real Real.natCast n)) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_nat_cast Complex.ofReal_nat_castₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
@@ -1407,7 +1407,7 @@ theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (Complex.re ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} Real (Complex.re (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} Real Real.natCast n)
+  forall (n : Nat), Eq.{1} Real (Complex.re (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (Nat.cast.{0} Real Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.nat_cast_re Complex.nat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
@@ -1417,7 +1417,7 @@ theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast,
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  forall (n : Nat), Eq.{1} Real (Complex.im (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+  forall (n : Nat), Eq.{1} Real (Complex.im (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align complex.nat_cast_im Complex.nat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
@@ -1503,7 +1503,7 @@ instance charZero : CharZero ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align complex.re_eq_add_conj Complex.re_eq_add_conjₓ'. -/
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
@@ -1515,7 +1515,7 @@ theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) Complex.I))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.im_eq_sub_conj Complex.im_eq_sub_conjₓ'. -/
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
@@ -1545,7 +1545,7 @@ private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
@@ -1591,7 +1591,7 @@ end AbsTheory
 lean 3 declaration is
   Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
 theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
@@ -1601,7 +1601,7 @@ theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
 theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
@@ -1632,7 +1632,7 @@ theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
 theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
@@ -1645,7 +1645,7 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
@@ -1655,7 +1655,7 @@ theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
 theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
@@ -1697,7 +1697,7 @@ theorem abs_I : abs I = 1 := by simp [abs]
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_two Complex.abs_twoₓ'. -/
 @[simp]
 theorem abs_two : abs 2 = 2 :=
@@ -1722,7 +1722,7 @@ theorem range_abs : range abs = Ici 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
 theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
@@ -1897,7 +1897,7 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (Semiring.toNatCast.{0} Complex Complex.instSemiringComplex) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
 theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
@@ -1919,7 +1919,7 @@ theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toMulZeroOneClass.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
 theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
@@ -2243,7 +2243,7 @@ theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
 theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
@@ -2265,7 +2265,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])

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

@@ -834,15 +834,33 @@ theorem conj_neg_I : conj (-I) = I :=
   ext_iff.2 <| by simp
 #align complex.conj_neg_I Complex.conj_neg_I
 
+/- warning: complex.conj_eq_iff_real -> Complex.conj_eq_iff_real is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)))
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
+Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_real Complex.conj_eq_iff_realₓ'. -/
 theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_of_real]⟩
 #align complex.conj_eq_iff_real Complex.conj_eq_iff_real
 
+/- warning: complex.conj_eq_iff_re -> Complex.conj_eq_iff_re is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
+Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_re Complex.conj_eq_iff_reₓ'. -/
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
 #align complex.conj_eq_iff_re Complex.conj_eq_iff_re
 
+/- warning: complex.conj_eq_iff_im -> Complex.conj_eq_iff_im is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.conj_eq_iff_im Complex.conj_eq_iff_imₓ'. -/
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
+! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -834,37 +834,19 @@ theorem conj_neg_I : conj (-I) = I :=
   ext_iff.2 <| by simp
 #align complex.conj_neg_I Complex.conj_neg_I
 
-/- warning: complex.eq_conj_iff_real -> Complex.eq_conj_iff_real is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)))
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-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
-Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_real Complex.eq_conj_iff_realₓ'. -/
-theorem eq_conj_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
+theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_of_real]⟩
-#align complex.eq_conj_iff_real Complex.eq_conj_iff_real
+#align complex.conj_eq_iff_real Complex.conj_eq_iff_real
 
-/- warning: complex.eq_conj_iff_re -> Complex.eq_conj_iff_re is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
-but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
-Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_re Complex.eq_conj_iff_reₓ'. -/
-theorem eq_conj_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
-  eq_conj_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
-#align complex.eq_conj_iff_re Complex.eq_conj_iff_re
+theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
+  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
+#align complex.conj_eq_iff_re Complex.conj_eq_iff_re
 
-/- warning: complex.eq_conj_iff_im -> Complex.eq_conj_iff_im is a dubious translation:
-lean 3 declaration is
-  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
-but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
-Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_im Complex.eq_conj_iff_imₓ'. -/
-theorem eq_conj_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
+theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
-#align complex.eq_conj_iff_im Complex.eq_conj_iff_im
+#align complex.conj_eq_iff_im Complex.conj_eq_iff_im
 
 /- warning: complex.star_def -> Complex.star_def is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/39478763114722f0ec7613cb2f3f7701f9b86c8d

@@ -732,7 +732,7 @@ theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit0.{0} Nat Nat.hasAdd n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit0.{0} Nat instAddNat n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) Complex.I (bit0.{0} Nat instAddNat n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
 Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit0 Complex.I_pow_bit0ₓ'. -/
 @[simp]
 theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
@@ -742,7 +742,7 @@ theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit1.{0} Nat Nat.hasOne Nat.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
 but is expected to have type
-  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) Complex.I (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit1 Complex.I_pow_bit1ₓ'. -/
 @[simp]
 theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
@@ -1126,7 +1126,7 @@ theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
 lean 3 declaration is
   Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
 but is expected to have type
-  Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+  Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) Complex.I (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.I_sq Complex.I_sqₓ'. -/
 @[simp]
 theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
@@ -1169,7 +1169,7 @@ theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
 lean 3 declaration is
   forall (r : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) n)
 but is expected to have type
-  forall (r : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Complex.ofReal' r) n)
+  forall (r : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) (Complex.ofReal' r) n)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_pow Complex.ofReal_powₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
@@ -1591,7 +1591,7 @@ end AbsTheory
 lean 3 declaration is
   Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
 theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
@@ -1601,7 +1601,7 @@ theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
 theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
@@ -1611,7 +1611,7 @@ theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_real Complex.abs_ofRealₓ'. -/
 @[simp, norm_cast]
 theorem abs_ofReal (r : ℝ) : abs r = |r| := by
@@ -1622,7 +1622,7 @@ theorem abs_ofReal (r : ℝ) : abs r = |r| := by
 lean 3 declaration is
   forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) r)
 but is expected to have type
-  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) r)
+  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nonneg Complex.abs_of_nonnegₓ'. -/
 theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
   (abs_ofReal _).trans (abs_of_nonneg h)
@@ -1632,7 +1632,7 @@ theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
 theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
@@ -1645,7 +1645,7 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
 theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
@@ -1655,7 +1655,7 @@ theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
 theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
@@ -1665,7 +1665,7 @@ theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_reₓ'. -/
 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
@@ -1676,7 +1676,7 @@ theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_imₓ'. -/
 @[simp]
 theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
@@ -1687,7 +1687,7 @@ theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_I Complex.abs_Iₓ'. -/
 @[simp]
 theorem abs_I : abs I = 1 := by simp [abs]
@@ -1697,7 +1697,7 @@ theorem abs_I : abs I = 1 := by simp [abs]
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_two Complex.abs_twoₓ'. -/
 @[simp]
 theorem abs_two : abs 2 = 2 :=
@@ -1711,7 +1711,7 @@ theorem abs_two : abs 2 = 2 :=
 lean 3 declaration is
   Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_abs Complex.range_absₓ'. -/
 @[simp]
 theorem range_abs : range abs = Ici 0 :=
@@ -1722,7 +1722,7 @@ theorem range_abs : range abs = Ici 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
 theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
@@ -1733,7 +1733,7 @@ theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
 lean 3 declaration is
   forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (f i)))
 but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (f i)))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (f i)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_prod Complex.abs_prodₓ'. -/
 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
@@ -1745,7 +1745,7 @@ theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
 lean 3 declaration is
   forall (z : Complex) (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) n)
+  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_pow Complex.abs_powₓ'. -/
 @[simp]
 theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
@@ -1756,7 +1756,7 @@ theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
 lean 3 declaration is
   forall (z : Complex) (n : Int), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) n)
+  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_zpow Complex.abs_zpowₓ'. -/
 @[simp]
 theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
@@ -1767,7 +1767,7 @@ theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_le_abs Complex.abs_re_le_absₓ'. -/
 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   Real.abs_le_sqrt <| by
@@ -1779,7 +1779,7 @@ theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_le_abs Complex.abs_im_le_absₓ'. -/
 theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
   Real.abs_le_sqrt <| by
@@ -1791,7 +1791,7 @@ theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.re_le_abs Complex.re_le_absₓ'. -/
 theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
@@ -1801,7 +1801,7 @@ theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.im_le_abs Complex.im_le_absₓ'. -/
 theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
@@ -1811,7 +1811,7 @@ theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_lt_abs Complex.abs_re_lt_absₓ'. -/
 @[simp]
 theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
@@ -1823,7 +1823,7 @@ theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_lt_abs Complex.abs_im_lt_absₓ'. -/
 @[simp]
 theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa using @abs_re_lt_abs (z * I)
@@ -1833,7 +1833,7 @@ theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa usin
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_abs Complex.abs_absₓ'. -/
 @[simp]
 theorem abs_abs (z : ℂ) : |abs z| = abs z :=
@@ -1844,7 +1844,7 @@ theorem abs_abs (z : ℂ) : |abs z| = abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_imₓ'. -/
 theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
@@ -1854,7 +1854,7 @@ theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (LinearOrder.max.{0} Real Real.linearOrder (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z))))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_maxₓ'. -/
 theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
   by
@@ -1875,7 +1875,7 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_oneₓ'. -/
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1886,7 +1886,7 @@ theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_oneₓ'. -/
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1897,7 +1897,7 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
 theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
@@ -1908,7 +1908,7 @@ theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
 lean 3 declaration is
   forall (n : Int), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) n)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
+  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
 Case conversion may be inaccurate. Consider using '#align complex.int_cast_abs Complex.int_cast_absₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
@@ -1919,7 +1919,7 @@ theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
 theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
@@ -2118,7 +2118,7 @@ local notation "abs'" => Abs.abs
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.re (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_re Complex.isCauSeq_reₓ'. -/
 theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
@@ -2129,7 +2129,7 @@ theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fu
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.im (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_im Complex.isCauSeq_imₓ'. -/
 theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
@@ -2140,7 +2140,7 @@ theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fu
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_re Complex.cauSeqReₓ'. -/
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
@@ -2151,7 +2151,7 @@ noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_im Complex.cauSeqImₓ'. -/
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
@@ -2162,7 +2162,7 @@ noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
 lean 3 declaration is
   forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, 1, 1} Nat Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) f))
 but is expected to have type
-  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f))
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_abs Complex.isCauSeq_absₓ'. -/
 theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
@@ -2173,7 +2173,7 @@ theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (ab
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> Complex
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> Complex
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> Complex
 Case conversion may be inaccurate. Consider using '#align complex.lim_aux Complex.limAuxₓ'. -/
 /-- The limit of a Cauchy sequence of complex numbers. -/
 noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
@@ -2184,7 +2184,7 @@ noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), HasEquivₓ.Equiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (setoidHasEquiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) (Complex.limAux f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) (Complex.limAux f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) (Complex.limAux f))
 Case conversion may be inaccurate. Consider using '#align complex.equiv_lim_aux Complex.equiv_limAuxₓ'. -/
 theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
@@ -2206,7 +2206,7 @@ open CauSeq
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f))) Complex.I))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_reₓ'. -/
 theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
     limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
@@ -2223,7 +2223,7 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_re Complex.lim_reₓ'. -/
 theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
@@ -2233,7 +2233,7 @@ theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_im Complex.lim_imₓ'. -/
 theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im := by
   rw [lim_eq_lim_im_add_lim_re] <;> simp
@@ -2243,7 +2243,7 @@ theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
 theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
@@ -2254,7 +2254,7 @@ theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) :=
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_conj Complex.cauSeqConjₓ'. -/
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
 noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
@@ -2265,7 +2265,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])
@@ -2276,7 +2276,7 @@ theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_abs Complex.cauSeqAbsₓ'. -/
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
@@ -2287,7 +2287,7 @@ noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real Complex.instSemiringComplex Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueInstSemiringComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_abs Complex.lim_absₓ'. -/
 theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f) :=
   lim_eq_of_equiv_const fun ε ε0 =>

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

@@ -1458,7 +1458,7 @@ theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast,
 lean 3 declaration is
   forall (n : Rat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) n)
 but is expected to have type
-  forall (n : Rat), Eq.{1} Complex (Complex.ofReal' (Rat.cast.{0} Real Real.ratCast n)) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) n)
+  forall (n : Rat), Eq.{1} Complex (Complex.ofReal' (Rat.cast.{0} Real Real.ratCast n)) (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) n)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_rat_cast Complex.ofReal_rat_castₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
@@ -1469,7 +1469,7 @@ theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
 lean 3 declaration is
   forall (q : Rat), Eq.{1} Real (Complex.re ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) q)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)
 but is expected to have type
-  forall (q : Rat), Eq.{1} Complex (Complex.ofReal' (Complex.re (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q))) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q)
+  forall (q : Rat), Eq.{1} Complex (Complex.ofReal' (Complex.re (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q))) (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q)
 Case conversion may be inaccurate. Consider using '#align complex.rat_cast_re Complex.rat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
@@ -1479,7 +1479,7 @@ theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast,
 lean 3 declaration is
   forall (q : Rat), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) q)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  forall (q : Rat), Eq.{1} Complex (Complex.ofReal' (Complex.im (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q))) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)))
+  forall (q : Rat), Eq.{1} Real (Complex.im (Rat.cast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align complex.rat_cast_im Complex.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
@@ -1488,16 +1488,16 @@ theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast,
 /-! ### Characteristic zero -/
 
 
-/- warning: complex.char_zero_complex -> Complex.charZero_complex is a dubious translation:
+/- warning: complex.char_zero_complex -> Complex.charZero is a dubious translation:
 lean 3 declaration is
   CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)
 but is expected to have type
   CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)
-Case conversion may be inaccurate. Consider using '#align complex.char_zero_complex Complex.charZero_complexₓ'. -/
-instance charZero_complex : CharZero ℂ :=
+Case conversion may be inaccurate. Consider using '#align complex.char_zero_complex Complex.charZeroₓ'. -/
+instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
-#align complex.char_zero_complex Complex.charZero_complex
+#align complex.char_zero_complex Complex.charZero
 
 /- warning: complex.re_eq_add_conj -> Complex.re_eq_add_conj is a dubious translation:
 lean 3 declaration is
@@ -1947,142 +1947,142 @@ section ComplexOrder
 
 scoped[ComplexOrder] attribute [instance] Complex.partialOrder
 
-/- warning: complex.le_def -> Complex.ComplexOrder.le_def is a dubious translation:
+/- warning: complex.le_def -> Complex.le_def is a dubious translation:
 lean 3 declaration is
   forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.hasLe (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.instLEReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.le_def Complex.ComplexOrder.le_defₓ'. -/
-theorem Complex.ComplexOrder.le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
+Case conversion may be inaccurate. Consider using '#align complex.le_def Complex.le_defₓ'. -/
+theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.le_def Complex.ComplexOrder.le_def
+#align complex.le_def Complex.le_def
 
-/- warning: complex.lt_def -> Complex.ComplexOrder.lt_def is a dubious translation:
+/- warning: complex.lt_def -> Complex.lt_def is a dubious translation:
 lean 3 declaration is
   forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.hasLt (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.instLTReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.lt_def Complex.ComplexOrder.lt_defₓ'. -/
-theorem Complex.ComplexOrder.lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
+Case conversion may be inaccurate. Consider using '#align complex.lt_def Complex.lt_defₓ'. -/
+theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.lt_def Complex.ComplexOrder.lt_def
+#align complex.lt_def Complex.lt_def
 
-/- warning: complex.real_le_real -> Complex.ComplexOrder.real_le_real is a dubious translation:
+/- warning: complex.real_le_real -> Complex.real_le_real is a dubious translation:
 lean 3 declaration is
   forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LE.le.{0} Real Real.hasLe x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LE.le.{0} Real Real.instLEReal x y)
-Case conversion may be inaccurate. Consider using '#align complex.real_le_real Complex.ComplexOrder.real_le_realₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.real_le_real Complex.real_le_realₓ'. -/
 @[simp, norm_cast]
-theorem Complex.ComplexOrder.real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
-#align complex.real_le_real Complex.ComplexOrder.real_le_real
+theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
+#align complex.real_le_real Complex.real_le_real
 
-/- warning: complex.real_lt_real -> Complex.ComplexOrder.real_lt_real is a dubious translation:
+/- warning: complex.real_lt_real -> Complex.real_lt_real is a dubious translation:
 lean 3 declaration is
   forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LT.lt.{0} Real Real.hasLt x y)
 but is expected to have type
   forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LT.lt.{0} Real Real.instLTReal x y)
-Case conversion may be inaccurate. Consider using '#align complex.real_lt_real Complex.ComplexOrder.real_lt_realₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.real_lt_real Complex.real_lt_realₓ'. -/
 @[simp, norm_cast]
-theorem Complex.ComplexOrder.real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
-#align complex.real_lt_real Complex.ComplexOrder.real_lt_real
+theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
+#align complex.real_lt_real Complex.real_lt_real
 
-/- warning: complex.zero_le_real -> Complex.ComplexOrder.zero_le_real is a dubious translation:
+/- warning: complex.zero_le_real -> Complex.zero_le_real is a dubious translation:
 lean 3 declaration is
   forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
-Case conversion may be inaccurate. Consider using '#align complex.zero_le_real Complex.ComplexOrder.zero_le_realₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.zero_le_real Complex.zero_le_realₓ'. -/
 @[simp, norm_cast]
-theorem Complex.ComplexOrder.zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
-  Complex.ComplexOrder.real_le_real
-#align complex.zero_le_real Complex.ComplexOrder.zero_le_real
+theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
+  real_le_real
+#align complex.zero_le_real Complex.zero_le_real
 
-/- warning: complex.zero_lt_real -> Complex.ComplexOrder.zero_lt_real is a dubious translation:
+/- warning: complex.zero_lt_real -> Complex.zero_lt_real is a dubious translation:
 lean 3 declaration is
   forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
 but is expected to have type
   forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
-Case conversion may be inaccurate. Consider using '#align complex.zero_lt_real Complex.ComplexOrder.zero_lt_realₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.zero_lt_real Complex.zero_lt_realₓ'. -/
 @[simp, norm_cast]
-theorem Complex.ComplexOrder.zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
-  Complex.ComplexOrder.real_lt_real
-#align complex.zero_lt_real Complex.ComplexOrder.zero_lt_real
+theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
+  real_lt_real
+#align complex.zero_lt_real Complex.zero_lt_real
 
-/- warning: complex.not_le_iff -> Complex.ComplexOrder.not_le_iff is a dubious translation:
+/- warning: complex.not_le_iff -> Complex.not_le_iff is a dubious translation:
 lean 3 declaration is
   forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.hasLt (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.instLTReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.not_le_iff Complex.ComplexOrder.not_le_iffₓ'. -/
-theorem Complex.ComplexOrder.not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
+Case conversion may be inaccurate. Consider using '#align complex.not_le_iff Complex.not_le_iffₓ'. -/
+theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
   rw [le_def, not_and_or, not_le]
-#align complex.not_le_iff Complex.ComplexOrder.not_le_iff
+#align complex.not_le_iff Complex.not_le_iff
 
-/- warning: complex.not_lt_iff -> Complex.ComplexOrder.not_lt_iff is a dubious translation:
+/- warning: complex.not_lt_iff -> Complex.not_lt_iff is a dubious translation:
 lean 3 declaration is
   forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.hasLe (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
 but is expected to have type
   forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.instLEReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
-Case conversion may be inaccurate. Consider using '#align complex.not_lt_iff Complex.ComplexOrder.not_lt_iffₓ'. -/
-theorem Complex.ComplexOrder.not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
+Case conversion may be inaccurate. Consider using '#align complex.not_lt_iff Complex.not_lt_iffₓ'. -/
+theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
   rw [lt_def, not_and_or, not_lt]
-#align complex.not_lt_iff Complex.ComplexOrder.not_lt_iff
+#align complex.not_lt_iff Complex.not_lt_iff
 
-/- warning: complex.not_le_zero_iff -> Complex.ComplexOrder.not_le_zero_iff is a dubious translation:
+/- warning: complex.not_le_zero_iff -> Complex.not_le_zero_iff is a dubious translation:
 lean 3 declaration is
   forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
 but is expected to have type
   forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
-Case conversion may be inaccurate. Consider using '#align complex.not_le_zero_iff Complex.ComplexOrder.not_le_zero_iffₓ'. -/
-theorem Complex.ComplexOrder.not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
-  Complex.ComplexOrder.not_le_iff
-#align complex.not_le_zero_iff Complex.ComplexOrder.not_le_zero_iff
+Case conversion may be inaccurate. Consider using '#align complex.not_le_zero_iff Complex.not_le_zero_iffₓ'. -/
+theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
+  not_le_iff
+#align complex.not_le_zero_iff Complex.not_le_zero_iff
 
-/- warning: complex.not_lt_zero_iff -> Complex.ComplexOrder.not_lt_zero_iff is a dubious translation:
+/- warning: complex.not_lt_zero_iff -> Complex.not_lt_zero_iff is a dubious translation:
 lean 3 declaration is
   forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
 but is expected to have type
   forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
-Case conversion may be inaccurate. Consider using '#align complex.not_lt_zero_iff Complex.ComplexOrder.not_lt_zero_iffₓ'. -/
-theorem Complex.ComplexOrder.not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
-  Complex.ComplexOrder.not_lt_iff
-#align complex.not_lt_zero_iff Complex.ComplexOrder.not_lt_zero_iff
+Case conversion may be inaccurate. Consider using '#align complex.not_lt_zero_iff Complex.not_lt_zero_iffₓ'. -/
+theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
+  not_lt_iff
+#align complex.not_lt_zero_iff Complex.not_lt_zero_iff
 
-/- warning: complex.eq_re_of_real_le -> Complex.ComplexOrder.eq_re_ofReal_le is a dubious translation:
+/- warning: complex.eq_re_of_real_le -> Complex.eq_re_ofReal_le is a dubious translation:
 lean 3 declaration is
   forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)))
 but is expected to have type
   forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' r) z) -> (Eq.{1} Complex z (Complex.ofReal' (Complex.re z)))
-Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.ComplexOrder.eq_re_ofReal_leₓ'. -/
-theorem Complex.ComplexOrder.eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
+Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.eq_re_ofReal_leₓ'. -/
+theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
   by
   ext
   rfl
-  simp only [← (Complex.ComplexOrder.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
-#align complex.eq_re_of_real_le Complex.ComplexOrder.eq_re_ofReal_le
+  simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
+#align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
 
-#print Complex.ComplexOrder.strictOrderedCommRing /-
+#print Complex.strictOrderedCommRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
 -/
-protected def Complex.ComplexOrder.strictOrderedCommRing : StrictOrderedCommRing ℂ :=
+protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
   { Complex.partialOrder, Complex.commRing,
     Complex.nontrivial with
     zero_le_one := ⟨zero_le_one, rfl⟩
     add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
     mul_pos := fun z w hz hw => by
       simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1] }
-#align complex.strict_ordered_comm_ring Complex.ComplexOrder.strictOrderedCommRing
+#align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
 -/
 
-scoped[ComplexOrder] attribute [instance] Complex.ComplexOrder.strictOrderedCommRing
+scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 
-#print Complex.ComplexOrder.starOrderedRing /-
+#print Complex.starOrderedRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a star ordered ring.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
-protected def Complex.ComplexOrder.starOrderedRing : StarOrderedRing ℂ :=
-  { Complex.ComplexOrder.strictOrderedCommRing with
+protected def starOrderedRing : StarOrderedRing ℂ :=
+  { Complex.strictOrderedCommRing with
     nonneg_iff := fun r =>
       by
       refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
@@ -2101,10 +2101,10 @@ protected def Complex.ComplexOrder.starOrderedRing : StarOrderedRing ℂ :=
             MulZeroClass.mul_zero, neg_zero]
       · obtain ⟨s, rfl⟩ := h
         simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def] }
-#align complex.star_ordered_ring Complex.ComplexOrder.starOrderedRing
+#align complex.star_ordered_ring Complex.starOrderedRing
 -/
 
-scoped[ComplexOrder] attribute [instance] Complex.ComplexOrder.starOrderedRing
+scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing
 
 end ComplexOrder
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Data.Real.Sqrt
 /-!
 # The complex numbers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
 of characteristic zero. The result that the complex numbers are algebraically closed, see
 `field_theory.algebraic_closure`.

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

@@ -508,58 +508,58 @@ def I : ℂ :=
 #align complex.I Complex.I
 -/
 
-/- warning: complex.I_re -> Complex.i_re is a dubious translation:
+/- warning: complex.I_re -> Complex.I_re is a dubious translation:
 lean 3 declaration is
   Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
   Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
-Case conversion may be inaccurate. Consider using '#align complex.I_re Complex.i_reₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_re Complex.I_reₓ'. -/
 @[simp]
-theorem i_re : I.re = 0 :=
+theorem I_re : I.re = 0 :=
   rfl
-#align complex.I_re Complex.i_re
+#align complex.I_re Complex.I_re
 
-/- warning: complex.I_im -> Complex.i_im is a dubious translation:
+/- warning: complex.I_im -> Complex.I_im is a dubious translation:
 lean 3 declaration is
   Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
   Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
-Case conversion may be inaccurate. Consider using '#align complex.I_im Complex.i_imₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_im Complex.I_imₓ'. -/
 @[simp]
-theorem i_im : I.im = 1 :=
+theorem I_im : I.im = 1 :=
   rfl
-#align complex.I_im Complex.i_im
+#align complex.I_im Complex.I_im
 
-/- warning: complex.I_mul_I -> Complex.i_mul_I is a dubious translation:
+/- warning: complex.I_mul_I -> Complex.I_mul_I is a dubious translation:
 lean 3 declaration is
   Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
 but is expected to have type
   Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_I Complex.i_mul_Iₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_I Complex.I_mul_Iₓ'. -/
 @[simp]
-theorem i_mul_I : I * I = -1 :=
+theorem I_mul_I : I * I = -1 :=
   ext_iff.2 <| by simp
-#align complex.I_mul_I Complex.i_mul_I
+#align complex.I_mul_I Complex.I_mul_I
 
-/- warning: complex.I_mul -> Complex.i_mul is a dubious translation:
+/- warning: complex.I_mul -> Complex.I_mul is a dubious translation:
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (Complex.re z))
 but is expected to have type
   forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (Complex.re z))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul Complex.i_mulₓ'. -/
-theorem i_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
+Case conversion may be inaccurate. Consider using '#align complex.I_mul Complex.I_mulₓ'. -/
+theorem I_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
   ext_iff.2 <| by simp
-#align complex.I_mul Complex.i_mul
+#align complex.I_mul Complex.I_mul
 
-/- warning: complex.I_ne_zero -> Complex.i_ne_zero is a dubious translation:
+/- warning: complex.I_ne_zero -> Complex.I_ne_zero is a dubious translation:
 lean 3 declaration is
   Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
 but is expected to have type
   Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
-Case conversion may be inaccurate. Consider using '#align complex.I_ne_zero Complex.i_ne_zeroₓ'. -/
-theorem i_ne_zero : (I : ℂ) ≠ 0 :=
+Case conversion may be inaccurate. Consider using '#align complex.I_ne_zero Complex.I_ne_zeroₓ'. -/
+theorem I_ne_zero : (I : ℂ) ≠ 0 :=
   mt (congr_arg im) zero_ne_one.symm
-#align complex.I_ne_zero Complex.i_ne_zero
+#align complex.I_ne_zero Complex.I_ne_zero
 
 /- warning: complex.mk_eq_add_mul_I -> Complex.mk_eq_add_mul_I is a dubious translation:
 lean 3 declaration is
@@ -600,23 +600,23 @@ Case conversion may be inaccurate. Consider using '#align complex.mul_I_im Compl
 theorem mul_I_im (z : ℂ) : (z * I).im = z.re := by simp
 #align complex.mul_I_im Complex.mul_I_im
 
-/- warning: complex.I_mul_re -> Complex.i_mul_re is a dubious translation:
+/- warning: complex.I_mul_re -> Complex.I_mul_re is a dubious translation:
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
 but is expected to have type
   forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_re Complex.i_mul_reₓ'. -/
-theorem i_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
-#align complex.I_mul_re Complex.i_mul_re
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_re Complex.I_mul_reₓ'. -/
+theorem I_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
+#align complex.I_mul_re Complex.I_mul_re
 
-/- warning: complex.I_mul_im -> Complex.i_mul_im is a dubious translation:
+/- warning: complex.I_mul_im -> Complex.I_mul_im is a dubious translation:
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Complex.re z)
 but is expected to have type
   forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Complex.re z)
-Case conversion may be inaccurate. Consider using '#align complex.I_mul_im Complex.i_mul_imₓ'. -/
-theorem i_mul_im (z : ℂ) : (I * z).im = z.re := by simp
-#align complex.I_mul_im Complex.i_mul_im
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_im Complex.I_mul_imₓ'. -/
+theorem I_mul_im (z : ℂ) : (I * z).im = z.re := by simp
+#align complex.I_mul_im Complex.I_mul_im
 
 #print Complex.equivRealProd_symm_apply /-
 @[simp]
@@ -725,25 +725,25 @@ theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
   rfl
 #align complex.coe_im_add_group_hom Complex.coe_imAddGroupHom
 
-/- warning: complex.I_pow_bit0 -> Complex.i_pow_bit0 is a dubious translation:
+/- warning: complex.I_pow_bit0 -> Complex.I_pow_bit0 is a dubious translation:
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit0.{0} Nat Nat.hasAdd n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n)
 but is expected to have type
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit0.{0} Nat instAddNat n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
-Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit0 Complex.i_pow_bit0ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit0 Complex.I_pow_bit0ₓ'. -/
 @[simp]
-theorem i_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
-#align complex.I_pow_bit0 Complex.i_pow_bit0
+theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
+#align complex.I_pow_bit0 Complex.I_pow_bit0
 
-/- warning: complex.I_pow_bit1 -> Complex.i_pow_bit1 is a dubious translation:
+/- warning: complex.I_pow_bit1 -> Complex.I_pow_bit1 is a dubious translation:
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit1.{0} Nat Nat.hasOne Nat.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
 but is expected to have type
   forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
-Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit1 Complex.i_pow_bit1ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit1 Complex.I_pow_bit1ₓ'. -/
 @[simp]
-theorem i_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
-#align complex.I_pow_bit1 Complex.i_pow_bit1
+theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
+#align complex.I_pow_bit1 Complex.I_pow_bit1
 
 /-! ### Complex conjugation -/
 
@@ -1119,15 +1119,15 @@ theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
   rfl
 #align complex.of_real_eq_coe Complex.ofReal_eq_coe
 
-/- warning: complex.I_sq -> Complex.i_sq is a dubious translation:
+/- warning: complex.I_sq -> Complex.I_sq is a dubious translation:
 lean 3 declaration is
   Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
 but is expected to have type
   Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
-Case conversion may be inaccurate. Consider using '#align complex.I_sq Complex.i_sqₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_sq Complex.I_sqₓ'. -/
 @[simp]
-theorem i_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
-#align complex.I_sq Complex.i_sq
+theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
+#align complex.I_sq Complex.I_sq
 
 /- warning: complex.sub_re -> Complex.sub_re is a dubious translation:
 lean 3 declaration is
@@ -1271,25 +1271,25 @@ noncomputable instance : Field ℂ :=
     mul_inv_cancel := @Complex.mul_inv_cancel
     inv_zero := Complex.inv_zero }
 
-/- warning: complex.I_zpow_bit0 -> Complex.i_zpow_bit0 is a dubious translation:
+/- warning: complex.I_zpow_bit0 -> Complex.I_zpow_bit0 is a dubious translation:
 lean 3 declaration is
   forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) Complex.I (bit0.{0} Int Int.hasAdd n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n)
 but is expected to have type
   forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit0.{0} Int Int.instAddInt n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
-Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit0 Complex.i_zpow_bit0ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit0 Complex.I_zpow_bit0ₓ'. -/
 @[simp]
-theorem i_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
-#align complex.I_zpow_bit0 Complex.i_zpow_bit0
+theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
+#align complex.I_zpow_bit0 Complex.I_zpow_bit0
 
-/- warning: complex.I_zpow_bit1 -> Complex.i_zpow_bit1 is a dubious translation:
+/- warning: complex.I_zpow_bit1 -> Complex.I_zpow_bit1 is a dubious translation:
 lean 3 declaration is
   forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) Complex.I (bit1.{0} Int Int.hasOne Int.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
 but is expected to have type
   forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
-Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit1 Complex.i_zpow_bit1ₓ'. -/
+Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit1 Complex.I_zpow_bit1ₓ'. -/
 @[simp]
-theorem i_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
-#align complex.I_zpow_bit1 Complex.i_zpow_bit1
+theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
+#align complex.I_zpow_bit1 Complex.I_zpow_bit1
 
 /- warning: complex.div_re -> Complex.div_re is a dubious translation:
 lean 3 declaration is
@@ -1351,7 +1351,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align complex.div_I Complex.div_Iₓ'. -/
 @[simp]
 theorem div_I (z : ℂ) : z / I = -(z * I) :=
-  (div_eq_iff_mul_eq i_ne_zero).2 <| by simp [mul_assoc]
+  (div_eq_iff_mul_eq I_ne_zero).2 <| by simp [mul_assoc]
 #align complex.div_I Complex.div_I
 
 /- warning: complex.inv_I -> Complex.inv_I is a dubious translation:
@@ -1570,211 +1570,203 @@ private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
     exact re_le_abs (z * conj w)
 #align complex.abs_theory.abs_add complex.abs_theory.abs_add
 
-#print Complex.AbsTheory.Complex.abs /-
+#print Complex.abs /-
 /-- The complex absolute value function, defined as the square root of the norm squared. -/
-noncomputable def Complex.AbsTheory.Complex.abs : AbsoluteValue ℂ ℝ
+noncomputable def Complex.abs : AbsoluteValue ℂ ℝ
     where
   toFun x := abs x
   map_mul' := abs_mul
   nonneg' := abs_nonneg'
   eq_zero' _ := (Real.sqrt_eq_zero <| normSq_nonneg _).trans normSq_eq_zero
   add_le' := abs_add
-#align complex.abs Complex.AbsTheory.Complex.abs
+#align complex.abs Complex.abs
 -/
 
 end AbsTheory
 
 /- warning: complex.abs_def -> Complex.abs_def is a dubious translation:
 lean 3 declaration is
-  Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.AbsTheory.Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+  Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
-theorem abs_def : (Complex.AbsTheory.Complex.abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
+theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
 #align complex.abs_def Complex.abs_def
 
 /- warning: complex.abs_apply -> Complex.abs_apply is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
-theorem abs_apply {z : ℂ} : Complex.AbsTheory.Complex.abs z = (normSq z).sqrt :=
+theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
   rfl
 #align complex.abs_apply Complex.abs_apply
 
 /- warning: complex.abs_of_real -> Complex.abs_ofReal is a dubious translation:
 lean 3 declaration is
-  forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
+  forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_real Complex.abs_ofRealₓ'. -/
 @[simp, norm_cast]
-theorem abs_ofReal (r : ℝ) : Complex.AbsTheory.Complex.abs r = |r| := by
+theorem abs_ofReal (r : ℝ) : abs r = |r| := by
   simp [abs, norm_sq_of_real, Real.sqrt_mul_self_eq_abs]
 #align complex.abs_of_real Complex.abs_ofReal
 
 /- warning: complex.abs_of_nonneg -> Complex.abs_of_nonneg is a dubious translation:
 lean 3 declaration is
-  forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) r)
+  forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) r)
 but is expected to have type
-  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) r)
+  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Complex.ofReal' r)) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nonneg Complex.abs_of_nonnegₓ'. -/
-theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.AbsTheory.Complex.abs r = r :=
+theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
   (abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 
 /- warning: complex.abs_of_nat -> Complex.abs_of_nat is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
-theorem abs_of_nat (n : ℕ) : Complex.AbsTheory.Complex.abs n = n :=
+theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
-    Complex.AbsTheory.Complex.abs n = Complex.AbsTheory.Complex.abs (n : ℝ) := by
-      rw [of_real_nat_cast]
+    Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
     _ = _ := abs_of_nonneg (Nat.cast_nonneg n)
     
 #align complex.abs_of_nat Complex.abs_of_nat
 
 /- warning: complex.mul_self_abs -> Complex.mul_self_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
-theorem mul_self_abs (z : ℂ) :
-    Complex.AbsTheory.Complex.abs z * Complex.AbsTheory.Complex.abs z = normSq z :=
+theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
 #align complex.mul_self_abs Complex.mul_self_abs
 
 /- warning: complex.sq_abs -> Complex.sq_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
-theorem sq_abs (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 = normSq z :=
+theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
 #align complex.sq_abs Complex.sq_abs
 
 /- warning: complex.sq_abs_sub_sq_re -> Complex.sq_abs_sub_sq_re is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+  forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_reₓ'. -/
 @[simp]
-theorem sq_abs_sub_sq_re (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
+theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
   rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel']
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
 
 /- warning: complex.sq_abs_sub_sq_im -> Complex.sq_abs_sub_sq_im is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+  forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_imₓ'. -/
 @[simp]
-theorem sq_abs_sub_sq_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
+theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
   rw [← sq_abs_sub_sq_re, sub_sub_cancel]
 #align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
 
 /- warning: complex.abs_I -> Complex.abs_I is a dubious translation:
 lean 3 declaration is
-  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_I Complex.abs_Iₓ'. -/
 @[simp]
-theorem abs_I : Complex.AbsTheory.Complex.abs I = 1 := by simp [abs]
+theorem abs_I : abs I = 1 := by simp [abs]
 #align complex.abs_I Complex.abs_I
 
 /- warning: complex.abs_two -> Complex.abs_two is a dubious translation:
 lean 3 declaration is
-  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_two Complex.abs_twoₓ'. -/
 @[simp]
-theorem abs_two : Complex.AbsTheory.Complex.abs 2 = 2 :=
+theorem abs_two : abs 2 = 2 :=
   calc
-    Complex.AbsTheory.Complex.abs 2 = Complex.AbsTheory.Complex.abs (2 : ℝ) := by
-      rw [of_real_bit0, of_real_one]
+    abs 2 = abs (2 : ℝ) := by rw [of_real_bit0, of_real_one]
     _ = (2 : ℝ) := abs_of_nonneg (by norm_num)
     
 #align complex.abs_two Complex.abs_two
 
 /- warning: complex.range_abs -> Complex.range_abs is a dubious translation:
 lean 3 declaration is
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_abs Complex.range_absₓ'. -/
 @[simp]
-theorem range_abs : range Complex.AbsTheory.Complex.abs = Ici 0 :=
-  Subset.antisymm (range_subset_iff.2 Complex.AbsTheory.Complex.abs.NonNeg) fun x hx =>
-    ⟨x, abs_of_nonneg hx⟩
+theorem range_abs : range abs = Ici 0 :=
+  Subset.antisymm (range_subset_iff.2 abs.NonNeg) fun x hx => ⟨x, abs_of_nonneg hx⟩
 #align complex.range_abs Complex.range_abs
 
 /- warning: complex.abs_conj -> Complex.abs_conj is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
-theorem abs_conj (z : ℂ) :
-    Complex.AbsTheory.Complex.abs (conj z) = Complex.AbsTheory.Complex.abs z :=
+theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
 
 /- warning: complex.abs_prod -> Complex.abs_prod is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (f i)))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (f i)))
 but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (f i)))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (f i)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_prod Complex.abs_prodₓ'. -/
 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
-    Complex.AbsTheory.Complex.abs (s.Prod f) =
-      s.Prod fun i => Complex.AbsTheory.Complex.abs (f i) :=
-  map_prod Complex.AbsTheory.Complex.abs _ _
+    abs (s.Prod f) = s.Prod fun i => abs (f i) :=
+  map_prod abs _ _
 #align complex.abs_prod Complex.abs_prod
 
 /- warning: complex.abs_pow -> Complex.abs_pow is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex) (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_pow Complex.abs_powₓ'. -/
 @[simp]
-theorem abs_pow (z : ℂ) (n : ℕ) :
-    Complex.AbsTheory.Complex.abs (z ^ n) = Complex.AbsTheory.Complex.abs z ^ n :=
-  map_pow Complex.AbsTheory.Complex.abs z n
+theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
+  map_pow abs z n
 #align complex.abs_pow Complex.abs_pow
 
 /- warning: complex.abs_zpow -> Complex.abs_zpow is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex) (n : Int), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Int), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_zpow Complex.abs_zpowₓ'. -/
 @[simp]
-theorem abs_zpow (z : ℂ) (n : ℤ) :
-    Complex.AbsTheory.Complex.abs (z ^ n) = Complex.AbsTheory.Complex.abs z ^ n :=
-  map_zpow₀ Complex.AbsTheory.Complex.abs z n
+theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
+  map_zpow₀ abs z n
 #align complex.abs_zpow Complex.abs_zpow
 
 /- warning: complex.abs_re_le_abs -> Complex.abs_re_le_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_le_abs Complex.abs_re_le_absₓ'. -/
-theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.AbsTheory.Complex.abs z :=
+theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
   Real.abs_le_sqrt <| by
     rw [norm_sq_apply, ← sq]
     exact le_add_of_nonneg_right (mul_self_nonneg _)
@@ -1782,11 +1774,11 @@ theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.AbsTheory.Complex.abs z :=
 
 /- warning: complex.abs_im_le_abs -> Complex.abs_im_le_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_le_abs Complex.abs_im_le_absₓ'. -/
-theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.AbsTheory.Complex.abs z :=
+theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
   Real.abs_le_sqrt <| by
     rw [norm_sq_apply, ← sq, ← sq]
     exact le_add_of_nonneg_left (sq_nonneg _)
@@ -1794,76 +1786,74 @@ theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.AbsTheory.Complex.abs z :=
 
 /- warning: complex.re_le_abs -> Complex.re_le_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.re_le_abs Complex.re_le_absₓ'. -/
-theorem re_le_abs (z : ℂ) : z.re ≤ Complex.AbsTheory.Complex.abs z :=
+theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
 #align complex.re_le_abs Complex.re_le_abs
 
 /- warning: complex.im_le_abs -> Complex.im_le_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.im_le_abs Complex.im_le_absₓ'. -/
-theorem im_le_abs (z : ℂ) : z.im ≤ Complex.AbsTheory.Complex.abs z :=
+theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
 #align complex.im_le_abs Complex.im_le_abs
 
 /- warning: complex.abs_re_lt_abs -> Complex.abs_re_lt_abs is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_lt_abs Complex.abs_re_lt_absₓ'. -/
 @[simp]
-theorem abs_re_lt_abs {z : ℂ} : |z.re| < Complex.AbsTheory.Complex.abs z ↔ z.im ≠ 0 := by
+theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
   rw [abs, AbsoluteValue.coe_mk, MulHom.coe_mk, Real.lt_sqrt (abs_nonneg _), norm_sq_apply,
     _root_.sq_abs, ← sq, lt_add_iff_pos_right, mul_self_pos]
 #align complex.abs_re_lt_abs Complex.abs_re_lt_abs
 
 /- warning: complex.abs_im_lt_abs -> Complex.abs_im_lt_abs is a dubious translation:
 lean 3 declaration is
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_lt_abs Complex.abs_im_lt_absₓ'. -/
 @[simp]
-theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.AbsTheory.Complex.abs z ↔ z.re ≠ 0 := by
-  simpa using @abs_re_lt_abs (z * I)
+theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa using @abs_re_lt_abs (z * I)
 #align complex.abs_im_lt_abs Complex.abs_im_lt_abs
 
 /- warning: complex.abs_abs -> Complex.abs_abs is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_abs Complex.abs_absₓ'. -/
 @[simp]
-theorem abs_abs (z : ℂ) : |Complex.AbsTheory.Complex.abs z| = Complex.AbsTheory.Complex.abs z :=
-  abs_of_nonneg (Complex.AbsTheory.Complex.abs.NonNeg _)
+theorem abs_abs (z : ℂ) : |abs z| = abs z :=
+  abs_of_nonneg (abs.NonNeg _)
 #align complex.abs_abs Complex.abs_abs
 
 /- warning: complex.abs_le_abs_re_add_abs_im -> Complex.abs_le_abs_re_add_abs_im is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_imₓ'. -/
-theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ≤ |z.re| + |z.im| := by
+theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
 #align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
 
 /- warning: complex.abs_le_sqrt_two_mul_max -> Complex.abs_le_sqrt_two_mul_max is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (LinearOrder.max.{0} Real Real.linearOrder (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z))))
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (LinearOrder.max.{0} Real Real.linearOrder (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z))))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_maxₓ'. -/
-theorem abs_le_sqrt_two_mul_max (z : ℂ) :
-    Complex.AbsTheory.Complex.abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
+theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
   by
   cases' z with x y
   simp only [abs_apply, norm_sq_mk, ← sq]
@@ -1880,9 +1870,9 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) :
 
 /- warning: complex.abs_re_div_abs_le_one -> Complex.abs_re_div_abs_le_one is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_oneₓ'. -/
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1891,9 +1881,9 @@ theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
 
 /- warning: complex.abs_im_div_abs_le_one -> Complex.abs_im_div_abs_le_one is a dubious translation:
 lean 3 declaration is
-  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_oneₓ'. -/
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1902,33 +1892,33 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
 
 /- warning: complex.abs_cast_nat -> Complex.abs_cast_nat is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
-theorem abs_cast_nat (n : ℕ) : Complex.AbsTheory.Complex.abs (n : ℂ) = n := by
+theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
   rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
 #align complex.abs_cast_nat Complex.abs_cast_nat
 
 /- warning: complex.int_cast_abs -> Complex.int_cast_abs is a dubious translation:
 lean 3 declaration is
-  forall (n : Int), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) n)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n))
+  forall (n : Int), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) n)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
+  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
 Case conversion may be inaccurate. Consider using '#align complex.int_cast_abs Complex.int_cast_absₓ'. -/
 @[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : ↑(|n|) = Complex.AbsTheory.Complex.abs n := by
+theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
   rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
 #align complex.int_cast_abs Complex.int_cast_abs
 
 /- warning: complex.norm_sq_eq_abs -> Complex.normSq_eq_abs is a dubious translation:
 lean 3 declaration is
-  forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+  forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
-theorem normSq_eq_abs (x : ℂ) : normSq x = Complex.AbsTheory.Complex.abs x ^ 2 := by
+theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
 #align complex.norm_sq_eq_abs Complex.normSq_eq_abs
 
@@ -2123,82 +2113,77 @@ local notation "abs'" => Abs.abs
 
 /- warning: complex.is_cau_seq_re -> Complex.isCauSeq_re is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.re (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.re (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_re Complex.isCauSeq_reₓ'. -/
-theorem isCauSeq_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
+theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_re Complex.isCauSeq_re
 
 /- warning: complex.is_cau_seq_im -> Complex.isCauSeq_im is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.im (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.im (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_im Complex.isCauSeq_imₓ'. -/
-theorem isCauSeq_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
+theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_im Complex.isCauSeq_im
 
 /- warning: complex.cau_seq_re -> Complex.cauSeqRe is a dubious translation:
 lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_re Complex.cauSeqReₓ'. -/
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqRe (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_re f⟩
 #align complex.cau_seq_re Complex.cauSeqRe
 
 /- warning: complex.cau_seq_im -> Complex.cauSeqIm is a dubious translation:
 lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_im Complex.cauSeqImₓ'. -/
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqIm (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_im f⟩
 #align complex.cau_seq_im Complex.cauSeqIm
 
 /- warning: complex.is_cau_seq_abs -> Complex.isCauSeq_abs is a dubious translation:
 lean 3 declaration is
-  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, 1, 1} Nat Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f))
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, 1, 1} Nat Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) f))
 but is expected to have type
-  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f))
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_abs Complex.isCauSeq_absₓ'. -/
-theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.AbsTheory.Complex.abs f) :
-    IsCauSeq abs' (Complex.AbsTheory.Complex.abs ∘ f) := fun ε ε0 =>
+theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
-  ⟨i, fun j hj =>
-    lt_of_le_of_lt (Complex.AbsTheory.Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
+  ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.is_cau_seq_abs Complex.isCauSeq_abs
 
 /- warning: complex.lim_aux -> Complex.limAux is a dubious translation:
 lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> Complex
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> Complex
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> Complex
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> Complex
 Case conversion may be inaccurate. Consider using '#align complex.lim_aux Complex.limAuxₓ'. -/
 /-- The limit of a Cauchy sequence of complex numbers. -/
-noncomputable def limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : ℂ :=
+noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
   ⟨CauSeq.lim (cauSeqRe f), CauSeq.lim (cauSeqIm f)⟩
 #align complex.lim_aux Complex.limAux
 
 /- warning: complex.equiv_lim_aux -> Complex.equiv_limAux is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), HasEquivₓ.Equiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (setoidHasEquiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), HasEquivₓ.Equiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (setoidHasEquiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) (Complex.limAux f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) (Complex.limAux f))
 Case conversion may be inaccurate. Consider using '#align complex.equiv_lim_aux Complex.equiv_limAuxₓ'. -/
-theorem equiv_limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    f ≈ CauSeq.const Complex.AbsTheory.Complex.abs (limAux f) := fun ε ε0 =>
+theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
         (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
     fun i H j ij => by
@@ -2209,25 +2194,23 @@ theorem equiv_limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     rwa [add_halves] at this
 #align complex.equiv_lim_aux Complex.equiv_limAux
 
-instance : CauSeq.IsComplete ℂ Complex.AbsTheory.Complex.abs :=
+instance : CauSeq.IsComplete ℂ abs :=
   ⟨fun f => ⟨limAux f, equiv_limAux f⟩⟩
 
 open CauSeq
 
 /- warning: complex.lim_eq_lim_im_add_lim_re -> Complex.lim_eq_lim_im_add_lim_re is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f))) Complex.I))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f))) Complex.I))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_reₓ'. -/
-theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
     limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
   lim_eq_of_equiv_const <|
     calc
       f ≈ _ := equiv_limAux f
-      _ =
-          CauSeq.const Complex.AbsTheory.Complex.abs
-            (↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I) :=
+      _ = CauSeq.const abs (↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I) :=
         CauSeq.ext fun _ =>
           Complex.ext (by simp [lim_aux, cau_seq_re]) (by simp [lim_aux, cau_seq_im])
       
@@ -2235,83 +2218,78 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs)
 
 /- warning: complex.lim_re -> Complex.lim_re is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_re Complex.lim_reₓ'. -/
-theorem lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    limUnder (cauSeqRe f) = (limUnder f).re := by rw [lim_eq_lim_im_add_lim_re] <;> simp
+theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by
+  rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_re Complex.lim_re
 
 /- warning: complex.lim_im -> Complex.lim_im is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_im Complex.lim_imₓ'. -/
-theorem lim_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    limUnder (cauSeqIm f) = (limUnder f).im := by rw [lim_eq_lim_im_add_lim_re] <;> simp
+theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im := by
+  rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_im Complex.lim_im
 
 /- warning: complex.is_cau_seq_conj -> Complex.isCauSeq_conj is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
-theorem isCauSeq_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    IsCauSeq Complex.AbsTheory.Complex.abs fun n => conj (f n) := fun ε ε0 =>
+theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by rw [← RingHom.map_sub, abs_conj] <;> exact hi j hj⟩
 #align complex.is_cau_seq_conj Complex.isCauSeq_conj
 
 /- warning: complex.cau_seq_conj -> Complex.cauSeqConj is a dubious translation:
 lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs))
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_conj Complex.cauSeqConjₓ'. -/
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
-noncomputable def cauSeqConj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    CauSeq ℂ Complex.AbsTheory.Complex.abs :=
+noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
   ⟨_, isCauSeq_conj f⟩
 #align complex.cau_seq_conj Complex.cauSeqConj
 
 /- warning: complex.lim_conj -> Complex.lim_conj is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
-theorem lim_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    limUnder (cauSeqConj f) = conj (limUnder f) :=
+theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])
     (by simp [cau_seq_conj, (lim_im _).symm, cau_seq_im, (lim_neg _).symm] <;> rfl)
 #align complex.lim_conj Complex.lim_conj
 
 /- warning: complex.cau_seq_abs -> Complex.cauSeqAbs is a dubious translation:
 lean 3 declaration is
-  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_abs Complex.cauSeqAbsₓ'. -/
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqAbs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_abs f.2⟩
 #align complex.cau_seq_abs Complex.cauSeqAbs
 
 /- warning: complex.lim_abs -> Complex.lim_abs is a dubious translation:
 lean 3 declaration is
-  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.abs) Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_abs Complex.lim_absₓ'. -/
-theorem lim_abs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
-    limUnder (cauSeqAbs f) = Complex.AbsTheory.Complex.abs (limUnder f) :=
+theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f) :=
   lim_eq_of_equiv_const fun ε ε0 =>
     let ⟨i, hi⟩ := equiv_lim f ε ε0
-    ⟨i, fun j hj =>
-      lt_of_le_of_lt (Complex.AbsTheory.Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
+    ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.lim_abs Complex.lim_abs
 
 variable {α : Type _} (s : Finset α)

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

@@ -694,7 +694,7 @@ def reAddGroupHom : ℂ →+ ℝ where
 lean 3 declaration is
   Eq.{1} ((fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) Complex.reAddGroupHom) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) Complex.reAddGroupHom) Complex.re
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.reAddGroupHom) Complex.re
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.reAddGroupHom) Complex.re
 Case conversion may be inaccurate. Consider using '#align complex.coe_re_add_group_hom Complex.coe_reAddGroupHomₓ'. -/
 @[simp]
 theorem coe_reAddGroupHom : (reAddGroupHom : ℂ → ℝ) = re :=
@@ -718,7 +718,7 @@ def imAddGroupHom : ℂ →+ ℝ where
 lean 3 declaration is
   Eq.{1} ((fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) Complex.imAddGroupHom) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) Complex.imAddGroupHom) Complex.im
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.imAddGroupHom) Complex.im
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.imAddGroupHom) Complex.im
 Case conversion may be inaccurate. Consider using '#align complex.coe_im_add_group_hom Complex.coe_imAddGroupHomₓ'. -/
 @[simp]
 theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
@@ -761,7 +761,7 @@ instance : StarRing ℂ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Complex.re z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.re z)
+  forall (z : Complex), Eq.{1} Real (Complex.re (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.re z)
 Case conversion may be inaccurate. Consider using '#align complex.conj_re Complex.conj_reₓ'. -/
 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
@@ -772,7 +772,7 @@ theorem conj_re (z : ℂ) : (conj z).re = z.re :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_im Complex.conj_imₓ'. -/
 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
@@ -783,7 +783,7 @@ theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Complex.ofReal' r)) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.conj_of_real Complex.conj_ofRealₓ'. -/
 theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
@@ -793,7 +793,7 @@ theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) Complex.I) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) Complex.I) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) Complex.I) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.conj_I Complex.conj_Iₓ'. -/
 @[simp]
 theorem conj_I : conj I = -I :=
@@ -804,7 +804,7 @@ theorem conj_I : conj I = -I :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Complex Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (bit0.{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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instAddComplex (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit0.{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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit0 Complex.conj_bit0ₓ'. -/
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -814,7 +814,7 @@ theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
 Case conversion may be inaccurate. Consider using '#align complex.conj_bit1 Complex.conj_bit1ₓ'. -/
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
@@ -824,7 +824,7 @@ theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
 lean 3 declaration is
   Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)) Complex.I
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
 Case conversion may be inaccurate. Consider using '#align complex.conj_neg_I Complex.conj_neg_Iₓ'. -/
 @[simp]
 theorem conj_neg_I : conj (-I) = I :=
@@ -835,7 +835,7 @@ theorem conj_neg_I : conj (-I) = I :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
 Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_real Complex.eq_conj_iff_realₓ'. -/
 theorem eq_conj_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
@@ -846,7 +846,7 @@ theorem eq_conj_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
 Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_re Complex.eq_conj_iff_reₓ'. -/
 theorem eq_conj_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   eq_conj_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
@@ -856,7 +856,7 @@ theorem eq_conj_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_im Complex.eq_conj_iff_imₓ'. -/
 theorem eq_conj_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
@@ -867,7 +867,7 @@ theorem eq_conj_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
 lean 3 declaration is
   Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toHasStar.{0} Complex (StarAddMonoid.toHasInvolutiveStar.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing)))))) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.starRing)))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
 but is expected to have type
-  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing)))) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))
+  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing)))) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))
 Case conversion may be inaccurate. Consider using '#align complex.star_def Complex.star_defₓ'. -/
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
@@ -896,7 +896,7 @@ def normSq : ℂ →*₀ ℝ where
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_apply Complex.normSq_applyₓ'. -/
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
@@ -906,7 +906,7 @@ theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_of_real Complex.normSq_ofRealₓ'. -/
 @[simp]
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
@@ -916,7 +916,7 @@ theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) y y))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Complex.mk x y)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) y y))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mk Complex.normSq_mkₓ'. -/
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
@@ -927,7 +927,7 @@ theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
 lean 3 declaration is
   forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) x (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) y (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))
 but is expected to have type
-  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall (x : Real) (y : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (HAdd.hAdd.{0, 0, 0} Real Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' x) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' y) Complex.I))) (instHAdd.{0} Real Real.instAddReal) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) x (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) y (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_Iₓ'. -/
 theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
@@ -937,7 +937,7 @@ theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z)
 but is expected to have type
-  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instMulComplex) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z)
+  forall {z : Complex}, Eq.{1} Complex (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_selfₓ'. -/
 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
@@ -947,7 +947,7 @@ theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_zero Complex.normSq_zeroₓ'. -/
 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
@@ -958,7 +958,7 @@ theorem normSq_zero : normSq 0 = 0 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_one Complex.normSq_oneₓ'. -/
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
@@ -969,7 +969,7 @@ theorem normSq_one : normSq 1 = 1 :=
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_I Complex.normSq_Iₓ'. -/
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [norm_sq]
@@ -979,7 +979,7 @@ theorem normSq_I : normSq I = 1 := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_nonneg Complex.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
@@ -989,7 +989,7 @@ theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
 lean 3 declaration is
   Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_norm_sq Complex.range_normSqₓ'. -/
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
@@ -1001,7 +1001,7 @@ theorem range_normSq : range normSq = Ici 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_zero Complex.normSq_eq_zeroₓ'. -/
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
@@ -1014,7 +1014,7 @@ theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_pos Complex.normSq_posₓ'. -/
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
@@ -1025,7 +1025,7 @@ theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Neg.neg.{0} Complex Complex.hasNeg z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_neg Complex.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
@@ -1035,7 +1035,7 @@ theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
@@ -1045,7 +1045,7 @@ theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
@@ -1055,7 +1055,7 @@ theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
@@ -1065,7 +1065,7 @@ theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z *
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.re_sq_le_norm_sq Complex.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
@@ -1075,7 +1075,7 @@ theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.im_sq_le_norm_sq Complex.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
@@ -1085,7 +1085,7 @@ theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.mul_conj Complex.mul_conjₓ'. -/
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
@@ -1095,7 +1095,7 @@ theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re z)))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
 Case conversion may be inaccurate. Consider using '#align complex.add_conj Complex.add_conjₓ'. -/
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
@@ -1112,7 +1112,7 @@ def ofReal : ℝ →+* ℂ :=
 lean 3 declaration is
   forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) Complex.ofReal r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))))) Complex.ofReal r) (Complex.ofReal' r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))))) Complex.ofReal r) (Complex.ofReal' r)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_coe Complex.ofReal_eq_coeₓ'. -/
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
@@ -1177,7 +1177,7 @@ theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.im z))) Complex.I)
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
+  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
 Case conversion may be inaccurate. Consider using '#align complex.sub_conj Complex.sub_conjₓ'. -/
 theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
@@ -1187,7 +1187,7 @@ theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
@@ -1205,7 +1205,7 @@ noncomputable instance : Inv ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instMulComplex) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))))
+  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex.instMulComplex) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))))
 Case conversion may be inaccurate. Consider using '#align complex.inv_def Complex.inv_defₓ'. -/
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
@@ -1215,7 +1215,7 @@ theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_re Complex.inv_reₓ'. -/
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
@@ -1225,7 +1225,7 @@ theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, divi
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.inv_im Complex.inv_imₓ'. -/
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
@@ -1295,7 +1295,7 @@ theorem i_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1',
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_re Complex.div_reₓ'. -/
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
@@ -1305,7 +1305,7 @@ theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im /
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
 Case conversion may be inaccurate. Consider using '#align complex.div_im Complex.div_imₓ'. -/
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
@@ -1315,7 +1315,7 @@ theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im /
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Inv.inv.{0} Complex Complex.hasInv x)) (Inv.inv.{0} Complex Complex.hasInv (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) x) Complex.instInvComplex (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) x))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) x) Complex.instInvComplex (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) x))
 Case conversion may be inaccurate. Consider using '#align complex.conj_inv Complex.conj_invₓ'. -/
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
@@ -1368,7 +1368,7 @@ theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Inv.inv.{0} Complex Complex.hasInv z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_inv Complex.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
@@ -1379,7 +1379,7 @@ theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
 lean 3 declaration is
   forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
 but is expected to have type
-  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
@@ -1455,7 +1455,7 @@ theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast,
 lean 3 declaration is
   forall (n : Rat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) n)
 but is expected to have type
-  forall (n : Rat), Eq.{1} Complex (Complex.ofReal' (RatCast.ratCast.{0} Real Real.ratCast n)) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) n)
+  forall (n : Rat), Eq.{1} Complex (Complex.ofReal' (Rat.cast.{0} Real Real.ratCast n)) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) n)
 Case conversion may be inaccurate. Consider using '#align complex.of_real_rat_cast Complex.ofReal_rat_castₓ'. -/
 @[simp, norm_cast]
 theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
@@ -1500,7 +1500,7 @@ instance charZero_complex : CharZero ℂ :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : 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.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
 Case conversion may be inaccurate. Consider using '#align complex.re_eq_add_conj Complex.re_eq_add_conjₓ'. -/
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
@@ -1512,7 +1512,7 @@ theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) Complex.I))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) z (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.im_eq_sub_conj Complex.im_eq_sub_conjₓ'. -/
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
@@ -1542,7 +1542,7 @@ private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall (z : Complex), Eq.{1} Real (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
@@ -1588,7 +1588,7 @@ end AbsTheory
 lean 3 declaration is
   Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.AbsTheory.Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
 theorem abs_def : (Complex.AbsTheory.Complex.abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
@@ -1598,7 +1598,7 @@ theorem abs_def : (Complex.AbsTheory.Complex.abs : ℂ → ℝ) = fun z => (norm
 lean 3 declaration is
   forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
 but is expected to have type
-  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
 theorem abs_apply {z : ℂ} : Complex.AbsTheory.Complex.abs z = (normSq z).sqrt :=
   rfl
@@ -1608,7 +1608,7 @@ theorem abs_apply {z : ℂ} : Complex.AbsTheory.Complex.abs z = (normSq z).sqrt
 lean 3 declaration is
   forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
 but is expected to have type
-  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_real Complex.abs_ofRealₓ'. -/
 @[simp, norm_cast]
 theorem abs_ofReal (r : ℝ) : Complex.AbsTheory.Complex.abs r = |r| := by
@@ -1619,7 +1619,7 @@ theorem abs_ofReal (r : ℝ) : Complex.AbsTheory.Complex.abs r = |r| := by
 lean 3 declaration is
   forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) r)
 but is expected to have type
-  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) r)
+  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) r)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nonneg Complex.abs_of_nonnegₓ'. -/
 theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.AbsTheory.Complex.abs r = r :=
   (abs_ofReal _).trans (abs_of_nonneg h)
@@ -1629,7 +1629,7 @@ theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.AbsTheory.Complex.abs r
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
 theorem abs_of_nat (n : ℕ) : Complex.AbsTheory.Complex.abs n = n :=
   calc
@@ -1643,7 +1643,7 @@ theorem abs_of_nat (n : ℕ) : Complex.AbsTheory.Complex.abs n = n :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
 theorem mul_self_abs (z : ℂ) :
     Complex.AbsTheory.Complex.abs z * Complex.AbsTheory.Complex.abs z = normSq z :=
@@ -1654,7 +1654,7 @@ theorem mul_self_abs (z : ℂ) :
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
 theorem sq_abs (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
@@ -1664,7 +1664,7 @@ theorem sq_abs (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 = normSq z :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_reₓ'. -/
 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
@@ -1675,7 +1675,7 @@ theorem sq_abs_sub_sq_re (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.re
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instSubReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.im z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HPow.hPow.{0, 0, 0} Real Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (Complex.re z) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_imₓ'. -/
 @[simp]
 theorem sq_abs_sub_sq_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
@@ -1686,7 +1686,7 @@ theorem sq_abs_sub_sq_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.im
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) Real.instOneReal))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) Complex.I) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_I Complex.abs_Iₓ'. -/
 @[simp]
 theorem abs_I : Complex.AbsTheory.Complex.abs I = 1 := by simp [abs]
@@ -1696,7 +1696,7 @@ theorem abs_I : Complex.AbsTheory.Complex.abs I = 1 := by simp [abs]
 lean 3 declaration is
   Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_two Complex.abs_twoₓ'. -/
 @[simp]
 theorem abs_two : Complex.AbsTheory.Complex.abs 2 = 2 :=
@@ -1711,7 +1711,7 @@ theorem abs_two : Complex.AbsTheory.Complex.abs 2 = 2 :=
 lean 3 declaration is
   Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.range_abs Complex.range_absₓ'. -/
 @[simp]
 theorem range_abs : range Complex.AbsTheory.Complex.abs = Ici 0 :=
@@ -1723,7 +1723,7 @@ theorem range_abs : range Complex.AbsTheory.Complex.abs = Ici 0 :=
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) a) (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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
 theorem abs_conj (z : ℂ) :
@@ -1735,7 +1735,7 @@ theorem abs_conj (z : ℂ) :
 lean 3 declaration is
   forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (f i)))
 but is expected to have type
-  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (f i)))
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (f i)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_prod Complex.abs_prodₓ'. -/
 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
@@ -1748,7 +1748,7 @@ theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
 lean 3 declaration is
   forall (z : Complex) (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_pow Complex.abs_powₓ'. -/
 @[simp]
 theorem abs_pow (z : ℂ) (n : ℕ) :
@@ -1760,7 +1760,7 @@ theorem abs_pow (z : ℂ) (n : ℕ) :
 lean 3 declaration is
   forall (z : Complex) (n : Int), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
 but is expected to have type
-  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_zpow Complex.abs_zpowₓ'. -/
 @[simp]
 theorem abs_zpow (z : ℂ) (n : ℤ) :
@@ -1772,7 +1772,7 @@ theorem abs_zpow (z : ℂ) (n : ℤ) :
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_le_abs Complex.abs_re_le_absₓ'. -/
 theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.AbsTheory.Complex.abs z :=
   Real.abs_le_sqrt <| by
@@ -1784,7 +1784,7 @@ theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.AbsTheory.Complex.abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_le_abs Complex.abs_im_le_absₓ'. -/
 theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.AbsTheory.Complex.abs z :=
   Real.abs_le_sqrt <| by
@@ -1796,7 +1796,7 @@ theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.AbsTheory.Complex.abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.re_le_abs Complex.re_le_absₓ'. -/
 theorem re_le_abs (z : ℂ) : z.re ≤ Complex.AbsTheory.Complex.abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
@@ -1806,7 +1806,7 @@ theorem re_le_abs (z : ℂ) : z.re ≤ Complex.AbsTheory.Complex.abs z :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.im_le_abs Complex.im_le_absₓ'. -/
 theorem im_le_abs (z : ℂ) : z.im ≤ Complex.AbsTheory.Complex.abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
@@ -1816,7 +1816,7 @@ theorem im_le_abs (z : ℂ) : z.im ≤ Complex.AbsTheory.Complex.abs z :=
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_lt_abs Complex.abs_re_lt_absₓ'. -/
 @[simp]
 theorem abs_re_lt_abs {z : ℂ} : |z.re| < Complex.AbsTheory.Complex.abs z ↔ z.im ≠ 0 := by
@@ -1828,7 +1828,7 @@ theorem abs_re_lt_abs {z : ℂ} : |z.re| < Complex.AbsTheory.Complex.abs z ↔ z
 lean 3 declaration is
   forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_lt_abs Complex.abs_im_lt_absₓ'. -/
 @[simp]
 theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.AbsTheory.Complex.abs z ↔ z.re ≠ 0 := by
@@ -1839,7 +1839,7 @@ theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.AbsTheory.Complex.abs z ↔ z
 lean 3 declaration is
   forall (z : Complex), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
 Case conversion may be inaccurate. Consider using '#align complex.abs_abs Complex.abs_absₓ'. -/
 @[simp]
 theorem abs_abs (z : ℂ) : |Complex.AbsTheory.Complex.abs z| = Complex.AbsTheory.Complex.abs z :=
@@ -1850,7 +1850,7 @@ theorem abs_abs (z : ℂ) : |Complex.AbsTheory.Complex.abs z| = Complex.AbsTheor
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_imₓ'. -/
 theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
@@ -1860,7 +1860,7 @@ theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ≤
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (LinearOrder.max.{0} Real Real.linearOrder (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z))))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
 Case conversion may be inaccurate. Consider using '#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_maxₓ'. -/
 theorem abs_le_sqrt_two_mul_max (z : ℂ) :
     Complex.AbsTheory.Complex.abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
@@ -1882,7 +1882,7 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) :
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_oneₓ'. -/
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1893,7 +1893,7 @@ theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
 lean 3 declaration is
   forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_oneₓ'. -/
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
@@ -1904,7 +1904,7 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
 lean 3 declaration is
   forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
 but is expected to have type
-  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
 Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
 theorem abs_cast_nat (n : ℕ) : Complex.AbsTheory.Complex.abs (n : ℂ) = n := by
@@ -1915,7 +1915,7 @@ theorem abs_cast_nat (n : ℕ) : Complex.AbsTheory.Complex.abs (n : ℂ) = n :=
 lean 3 declaration is
   forall (n : Int), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) n)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n))
 but is expected to have type
-  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
+  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
 Case conversion may be inaccurate. Consider using '#align complex.int_cast_abs Complex.int_cast_absₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_abs (n : ℤ) : ↑(|n|) = Complex.AbsTheory.Complex.abs n := by
@@ -1926,7 +1926,7 @@ theorem int_cast_abs (n : ℤ) : ↑(|n|) = Complex.AbsTheory.Complex.abs n := b
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
 but is expected to have type
-  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
 Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
 theorem normSq_eq_abs (x : ℂ) : normSq x = Complex.AbsTheory.Complex.abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
@@ -2125,7 +2125,7 @@ local notation "abs'" => Abs.abs
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.re (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_re Complex.isCauSeq_reₓ'. -/
 theorem isCauSeq_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
@@ -2137,7 +2137,7 @@ theorem isCauSeq_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.im (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_im Complex.isCauSeq_imₓ'. -/
 theorem isCauSeq_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
@@ -2149,7 +2149,7 @@ theorem isCauSeq_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_re Complex.cauSeqReₓ'. -/
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqRe (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
@@ -2160,7 +2160,7 @@ noncomputable def cauSeqRe (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauS
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_im Complex.cauSeqImₓ'. -/
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqIm (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
@@ -2171,7 +2171,7 @@ noncomputable def cauSeqIm (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauS
 lean 3 declaration is
   forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, 1, 1} Nat Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f))
 but is expected to have type
-  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f))
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_abs Complex.isCauSeq_absₓ'. -/
 theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.AbsTheory.Complex.abs f) :
     IsCauSeq abs' (Complex.AbsTheory.Complex.abs ∘ f) := fun ε ε0 =>
@@ -2184,7 +2184,7 @@ theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.AbsTheory.Complex.
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> Complex
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> Complex
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> Complex
 Case conversion may be inaccurate. Consider using '#align complex.lim_aux Complex.limAuxₓ'. -/
 /-- The limit of a Cauchy sequence of complex numbers. -/
 noncomputable def limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : ℂ :=
@@ -2195,7 +2195,7 @@ noncomputable def limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : ℂ :=
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), HasEquivₓ.Equiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (setoidHasEquiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
 Case conversion may be inaccurate. Consider using '#align complex.equiv_lim_aux Complex.equiv_limAuxₓ'. -/
 theorem equiv_limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     f ≈ CauSeq.const Complex.AbsTheory.Complex.abs (limAux f) := fun ε ε0 =>
@@ -2218,7 +2218,7 @@ open CauSeq
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f))) Complex.I))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_reₓ'. -/
 theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
@@ -2237,7 +2237,7 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs)
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_re Complex.lim_reₓ'. -/
 theorem lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     limUnder (cauSeqRe f) = (limUnder f).re := by rw [lim_eq_lim_im_add_lim_re] <;> simp
@@ -2247,7 +2247,7 @@ theorem lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_im Complex.lim_imₓ'. -/
 theorem lim_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     limUnder (cauSeqIm f) = (limUnder f).im := by rw [lim_eq_lim_im_add_lim_re] <;> simp
@@ -2257,7 +2257,7 @@ theorem lim_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
 theorem isCauSeq_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     IsCauSeq Complex.AbsTheory.Complex.abs fun n => conj (f n) := fun ε ε0 =>
@@ -2269,7 +2269,7 @@ theorem isCauSeq_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_conj Complex.cauSeqConjₓ'. -/
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
 noncomputable def cauSeqConj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
@@ -2281,7 +2281,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
 theorem lim_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     limUnder (cauSeqConj f) = conj (limUnder f) :=
@@ -2293,7 +2293,7 @@ theorem lim_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
 lean 3 declaration is
   (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
 but is expected to have type
-  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
 Case conversion may be inaccurate. Consider using '#align complex.cau_seq_abs Complex.cauSeqAbsₓ'. -/
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
 noncomputable def cauSeqAbs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
@@ -2304,7 +2304,7 @@ noncomputable def cauSeqAbs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : Cau
 lean 3 declaration is
   forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
 but is expected to have type
-  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
 Case conversion may be inaccurate. Consider using '#align complex.lim_abs Complex.lim_absₓ'. -/
 theorem lim_abs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
     limUnder (cauSeqAbs f) = Complex.AbsTheory.Complex.abs (limUnder f) :=

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

@@ -2101,11 +2101,11 @@ protected def Complex.ComplexOrder.starOrderedRing : StarOrderedRing ℂ :=
           exact hr.2.symm
         ext
         ·
-          simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re, mul_zero, ←
-            Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
+          simp only [of_real_im, star_def, of_real_re, sub_zero, conj_re, mul_re,
+            MulZeroClass.mul_zero, ← Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
         ·
-          simp only [h₂, add_zero, of_real_im, star_def, zero_mul, conj_im, mul_im, mul_zero,
-            neg_zero]
+          simp only [h₂, add_zero, of_real_im, star_def, MulZeroClass.zero_mul, conj_im, mul_im,
+            MulZeroClass.mul_zero, neg_zero]
       · obtain ⟨s, rfl⟩ := h
         simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def] }
 #align complex.star_ordered_ring Complex.ComplexOrder.starOrderedRing

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

@@ -26,11 +26,13 @@ open Set Function
 /-! ### Definition and basic arithmmetic -/
 
 
+#print Complex /-
 /-- Complex numbers consist of two `real`s: a real part `re` and an imaginary part `im`. -/
 structure Complex : Type where
   re : ℝ
   im : ℝ
 #align complex Complex
+-/
 
 -- mathport name: exprℂ
 notation "ℂ" => Complex
@@ -42,6 +44,7 @@ open ComplexConjugate
 noncomputable instance : DecidableEq ℂ :=
   Classical.decEq _
 
+#print Complex.equivRealProd /-
 /-- The equivalence between the complex numbers and `ℝ × ℝ`. -/
 @[simps apply]
 def equivRealProd : ℂ ≃ ℝ × ℝ where
@@ -50,77 +53,128 @@ def equivRealProd : ℂ ≃ ℝ × ℝ where
   left_inv := fun ⟨x, y⟩ => rfl
   right_inv := fun ⟨x, y⟩ => rfl
 #align complex.equiv_real_prod Complex.equivRealProd
+-/
 
+#print Complex.eta /-
 @[simp]
 theorem eta : ∀ z : ℂ, Complex.mk z.re z.im = z
   | ⟨a, b⟩ => rfl
 #align complex.eta Complex.eta
+-/
 
+#print Complex.ext /-
 @[ext]
 theorem ext : ∀ {z w : ℂ}, z.re = w.re → z.im = w.im → z = w
   | ⟨zr, zi⟩, ⟨_, _⟩, rfl, rfl => rfl
 #align complex.ext Complex.ext
+-/
 
+#print Complex.ext_iff /-
 theorem ext_iff {z w : ℂ} : z = w ↔ z.re = w.re ∧ z.im = w.im :=
   ⟨fun H => by simp [H], fun h => ext h.1 h.2⟩
 #align complex.ext_iff Complex.ext_iff
+-/
 
+#print Complex.re_surjective /-
 theorem re_surjective : Surjective re := fun x => ⟨⟨x, 0⟩, rfl⟩
 #align complex.re_surjective Complex.re_surjective
+-/
 
+#print Complex.im_surjective /-
 theorem im_surjective : Surjective im := fun y => ⟨⟨0, y⟩, rfl⟩
 #align complex.im_surjective Complex.im_surjective
+-/
 
+#print Complex.range_re /-
 @[simp]
 theorem range_re : range re = univ :=
   re_surjective.range_eq
 #align complex.range_re Complex.range_re
+-/
 
+#print Complex.range_im /-
 @[simp]
 theorem range_im : range im = univ :=
   im_surjective.range_eq
 #align complex.range_im Complex.range_im
+-/
 
 instance : Coe ℝ ℂ :=
   ⟨fun r => ⟨r, 0⟩⟩
 
+#print Complex.ofReal_re /-
 @[simp, norm_cast]
-theorem of_real_re (r : ℝ) : (r : ℂ).re = r :=
+theorem ofReal_re (r : ℝ) : (r : ℂ).re = r :=
   rfl
-#align complex.of_real_re Complex.of_real_re
+#align complex.of_real_re Complex.ofReal_re
+-/
 
+/- warning: complex.of_real_im -> Complex.ofReal_im is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall (r : Real), Eq.{1} Real (Complex.im (Complex.ofReal' r)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_im Complex.ofReal_imₓ'. -/
 @[simp, norm_cast]
-theorem of_real_im (r : ℝ) : (r : ℂ).im = 0 :=
+theorem ofReal_im (r : ℝ) : (r : ℂ).im = 0 :=
   rfl
-#align complex.of_real_im Complex.of_real_im
-
-theorem of_real_def (r : ℝ) : (r : ℂ) = ⟨r, 0⟩ :=
+#align complex.of_real_im Complex.ofReal_im
+
+/- warning: complex.of_real_def -> Complex.ofReal_def is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) (Complex.mk r (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall (r : Real), Eq.{1} Complex (Complex.ofReal' r) (Complex.mk r (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_def Complex.ofReal_defₓ'. -/
+theorem ofReal_def (r : ℝ) : (r : ℂ) = ⟨r, 0⟩ :=
   rfl
-#align complex.of_real_def Complex.of_real_def
-
+#align complex.of_real_def Complex.ofReal_def
+
+/- warning: complex.of_real_inj -> Complex.ofReal_inj is a dubious translation:
+lean 3 declaration is
+  forall {z : Real} {w : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) w)) (Eq.{1} Real z w)
+but is expected to have type
+  forall {z : Real} {w : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (Complex.ofReal' w)) (Eq.{1} Real z w)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_inj Complex.ofReal_injₓ'. -/
 @[simp, norm_cast]
-theorem of_real_inj {z w : ℝ} : (z : ℂ) = w ↔ z = w :=
+theorem ofReal_inj {z w : ℝ} : (z : ℂ) = w ↔ z = w :=
   ⟨congr_arg re, congr_arg _⟩
-#align complex.of_real_inj Complex.of_real_inj
-
-theorem of_real_injective : Function.Injective (coe : ℝ → ℂ) := fun z w => congr_arg re
-#align complex.of_real_injective Complex.of_real_injective
-
+#align complex.of_real_inj Complex.ofReal_inj
+
+/- warning: complex.of_real_injective -> Complex.ofReal_injective is a dubious translation:
+lean 3 declaration is
+  Function.Injective.{1, 1} Real Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))))
+but is expected to have type
+  Function.Injective.{1, 1} Real Complex Complex.ofReal'
+Case conversion may be inaccurate. Consider using '#align complex.of_real_injective Complex.ofReal_injectiveₓ'. -/
+theorem ofReal_injective : Function.Injective (coe : ℝ → ℂ) := fun z w => congr_arg re
+#align complex.of_real_injective Complex.ofReal_injective
+
+/- warning: complex.can_lift -> Complex.canLift is a dubious translation:
+lean 3 declaration is
+  CanLift.{1, 1} Complex Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe)))) (fun (z : Complex) => Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  CanLift.{1, 1} Complex Real Complex.ofReal' (fun (z : Complex) => Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.can_lift Complex.canLiftₓ'. -/
 instance canLift : CanLift ℂ ℝ coe fun z => z.im = 0 where prf z hz := ⟨z.re, ext rfl hz.symm⟩
 #align complex.can_lift Complex.canLift
 
+#print Complex.Set.reProdIm /-
 /-- The product of a set on the real axis and a set on the imaginary axis of the complex plane,
 denoted by `s ×ℂ t`. -/
-def Set.reProdIm (s t : Set ℝ) : Set ℂ :=
+def Complex.Set.reProdIm (s t : Set ℝ) : Set ℂ :=
   re ⁻¹' s ∩ im ⁻¹' t
-#align set.re_prod_im Set.reProdIm
+#align set.re_prod_im Complex.Set.reProdIm
+-/
 
 -- mathport name: «expr ×ℂ »
-infixl:72 " ×ℂ " => Set.reProdIm
+infixl:72 " ×ℂ " => Complex.Set.reProdIm
 
+#print Complex.mem_reProdIm /-
 theorem mem_reProdIm {z : ℂ} {s t : Set ℝ} : z ∈ s ×ℂ t ↔ z.re ∈ s ∧ z.im ∈ t :=
   Iff.rfl
 #align complex.mem_re_prod_im Complex.mem_reProdIm
+-/
 
 instance : Zero ℂ :=
   ⟨(0 : ℝ)⟩
@@ -128,122 +182,254 @@ instance : Zero ℂ :=
 instance : Inhabited ℂ :=
   ⟨0⟩
 
+/- warning: complex.zero_re -> Complex.zero_re is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.zero_re Complex.zero_reₓ'. -/
 @[simp]
 theorem zero_re : (0 : ℂ).re = 0 :=
   rfl
 #align complex.zero_re Complex.zero_re
 
+/- warning: complex.zero_im -> Complex.zero_im is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.zero_im Complex.zero_imₓ'. -/
 @[simp]
 theorem zero_im : (0 : ℂ).im = 0 :=
   rfl
 #align complex.zero_im Complex.zero_im
 
+/- warning: complex.of_real_zero -> Complex.ofReal_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
+but is expected to have type
+  Eq.{1} Complex (Complex.ofReal' (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_zero Complex.ofReal_zeroₓ'. -/
 @[simp, norm_cast]
-theorem of_real_zero : ((0 : ℝ) : ℂ) = 0 :=
+theorem ofReal_zero : ((0 : ℝ) : ℂ) = 0 :=
   rfl
-#align complex.of_real_zero Complex.of_real_zero
-
-@[simp]
-theorem of_real_eq_zero {z : ℝ} : (z : ℂ) = 0 ↔ z = 0 :=
-  of_real_inj
-#align complex.of_real_eq_zero Complex.of_real_eq_zero
-
-theorem of_real_ne_zero {z : ℝ} : (z : ℂ) ≠ 0 ↔ z ≠ 0 :=
-  not_congr of_real_eq_zero
-#align complex.of_real_ne_zero Complex.of_real_ne_zero
+#align complex.of_real_zero Complex.ofReal_zero
+
+/- warning: complex.of_real_eq_zero -> Complex.ofReal_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {z : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_zero Complex.ofReal_eq_zeroₓ'. -/
+@[simp]
+theorem ofReal_eq_zero {z : ℝ} : (z : ℂ) = 0 ↔ z = 0 :=
+  ofReal_inj
+#align complex.of_real_eq_zero Complex.ofReal_eq_zero
+
+/- warning: complex.of_real_ne_zero -> Complex.ofReal_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {z : Real}, Iff (Ne.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Real}, Iff (Ne.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_ne_zero Complex.ofReal_ne_zeroₓ'. -/
+theorem ofReal_ne_zero {z : ℝ} : (z : ℂ) ≠ 0 ↔ z ≠ 0 :=
+  not_congr ofReal_eq_zero
+#align complex.of_real_ne_zero Complex.ofReal_ne_zero
 
 instance : One ℂ :=
   ⟨(1 : ℝ)⟩
 
+/- warning: complex.one_re -> Complex.one_re is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} Real (Complex.re (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.one_re Complex.one_reₓ'. -/
 @[simp]
 theorem one_re : (1 : ℂ).re = 1 :=
   rfl
 #align complex.one_re Complex.one_re
 
+/- warning: complex.one_im -> Complex.one_im is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Complex.im (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.one_im Complex.one_imₓ'. -/
 @[simp]
 theorem one_im : (1 : ℂ).im = 0 :=
   rfl
 #align complex.one_im Complex.one_im
 
+/- warning: complex.of_real_one -> Complex.ofReal_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
+but is expected to have type
+  Eq.{1} Complex (Complex.ofReal' (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_one Complex.ofReal_oneₓ'. -/
 @[simp, norm_cast]
-theorem of_real_one : ((1 : ℝ) : ℂ) = 1 :=
+theorem ofReal_one : ((1 : ℝ) : ℂ) = 1 :=
   rfl
-#align complex.of_real_one Complex.of_real_one
-
-@[simp]
-theorem of_real_eq_one {z : ℝ} : (z : ℂ) = 1 ↔ z = 1 :=
-  of_real_inj
-#align complex.of_real_eq_one Complex.of_real_eq_one
-
-theorem of_real_ne_one {z : ℝ} : (z : ℂ) ≠ 1 ↔ z ≠ 1 :=
-  not_congr of_real_eq_one
-#align complex.of_real_ne_one Complex.of_real_ne_one
+#align complex.of_real_one Complex.ofReal_one
+
+/- warning: complex.of_real_eq_one -> Complex.ofReal_eq_one is a dubious translation:
+lean 3 declaration is
+  forall {z : Real}, Iff (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {z : Real}, Iff (Eq.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Eq.{1} Real z (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_one Complex.ofReal_eq_oneₓ'. -/
+@[simp]
+theorem ofReal_eq_one {z : ℝ} : (z : ℂ) = 1 ↔ z = 1 :=
+  ofReal_inj
+#align complex.of_real_eq_one Complex.ofReal_eq_one
+
+/- warning: complex.of_real_ne_one -> Complex.ofReal_ne_one is a dubious translation:
+lean 3 declaration is
+  forall {z : Real}, Iff (Ne.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) z) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  forall {z : Real}, Iff (Ne.{1} Complex (Complex.ofReal' z) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (Ne.{1} Real z (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_ne_one Complex.ofReal_ne_oneₓ'. -/
+theorem ofReal_ne_one {z : ℝ} : (z : ℂ) ≠ 1 ↔ z ≠ 1 :=
+  not_congr ofReal_eq_one
+#align complex.of_real_ne_one Complex.ofReal_ne_one
 
 instance : Add ℂ :=
   ⟨fun z w => ⟨z.re + w.re, z.im + w.im⟩⟩
 
+/- warning: complex.add_re -> Complex.add_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Complex.re z) (Complex.re w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Complex.re z) (Complex.re w))
+Case conversion may be inaccurate. Consider using '#align complex.add_re Complex.add_reₓ'. -/
 @[simp]
 theorem add_re (z w : ℂ) : (z + w).re = z.re + w.re :=
   rfl
 #align complex.add_re Complex.add_re
 
+/- warning: complex.add_im -> Complex.add_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Complex.im z) (Complex.im w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Complex.im z) (Complex.im w))
+Case conversion may be inaccurate. Consider using '#align complex.add_im Complex.add_imₓ'. -/
 @[simp]
 theorem add_im (z w : ℂ) : (z + w).im = z.im + w.im :=
   rfl
 #align complex.add_im Complex.add_im
 
+/- warning: complex.bit0_re -> Complex.bit0_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.re z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.bit0_re Complex.bit0_reₓ'. -/
 @[simp]
 theorem bit0_re (z : ℂ) : (bit0 z).re = bit0 z.re :=
   rfl
 #align complex.bit0_re Complex.bit0_re
 
+/- warning: complex.bit1_re -> Complex.bit1_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Real Real.hasOne Real.hasAdd (Complex.re z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} Real Real.instOneReal Real.instAddReal (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.bit1_re Complex.bit1_reₓ'. -/
 @[simp]
 theorem bit1_re (z : ℂ) : (bit1 z).re = bit1 z.re :=
   rfl
 #align complex.bit1_re Complex.bit1_re
 
+/- warning: complex.bit0_im -> Complex.bit0_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (bit0.{0} Complex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.bit0_im Complex.bit0_imₓ'. -/
 @[simp]
 theorem bit0_im (z : ℂ) : (bit0 z).im = bit0 z.im :=
   Eq.refl _
 #align complex.bit0_im Complex.bit0_im
 
+/- warning: complex.bit1_im -> Complex.bit1_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit0.{0} Real Real.hasAdd (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit0.{0} Real Real.instAddReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.bit1_im Complex.bit1_imₓ'. -/
 @[simp]
 theorem bit1_im (z : ℂ) : (bit1 z).im = bit0 z.im :=
   add_zero _
 #align complex.bit1_im Complex.bit1_im
 
+/- warning: complex.of_real_add -> Complex.ofReal_add is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) r s)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
+but is expected to have type
+  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) r s)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' r) (Complex.ofReal' s))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_add Complex.ofReal_addₓ'. -/
 @[simp, norm_cast]
-theorem of_real_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
+theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
   ext_iff.2 <| by simp
-#align complex.of_real_add Complex.of_real_add
-
+#align complex.of_real_add Complex.ofReal_add
+
+/- warning: complex.of_real_bit0 -> Complex.ofReal_bit0 is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (bit0.{0} Real Real.hasAdd r)) (bit0.{0} Complex Complex.hasAdd ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
+but is expected to have type
+  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (bit0.{0} Real Real.instAddReal r)) (bit0.{0} Complex Complex.instAddComplex (Complex.ofReal' r))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_bit0 Complex.ofReal_bit0ₓ'. -/
 @[simp, norm_cast]
-theorem of_real_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
+theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 r :=
   ext_iff.2 <| by simp [bit0]
-#align complex.of_real_bit0 Complex.of_real_bit0
-
+#align complex.of_real_bit0 Complex.ofReal_bit0
+
+/- warning: complex.of_real_bit1 -> Complex.ofReal_bit1 is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (bit1.{0} Real Real.hasOne Real.hasAdd r)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
+but is expected to have type
+  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (bit1.{0} Real Real.instOneReal Real.instAddReal r)) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex (Complex.ofReal' r))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_bit1 Complex.ofReal_bit1ₓ'. -/
 @[simp, norm_cast]
-theorem of_real_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
+theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 r :=
   ext_iff.2 <| by simp [bit1]
-#align complex.of_real_bit1 Complex.of_real_bit1
+#align complex.of_real_bit1 Complex.ofReal_bit1
 
 instance : Neg ℂ :=
   ⟨fun z => ⟨-z.re, -z.im⟩⟩
 
+/- warning: complex.neg_re -> Complex.neg_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (Neg.neg.{0} Complex Complex.hasNeg z)) (Neg.neg.{0} Real Real.hasNeg (Complex.re z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (Neg.neg.{0} Complex Complex.instNegComplex z)) (Neg.neg.{0} Real Real.instNegReal (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.neg_re Complex.neg_reₓ'. -/
 @[simp]
 theorem neg_re (z : ℂ) : (-z).re = -z.re :=
   rfl
 #align complex.neg_re Complex.neg_re
 
+/- warning: complex.neg_im -> Complex.neg_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (Neg.neg.{0} Complex Complex.hasNeg z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (Neg.neg.{0} Complex Complex.instNegComplex z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.neg_im Complex.neg_imₓ'. -/
 @[simp]
 theorem neg_im (z : ℂ) : (-z).im = -z.im :=
   rfl
 #align complex.neg_im Complex.neg_im
 
+/- warning: complex.of_real_neg -> Complex.ofReal_neg is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Neg.neg.{0} Real Real.hasNeg r)) (Neg.neg.{0} Complex Complex.hasNeg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
+but is expected to have type
+  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (Neg.neg.{0} Real Real.instNegReal r)) (Neg.neg.{0} Complex Complex.instNegComplex (Complex.ofReal' r))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_neg Complex.ofReal_negₓ'. -/
 @[simp, norm_cast]
-theorem of_real_neg (r : ℝ) : ((-r : ℝ) : ℂ) = -r :=
+theorem ofReal_neg (r : ℝ) : ((-r : ℝ) : ℂ) = -r :=
   ext_iff.2 <| by simp
-#align complex.of_real_neg Complex.of_real_neg
+#align complex.of_real_neg Complex.ofReal_neg
 
 instance : Sub ℂ :=
   ⟨fun z w => ⟨z.re - w.re, z.im - w.im⟩⟩
@@ -251,87 +437,193 @@ instance : Sub ℂ :=
 instance : Mul ℂ :=
   ⟨fun z w => ⟨z.re * w.re - z.im * w.im, z.re * w.im + z.im * w.re⟩⟩
 
+/- warning: complex.mul_re -> Complex.mul_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.mul_re Complex.mul_reₓ'. -/
 @[simp]
 theorem mul_re (z w : ℂ) : (z * w).re = z.re * w.re - z.im * w.im :=
   rfl
 #align complex.mul_re Complex.mul_re
 
+/- warning: complex.mul_im -> Complex.mul_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)))
+Case conversion may be inaccurate. Consider using '#align complex.mul_im Complex.mul_imₓ'. -/
 @[simp]
 theorem mul_im (z w : ℂ) : (z * w).im = z.re * w.im + z.im * w.re :=
   rfl
 #align complex.mul_im Complex.mul_im
 
+/- warning: complex.of_real_mul -> Complex.ofReal_mul is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r s)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
+but is expected to have type
+  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r s)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) (Complex.ofReal' s))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_mul Complex.ofReal_mulₓ'. -/
 @[simp, norm_cast]
-theorem of_real_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
+theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
   ext_iff.2 <| by simp
-#align complex.of_real_mul Complex.of_real_mul
-
-theorem of_real_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
-#align complex.of_real_mul_re Complex.of_real_mul_re
-
-theorem of_real_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
-#align complex.of_real_mul_im Complex.of_real_mul_im
-
-theorem of_real_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
-  ext (of_real_mul_re _ _) (of_real_mul_im _ _)
-#align complex.of_real_mul' Complex.of_real_mul'
+#align complex.of_real_mul Complex.ofReal_mul
+
+/- warning: complex.of_real_mul_re -> Complex.ofReal_mul_re is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.re z))
+but is expected to have type
+  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_mul_re Complex.ofReal_mul_reₓ'. -/
+theorem ofReal_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp
+#align complex.of_real_mul_re Complex.ofReal_mul_re
+
+/- warning: complex.of_real_mul_im -> Complex.ofReal_mul_im is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.im z))
+but is expected to have type
+  forall (r : Real) (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_mul_im Complex.ofReal_mul_imₓ'. -/
+theorem ofReal_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp
+#align complex.of_real_mul_im Complex.ofReal_mul_im
+
+/- warning: complex.of_real_mul' -> Complex.ofReal_mul' is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) (Complex.mk (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r (Complex.im z)))
+but is expected to have type
+  forall (r : Real) (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' r) z) (Complex.mk (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_mul' Complex.ofReal_mul'ₓ'. -/
+theorem ofReal_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
+  ext (ofReal_mul_re _ _) (ofReal_mul_im _ _)
+#align complex.of_real_mul' Complex.ofReal_mul'
 
 /-! ### The imaginary unit, `I` -/
 
 
+#print Complex.I /-
 /-- The imaginary unit. -/
-def i : ℂ :=
+def I : ℂ :=
   ⟨0, 1⟩
-#align complex.I Complex.i
+#align complex.I Complex.I
+-/
 
+/- warning: complex.I_re -> Complex.i_re is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} Real (Complex.re Complex.I) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.I_re Complex.i_reₓ'. -/
 @[simp]
-theorem i_re : i.re = 0 :=
+theorem i_re : I.re = 0 :=
   rfl
 #align complex.I_re Complex.i_re
 
+/- warning: complex.I_im -> Complex.i_im is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} Real (Complex.im Complex.I) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.I_im Complex.i_imₓ'. -/
 @[simp]
-theorem i_im : i.im = 1 :=
+theorem i_im : I.im = 1 :=
   rfl
 #align complex.I_im Complex.i_im
 
+/- warning: complex.I_mul_I -> Complex.i_mul_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
+but is expected to have type
+  Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_I Complex.i_mul_Iₓ'. -/
 @[simp]
-theorem i_mul_i : i * i = -1 :=
+theorem i_mul_I : I * I = -1 :=
   ext_iff.2 <| by simp
-#align complex.I_mul_I Complex.i_mul_i
-
-theorem i_mul (z : ℂ) : i * z = ⟨-z.im, z.re⟩ :=
+#align complex.I_mul_I Complex.i_mul_I
+
+/- warning: complex.I_mul -> Complex.i_mul is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (Complex.re z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z) (Complex.mk (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.I_mul Complex.i_mulₓ'. -/
+theorem i_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
   ext_iff.2 <| by simp
 #align complex.I_mul Complex.i_mul
 
-theorem i_ne_zero : (i : ℂ) ≠ 0 :=
+/- warning: complex.I_ne_zero -> Complex.i_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
+but is expected to have type
+  Ne.{1} Complex Complex.I (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
+Case conversion may be inaccurate. Consider using '#align complex.I_ne_zero Complex.i_ne_zeroₓ'. -/
+theorem i_ne_zero : (I : ℂ) ≠ 0 :=
   mt (congr_arg im) zero_ne_one.symm
 #align complex.I_ne_zero Complex.i_ne_zero
 
-theorem mk_eq_add_mul_i (a b : ℝ) : Complex.mk a b = a + b * i :=
+/- warning: complex.mk_eq_add_mul_I -> Complex.mk_eq_add_mul_I is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real), Eq.{1} Complex (Complex.mk a b) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) a) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) b) Complex.I))
+but is expected to have type
+  forall (a : Real) (b : Real), Eq.{1} Complex (Complex.mk a b) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' a) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' b) Complex.I))
+Case conversion may be inaccurate. Consider using '#align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_Iₓ'. -/
+theorem mk_eq_add_mul_I (a b : ℝ) : Complex.mk a b = a + b * I :=
   ext_iff.2 <| by simp
-#align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_i
+#align complex.mk_eq_add_mul_I Complex.mk_eq_add_mul_I
 
+/- warning: complex.re_add_im -> Complex.re_add_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re 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) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) Complex.I)) z
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (Complex.re z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (Complex.im z)) Complex.I)) z
+Case conversion may be inaccurate. Consider using '#align complex.re_add_im Complex.re_add_imₓ'. -/
 @[simp]
-theorem re_add_im (z : ℂ) : (z.re : ℂ) + z.im * i = z :=
+theorem re_add_im (z : ℂ) : (z.re : ℂ) + z.im * I = z :=
   ext_iff.2 <| by simp
 #align complex.re_add_im Complex.re_add_im
 
-theorem mul_i_re (z : ℂ) : (z * i).re = -z.im := by simp
-#align complex.mul_I_re Complex.mul_i_re
-
-theorem mul_i_im (z : ℂ) : (z * i).im = z.re := by simp
-#align complex.mul_I_im Complex.mul_i_im
-
-theorem i_mul_re (z : ℂ) : (i * z).re = -z.im := by simp
+/- warning: complex.mul_I_re -> Complex.mul_I_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z Complex.I)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z Complex.I)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.mul_I_re Complex.mul_I_reₓ'. -/
+theorem mul_I_re (z : ℂ) : (z * I).re = -z.im := by simp
+#align complex.mul_I_re Complex.mul_I_re
+
+/- warning: complex.mul_I_im -> Complex.mul_I_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z Complex.I)) (Complex.re z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z Complex.I)) (Complex.re z)
+Case conversion may be inaccurate. Consider using '#align complex.mul_I_im Complex.mul_I_imₓ'. -/
+theorem mul_I_im (z : ℂ) : (z * I).im = z.re := by simp
+#align complex.mul_I_im Complex.mul_I_im
+
+/- warning: complex.I_mul_re -> Complex.i_mul_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_re Complex.i_mul_reₓ'. -/
+theorem i_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
 #align complex.I_mul_re Complex.i_mul_re
 
-theorem i_mul_im (z : ℂ) : (i * z).im = z.re := by simp
+/- warning: complex.I_mul_im -> Complex.i_mul_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) Complex.I z)) (Complex.re z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) Complex.I z)) (Complex.re z)
+Case conversion may be inaccurate. Consider using '#align complex.I_mul_im Complex.i_mul_imₓ'. -/
+theorem i_mul_im (z : ℂ) : (I * z).im = z.re := by simp
 #align complex.I_mul_im Complex.i_mul_im
 
+#print Complex.equivRealProd_symm_apply /-
 @[simp]
-theorem equivRealProd_symm_apply (p : ℝ × ℝ) : equivRealProd.symm p = p.1 + p.2 * i := by
+theorem equivRealProd_symm_apply (p : ℝ × ℝ) : equivRealProd.symm p = p.1 + p.2 * I := by
   ext <;> simp [equiv_real_prod]
 #align complex.equiv_real_prod_symm_apply Complex.equivRealProd_symm_apply
+-/
 
 /-! ### Commutative ring instance and lemmas -/
 
@@ -385,6 +677,12 @@ instance : Ring ℂ := by infer_instance
 instance : CommSemiring ℂ :=
   inferInstance
 
+/- warning: complex.re_add_group_hom -> Complex.reAddGroupHom is a dubious translation:
+lean 3 declaration is
+  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)
+but is expected to have type
+  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)
+Case conversion may be inaccurate. Consider using '#align complex.re_add_group_hom Complex.reAddGroupHomₓ'. -/
 /-- The "real part" map, considered as an additive group homomorphism. -/
 def reAddGroupHom : ℂ →+ ℝ where
   toFun := re
@@ -392,11 +690,23 @@ def reAddGroupHom : ℂ →+ ℝ where
   map_add' := add_re
 #align complex.re_add_group_hom Complex.reAddGroupHom
 
+/- warning: complex.coe_re_add_group_hom -> Complex.coe_reAddGroupHom is a dubious translation:
+lean 3 declaration is
+  Eq.{1} ((fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) Complex.reAddGroupHom) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) Complex.reAddGroupHom) Complex.re
+but is expected to have type
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.reAddGroupHom) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.coe_re_add_group_hom Complex.coe_reAddGroupHomₓ'. -/
 @[simp]
 theorem coe_reAddGroupHom : (reAddGroupHom : ℂ → ℝ) = re :=
   rfl
 #align complex.coe_re_add_group_hom Complex.coe_reAddGroupHom
 
+/- warning: complex.im_add_group_hom -> Complex.imAddGroupHom is a dubious translation:
+lean 3 declaration is
+  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)
+but is expected to have type
+  AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)
+Case conversion may be inaccurate. Consider using '#align complex.im_add_group_hom Complex.imAddGroupHomₓ'. -/
 /-- The "imaginary part" map, considered as an additive group homomorphism. -/
 def imAddGroupHom : ℂ →+ ℝ where
   toFun := im
@@ -404,17 +714,35 @@ def imAddGroupHom : ℂ →+ ℝ where
   map_add' := add_im
 #align complex.im_add_group_hom Complex.imAddGroupHom
 
+/- warning: complex.coe_im_add_group_hom -> Complex.coe_imAddGroupHom is a dubious translation:
+lean 3 declaration is
+  Eq.{1} ((fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) Complex.imAddGroupHom) (coeFn.{1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) (fun (_x : AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) => Complex -> Real) (AddMonoidHom.hasCoeToFun.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.addMonoid)) Complex.imAddGroupHom) Complex.im
+but is expected to have type
+  Eq.{1} (forall (a : Complex), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) a) (FunLike.coe.{1, 1, 1} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Complex) => Real) _x) (AddHomClass.toFunLike.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddZeroClass.toAdd.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)))) (AddZeroClass.toAdd.{0} Real (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) (AddMonoidHomClass.toAddHomClass.{0, 0, 0} (AddMonoidHom.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)) Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal) (AddMonoidHom.addMonoidHomClass.{0, 0} Complex Real (AddMonoid.toAddZeroClass.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne))) (AddMonoid.toAddZeroClass.{0} Real Real.instAddMonoidReal)))) Complex.imAddGroupHom) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.coe_im_add_group_hom Complex.coe_imAddGroupHomₓ'. -/
 @[simp]
 theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
   rfl
 #align complex.coe_im_add_group_hom Complex.coe_imAddGroupHom
 
+/- warning: complex.I_pow_bit0 -> Complex.i_pow_bit0 is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit0.{0} Nat Nat.hasAdd n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit0.{0} Nat instAddNat n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
+Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit0 Complex.i_pow_bit0ₓ'. -/
 @[simp]
-theorem i_pow_bit0 (n : ℕ) : i ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
+theorem i_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', I_mul_I]
 #align complex.I_pow_bit0 Complex.i_pow_bit0
 
+/- warning: complex.I_pow_bit1 -> Complex.i_pow_bit1 is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (bit1.{0} Nat Nat.hasOne Nat.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (bit1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring) instAddNat n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.I_pow_bit1 Complex.i_pow_bit1ₓ'. -/
 @[simp]
-theorem i_pow_bit1 (n : ℕ) : i ^ bit1 n = (-1) ^ n * i := by rw [pow_bit1', I_mul_I]
+theorem i_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', I_mul_I]
 #align complex.I_pow_bit1 Complex.i_pow_bit1
 
 /-! ### Complex conjugation -/
@@ -429,52 +757,118 @@ instance : StarRing ℂ where
   star_mul a b := by ext <;> simp [add_comm] <;> ring
   star_add a b := by ext <;> simp [add_comm]
 
+/- warning: complex.conj_re -> Complex.conj_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Complex.re z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.re z)
+Case conversion may be inaccurate. Consider using '#align complex.conj_re Complex.conj_reₓ'. -/
 @[simp]
 theorem conj_re (z : ℂ) : (conj z).re = z.re :=
   rfl
 #align complex.conj_re Complex.conj_re
 
+/- warning: complex.conj_im -> Complex.conj_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (Neg.neg.{0} Real Real.hasNeg (Complex.im z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.conj_im Complex.conj_imₓ'. -/
 @[simp]
 theorem conj_im (z : ℂ) : (conj z).im = -z.im :=
   rfl
 #align complex.conj_im Complex.conj_im
 
-theorem conj_of_real (r : ℝ) : conj (r : ℂ) = r :=
+/- warning: complex.conj_of_real -> Complex.conj_ofReal is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
+but is expected to have type
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Complex.ofReal' r)) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Complex.ofReal' r)) (Complex.ofReal' r)
+Case conversion may be inaccurate. Consider using '#align complex.conj_of_real Complex.conj_ofRealₓ'. -/
+theorem conj_ofReal (r : ℝ) : conj (r : ℂ) = r :=
   ext_iff.2 <| by simp [conj]
-#align complex.conj_of_real Complex.conj_of_real
+#align complex.conj_of_real Complex.conj_ofReal
 
+/- warning: complex.conj_I -> Complex.conj_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) Complex.I) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align complex.conj_I Complex.conj_Iₓ'. -/
 @[simp]
-theorem conj_i : conj i = -i :=
+theorem conj_I : conj I = -I :=
   ext_iff.2 <| by simp
-#align complex.conj_I Complex.conj_i
-
+#align complex.conj_I Complex.conj_I
+
+/- warning: complex.conj_bit0 -> Complex.conj_bit0 is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit0.{0} Complex Complex.hasAdd z)) (bit0.{0} Complex Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (bit0.{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.2372 : 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 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+Case conversion may be inaccurate. Consider using '#align complex.conj_bit0 Complex.conj_bit0ₓ'. -/
 theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit0 Complex.conj_bit0
 
+/- warning: complex.conj_bit1 -> Complex.conj_bit1 is a dubious translation:
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+  forall (z : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (bit1.{0} Complex Complex.hasOne Complex.hasAdd z)) (bit1.{0} Complex Complex.hasOne Complex.hasAdd (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (bit1.{0} Complex Complex.instOneComplex 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (bit1.{0} Complex Complex.instOneComplex Complex.instAddComplex z)) (bit1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instOneComplex Complex.instAddComplex (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z))
+Case conversion may be inaccurate. Consider using '#align complex.conj_bit1 Complex.conj_bit1ₓ'. -/
 theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.conj_bit1 Complex.conj_bit1
 
+/- warning: complex.conj_neg_I -> Complex.conj_neg_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)) Complex.I
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)) Complex.I
+Case conversion may be inaccurate. Consider using '#align complex.conj_neg_I Complex.conj_neg_Iₓ'. -/
 @[simp]
-theorem conj_neg_i : conj (-i) = i :=
+theorem conj_neg_I : conj (-I) = I :=
   ext_iff.2 <| by simp
-#align complex.conj_neg_I Complex.conj_neg_i
-
+#align complex.conj_neg_I Complex.conj_neg_I
+
+/- warning: complex.eq_conj_iff_real -> Complex.eq_conj_iff_real is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Exists.{1} Real (fun (r : Real) => Eq.{1} Complex z (Complex.ofReal' r)))
+Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_real Complex.eq_conj_iff_realₓ'. -/
 theorem eq_conj_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_of_real]⟩
 #align complex.eq_conj_iff_real Complex.eq_conj_iff_real
 
+/- warning: complex.eq_conj_iff_re -> Complex.eq_conj_iff_re is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) z)
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Complex (Complex.ofReal' (Complex.re z)) z)
+Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_re Complex.eq_conj_iff_reₓ'. -/
 theorem eq_conj_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
   eq_conj_iff_real.trans ⟨by rintro ⟨r, rfl⟩ <;> simp, fun h => ⟨_, h.symm⟩⟩
 #align complex.eq_conj_iff_re Complex.eq_conj_iff_re
 
+/- warning: complex.eq_conj_iff_im -> Complex.eq_conj_iff_im is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) z) (Eq.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.eq_conj_iff_im Complex.eq_conj_iff_imₓ'. -/
 theorem eq_conj_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
 #align complex.eq_conj_iff_im Complex.eq_conj_iff_im
 
+/- warning: complex.star_def -> Complex.star_def is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toHasStar.{0} Complex (StarAddMonoid.toHasInvolutiveStar.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing)))))) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.starRing)))) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing))
+but is expected to have type
+  Eq.{1} (Complex -> Complex) (Star.star.{0} Complex (InvolutiveStar.toStar.{0} Complex (StarAddMonoid.toInvolutiveStar.{0} Complex (AddMonoidWithOne.toAddMonoid.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)) (StarRing.toStarAddMonoid.{0} Complex (NonUnitalRing.toNonUnitalSemiring.{0} Complex (NonUnitalCommRing.toNonUnitalRing.{0} Complex (CommRing.toNonUnitalCommRing.{0} Complex Complex.commRing))) Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing)))) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))
+Case conversion may be inaccurate. Consider using '#align complex.star_def Complex.star_defₓ'. -/
 -- `simp_nf` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.
 @[simp, nolint simp_nf]
@@ -485,6 +879,7 @@ theorem star_def : (Star.star : ℂ → ℂ) = conj :=
 /-! ### Norm squared -/
 
 
+#print Complex.normSq /-
 /-- The norm squared function. -/
 @[pp_nodot]
 def normSq : ℂ →*₀ ℝ where
@@ -495,52 +890,119 @@ def normSq : ℂ →*₀ ℝ where
     dsimp
     ring
 #align complex.norm_sq Complex.normSq
+-/
 
+/- warning: complex.norm_sq_apply -> Complex.normSq_apply is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_apply Complex.normSq_applyₓ'. -/
 theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
   rfl
 #align complex.norm_sq_apply Complex.normSq_apply
 
+/- warning: complex.norm_sq_of_real -> Complex.normSq_ofReal is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) r r)
+but is expected to have type
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Complex.ofReal' r)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) r r)
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_of_real Complex.normSq_ofRealₓ'. -/
 @[simp]
-theorem normSq_of_real (r : ℝ) : normSq r = r * r := by simp [norm_sq]
-#align complex.norm_sq_of_real Complex.normSq_of_real
+theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by simp [norm_sq]
+#align complex.norm_sq_of_real Complex.normSq_ofReal
 
+/- warning: complex.norm_sq_mk -> Complex.normSq_mk is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (y : Real), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Complex.mk x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x x) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) y y))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mk Complex.normSq_mkₓ'. -/
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
   rfl
 #align complex.norm_sq_mk Complex.normSq_mk
 
-theorem normSq_add_mul_i (x y : ℝ) : normSq (x + y * i) = x ^ 2 + y ^ 2 := by
+/- warning: complex.norm_sq_add_mul_I -> Complex.normSq_add_mul_I is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_Iₓ'. -/
+theorem normSq_add_mul_I (x y : ℝ) : normSq (x + y * I) = x ^ 2 + y ^ 2 := by
   rw [← mk_eq_add_mul_I, norm_sq_mk, sq, sq]
-#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_i
-
+#align complex.norm_sq_add_mul_I Complex.normSq_add_mul_I
+
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+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_selfₓ'. -/
 theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
   ext <;> simp [norm_sq, mul_comm]
 #align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_self
 
+/- warning: complex.norm_sq_zero -> Complex.normSq_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_zero Complex.normSq_zeroₓ'. -/
 @[simp]
 theorem normSq_zero : normSq 0 = 0 :=
   normSq.map_zero
 #align complex.norm_sq_zero Complex.normSq_zero
 
+/- warning: complex.norm_sq_one -> Complex.normSq_one is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_one Complex.normSq_oneₓ'. -/
 @[simp]
 theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
 
-@[simp]
-theorem normSq_i : normSq i = 1 := by simp [norm_sq]
-#align complex.norm_sq_I Complex.normSq_i
-
+/- warning: complex.norm_sq_I -> Complex.normSq_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) Complex.I) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_I Complex.normSq_Iₓ'. -/
+@[simp]
+theorem normSq_I : normSq I = 1 := by simp [norm_sq]
+#align complex.norm_sq_I Complex.normSq_I
+
+/- warning: complex.norm_sq_nonneg -> Complex.normSq_nonneg is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLEReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_nonneg Complex.normSq_nonnegₓ'. -/
 theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align complex.norm_sq_nonneg Complex.normSq_nonneg
 
+/- warning: complex.range_norm_sq -> Complex.range_normSq is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.range_norm_sq Complex.range_normSqₓ'. -/
 @[simp]
 theorem range_normSq : range normSq = Ici 0 :=
   Subset.antisymm (range_subset_iff.2 normSq_nonneg) fun x hx =>
     ⟨Real.sqrt x, by rw [norm_sq_of_real, Real.mul_self_sqrt hx]⟩
 #align complex.range_norm_sq Complex.range_normSq
 
+/- warning: complex.norm_sq_eq_zero -> Complex.normSq_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal))) (Eq.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_zero Complex.normSq_eq_zeroₓ'. -/
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
     ext (eq_zero_of_mul_self_add_mul_self_eq_zero h)
@@ -548,81 +1010,185 @@ theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
     fun h => h.symm ▸ normSq_zero⟩
 #align complex.norm_sq_eq_zero Complex.normSq_eq_zero
 
+/- warning: complex.norm_sq_pos -> Complex.normSq_pos is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (LT.lt.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLTReal (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instZeroReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)) (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_pos Complex.normSq_posₓ'. -/
 @[simp]
 theorem normSq_pos {z : ℂ} : 0 < normSq z ↔ z ≠ 0 :=
   (normSq_nonneg z).lt_iff_ne.trans <| not_congr (eq_comm.trans normSq_eq_zero)
 #align complex.norm_sq_pos Complex.normSq_pos
 
+/- warning: complex.norm_sq_neg -> Complex.normSq_neg is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Neg.neg.{0} Complex Complex.hasNeg z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
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(MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Neg.neg.{0} Complex Complex.instNegComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_neg Complex.normSq_negₓ'. -/
 @[simp]
 theorem normSq_neg (z : ℂ) : normSq (-z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_neg Complex.normSq_neg
 
+/- warning: complex.norm_sq_conj -> Complex.normSq_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
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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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_conj Complex.normSq_conjₓ'. -/
 @[simp]
 theorem normSq_conj (z : ℂ) : normSq (conj z) = normSq z := by simp [norm_sq]
 #align complex.norm_sq_conj Complex.normSq_conj
 
+/- warning: complex.norm_sq_mul -> Complex.normSq_mul is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) 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Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_mul Complex.normSq_mulₓ'. -/
 theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
   normSq.map_mul z w
 #align complex.norm_sq_mul Complex.normSq_mul
 
+/- warning: complex.norm_sq_add -> Complex.normSq_add is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
+but is expected to have type
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(Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) 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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real 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(NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_add Complex.normSq_addₓ'. -/
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
   dsimp [norm_sq] <;> ring
 #align complex.norm_sq_add Complex.normSq_add
 
+/- warning: complex.re_sq_le_norm_sq -> Complex.re_sq_le_normSq is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.re_sq_le_norm_sq Complex.re_sq_le_normSqₓ'. -/
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
   le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.re_sq_le_norm_sq Complex.re_sq_le_normSq
 
+/- warning: complex.im_sq_le_norm_sq -> Complex.im_sq_le_normSq is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.im_sq_le_norm_sq Complex.im_sq_le_normSqₓ'. -/
 theorem im_sq_le_normSq (z : ℂ) : z.im * z.im ≤ normSq z :=
   le_add_of_nonneg_left (mul_self_nonneg _)
 #align complex.im_sq_le_norm_sq Complex.im_sq_le_normSq
 
+/- warning: complex.mul_conj -> Complex.mul_conj is a dubious translation:
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+but is expected to have type
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(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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.mul_conj Complex.mul_conjₓ'. -/
 theorem mul_conj (z : ℂ) : z * conj z = normSq z :=
   ext_iff.2 <| by simp [norm_sq, mul_comm, sub_eq_neg_add, add_comm]
 #align complex.mul_conj Complex.mul_conj
 
+/- warning: complex.add_conj -> Complex.add_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re z)))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re z)))
+Case conversion may be inaccurate. Consider using '#align complex.add_conj Complex.add_conjₓ'. -/
 theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul]
 #align complex.add_conj Complex.add_conj
 
+#print Complex.ofReal /-
 /-- The coercion `ℝ → ℂ` as a `ring_hom`. -/
 def ofReal : ℝ →+* ℂ :=
-  ⟨coe, of_real_one, of_real_mul, of_real_zero, of_real_add⟩
+  ⟨coe, ofReal_one, ofReal_mul, ofReal_zero, ofReal_add⟩
 #align complex.of_real Complex.ofReal
+-/
 
+/- warning: complex.of_real_eq_coe -> Complex.ofReal_eq_coe is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) Complex.ofReal r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)
+but is expected to have type
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => Complex) r) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Real) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)) (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))))) Complex.ofReal r) (Complex.ofReal' r)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_eq_coe Complex.ofReal_eq_coeₓ'. -/
 @[simp]
 theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
   rfl
 #align complex.of_real_eq_coe Complex.ofReal_eq_coe
 
+/- warning: complex.I_sq -> Complex.i_sq is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) Complex.I (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
+but is expected to have type
+  Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) Complex.I (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.I_sq Complex.i_sqₓ'. -/
 @[simp]
-theorem i_sq : i ^ 2 = -1 := by rw [sq, I_mul_I]
+theorem i_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
 #align complex.I_sq Complex.i_sq
 
+/- warning: complex.sub_re -> Complex.sub_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Complex.re z) (Complex.re w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.re z) (Complex.re w))
+Case conversion may be inaccurate. Consider using '#align complex.sub_re Complex.sub_reₓ'. -/
 @[simp]
 theorem sub_re (z w : ℂ) : (z - w).re = z.re - w.re :=
   rfl
 #align complex.sub_re Complex.sub_re
 
+/- warning: complex.sub_im -> Complex.sub_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (Complex.im z) (Complex.im w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (Complex.im z) (Complex.im w))
+Case conversion may be inaccurate. Consider using '#align complex.sub_im Complex.sub_imₓ'. -/
 @[simp]
 theorem sub_im (z w : ℂ) : (z - w).im = z.im - w.im :=
   rfl
 #align complex.sub_im Complex.sub_im
 
+/- warning: complex.of_real_sub -> Complex.ofReal_sub is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) r s)) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
+but is expected to have type
+  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) r s)) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.ofReal' r) (Complex.ofReal' s))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_sub Complex.ofReal_subₓ'. -/
 @[simp, norm_cast]
-theorem of_real_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
+theorem ofReal_sub (r s : ℝ) : ((r - s : ℝ) : ℂ) = r - s :=
   ext_iff.2 <| by simp
-#align complex.of_real_sub Complex.of_real_sub
-
+#align complex.of_real_sub Complex.ofReal_sub
+
+/- warning: complex.of_real_pow -> Complex.ofReal_pow is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) r n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) n)
+but is expected to have type
+  forall (r : Real) (n : Nat), Eq.{1} Complex (Complex.ofReal' (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) r n)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex))))) (Complex.ofReal' r) n)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_pow Complex.ofReal_powₓ'. -/
 @[simp, norm_cast]
-theorem of_real_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
+theorem ofReal_pow (r : ℝ) (n : ℕ) : ((r ^ n : ℝ) : ℂ) = r ^ n := by
   induction n <;> simp [*, of_real_mul, pow_succ]
-#align complex.of_real_pow Complex.of_real_pow
-
-theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * i :=
+#align complex.of_real_pow Complex.ofReal_pow
+
+/- warning: complex.sub_conj -> Complex.sub_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.im z))) Complex.I)
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.im z))) Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.sub_conj Complex.sub_conjₓ'. -/
+theorem sub_conj (z : ℂ) : z - conj z = (2 * z.im : ℝ) * I :=
   ext_iff.2 <| by simp [two_mul, sub_eq_add_neg]
 #align complex.sub_conj Complex.sub_conj
 
+/- warning: complex.norm_sq_sub -> Complex.normSq_sub is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (Complex.re (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) w)))))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (HSub.hSub.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHSub.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instSubReal) (HAdd.hAdd.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHAdd.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instAddReal) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) z w)) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Complex.re (HMul.hMul.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) w) Complex (instHMul.{0} Complex Complex.instMulComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) w)))))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_sub Complex.normSq_subₓ'. -/
 theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z * conj w).re :=
   by
   rw [sub_eq_add_neg, norm_sq_add]
@@ -635,26 +1201,62 @@ theorem normSq_sub (z w : ℂ) : normSq (z - w) = normSq z + normSq w - 2 * (z *
 noncomputable instance : Inv ℂ :=
   ⟨fun z => conj z * ((normSq z)⁻¹ : ℝ)⟩
 
+/- warning: complex.inv_def -> Complex.inv_def is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex.instMulComplex) (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z) (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))))
+Case conversion may be inaccurate. Consider using '#align complex.inv_def Complex.inv_defₓ'. -/
 theorem inv_def (z : ℂ) : z⁻¹ = conj z * ((normSq z)⁻¹ : ℝ) :=
   rfl
 #align complex.inv_def Complex.inv_def
 
+/- warning: complex.inv_re -> Complex.inv_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.re (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.inv_re Complex.inv_reₓ'. -/
 @[simp]
 theorem inv_re (z : ℂ) : z⁻¹.re = z.re / normSq z := by simp [inv_def, division_def]
 #align complex.inv_re Complex.inv_re
 
+/- warning: complex.inv_im -> Complex.inv_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.hasInv z)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Neg.neg.{0} Real Real.hasNeg (Complex.im z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Real (Complex.im (Inv.inv.{0} Complex Complex.instInvComplex z)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Neg.neg.{0} Real Real.instNegReal (Complex.im z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.inv_im Complex.inv_imₓ'. -/
 @[simp]
 theorem inv_im (z : ℂ) : z⁻¹.im = -z.im / normSq z := by simp [inv_def, division_def]
 #align complex.inv_im Complex.inv_im
 
+/- warning: complex.of_real_inv -> Complex.ofReal_inv is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Inv.inv.{0} Real Real.hasInv r)) (Inv.inv.{0} Complex Complex.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r))
+but is expected to have type
+  forall (r : Real), Eq.{1} Complex (Complex.ofReal' (Inv.inv.{0} Real Real.instInvReal r)) (Inv.inv.{0} Complex Complex.instInvComplex (Complex.ofReal' r))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_inv Complex.ofReal_invₓ'. -/
 @[simp, norm_cast]
-theorem of_real_inv (r : ℝ) : ((r⁻¹ : ℝ) : ℂ) = r⁻¹ :=
+theorem ofReal_inv (r : ℝ) : ((r⁻¹ : ℝ) : ℂ) = r⁻¹ :=
   ext_iff.2 <| by simp
-#align complex.of_real_inv Complex.of_real_inv
-
+#align complex.of_real_inv Complex.ofReal_inv
+
+/- warning: complex.inv_zero -> Complex.inv_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))
+but is expected to have type
+  Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))
+Case conversion may be inaccurate. Consider using '#align complex.inv_zero Complex.inv_zeroₓ'. -/
 protected theorem inv_zero : (0⁻¹ : ℂ) = 0 := by rw [← of_real_zero, ← of_real_inv, inv_zero]
 #align complex.inv_zero Complex.inv_zero
 
+/- warning: complex.mul_inv_cancel -> Complex.mul_inv_cancel is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z (Inv.inv.{0} Complex Complex.hasInv z)) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
+but is expected to have type
+  forall {z : Complex}, (Ne.{1} Complex z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Eq.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z (Inv.inv.{0} Complex Complex.instInvComplex z)) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+Case conversion may be inaccurate. Consider using '#align complex.mul_inv_cancel Complex.mul_inv_cancelₓ'. -/
 protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
   rw [inv_def, ← mul_assoc, mul_conj, ← of_real_mul, mul_inv_cancel (mt norm_sq_eq_zero.1 h),
     of_real_one]
@@ -669,50 +1271,116 @@ noncomputable instance : Field ℂ :=
     mul_inv_cancel := @Complex.mul_inv_cancel
     inv_zero := Complex.inv_zero }
 
+/- warning: complex.I_zpow_bit0 -> Complex.i_zpow_bit0 is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) Complex.I (bit0.{0} Int Int.hasAdd n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n)
+but is expected to have type
+  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit0.{0} Int Int.instAddInt n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n)
+Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit0 Complex.i_zpow_bit0ₓ'. -/
 @[simp]
-theorem i_zpow_bit0 (n : ℤ) : i ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
+theorem i_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
 #align complex.I_zpow_bit0 Complex.i_zpow_bit0
 
+/- warning: complex.I_zpow_bit1 -> Complex.i_zpow_bit1 is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) Complex.I (bit1.{0} Int Int.hasOne Int.hasAdd n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (Neg.neg.{0} Complex Complex.hasNeg (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) n) Complex.I)
+but is expected to have type
+  forall (n : Int), Eq.{1} Complex (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) Complex.I (bit1.{0} Int (NonAssocRing.toOne.{0} Int (Ring.toNonAssocRing.{0} Int Int.instRingInt)) Int.instAddInt n)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Neg.neg.{0} Complex Complex.instNegComplex (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) n) Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.I_zpow_bit1 Complex.i_zpow_bit1ₓ'. -/
 @[simp]
-theorem i_zpow_bit1 (n : ℤ) : i ^ bit1 n = (-1) ^ n * i := by rw [zpow_bit1', I_mul_I]
+theorem i_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
 #align complex.I_zpow_bit1 Complex.i_zpow_bit1
 
+/- warning: complex.div_re -> Complex.div_re is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.re (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+Case conversion may be inaccurate. Consider using '#align complex.div_re Complex.div_reₓ'. -/
 theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
 #align complex.div_re Complex.div_re
 
+/- warning: complex.div_im -> Complex.div_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.im z) (Complex.re w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Complex.re z) (Complex.im w)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w)))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} Real (Complex.im (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.im z) (Complex.re w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Complex.re z) (Complex.im w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w)))
+Case conversion may be inaccurate. Consider using '#align complex.div_im Complex.div_imₓ'. -/
 theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
   simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
 #align complex.div_im Complex.div_im
 
+/- warning: complex.conj_inv -> Complex.conj_inv is a dubious translation:
+lean 3 declaration is
+  forall (x : Complex), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Inv.inv.{0} Complex Complex.hasInv x)) (Inv.inv.{0} Complex Complex.hasInv (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) x))
+but is expected to have type
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) (Inv.inv.{0} Complex Complex.instInvComplex x)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Inv.inv.{0} Complex Complex.instInvComplex x)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) x) Complex.instInvComplex (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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) x))
+Case conversion may be inaccurate. Consider using '#align complex.conj_inv Complex.conj_invₓ'. -/
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align complex.conj_inv Complex.conj_inv
 
+/- warning: complex.of_real_div -> Complex.ofReal_div is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (s : Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) r s)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) s))
+but is expected to have type
+  forall (r : Real) (s : Real), Eq.{1} Complex (Complex.ofReal' (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) r s)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (Complex.ofReal' r) (Complex.ofReal' s))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_div Complex.ofReal_divₓ'. -/
 @[simp, norm_cast]
-theorem of_real_div (r s : ℝ) : ((r / s : ℝ) : ℂ) = r / s :=
+theorem ofReal_div (r s : ℝ) : ((r / s : ℝ) : ℂ) = r / s :=
   map_div₀ ofReal r s
-#align complex.of_real_div Complex.of_real_div
-
+#align complex.of_real_div Complex.ofReal_div
+
+/- warning: complex.of_real_zpow -> Complex.ofReal_zpow is a dubious translation:
+lean 3 declaration is
+  forall (r : Real) (n : Int), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) r n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) n)
+but is expected to have type
+  forall (r : Real) (n : Int), Eq.{1} Complex (Complex.ofReal' (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.instDivisionRingReal))) r n)) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) (Complex.ofReal' r) n)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_zpow Complex.ofReal_zpowₓ'. -/
 @[simp, norm_cast]
-theorem of_real_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : ℂ) = (r : ℂ) ^ n :=
+theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : ℂ) = (r : ℂ) ^ n :=
   map_zpow₀ ofReal r n
-#align complex.of_real_zpow Complex.of_real_zpow
+#align complex.of_real_zpow Complex.ofReal_zpow
 
+/- warning: complex.div_I -> Complex.div_I is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z Complex.I) (Neg.neg.{0} Complex Complex.hasNeg (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) z Complex.I))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) z Complex.I))
+Case conversion may be inaccurate. Consider using '#align complex.div_I Complex.div_Iₓ'. -/
 @[simp]
-theorem div_i (z : ℂ) : z / i = -(z * i) :=
+theorem div_I (z : ℂ) : z / I = -(z * I) :=
   (div_eq_iff_mul_eq i_ne_zero).2 <| by simp [mul_assoc]
-#align complex.div_I Complex.div_i
+#align complex.div_I Complex.div_I
 
+/- warning: complex.inv_I -> Complex.inv_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv Complex.I) (Neg.neg.{0} Complex Complex.hasNeg Complex.I)
+but is expected to have type
+  Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex Complex.I) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I)
+Case conversion may be inaccurate. Consider using '#align complex.inv_I Complex.inv_Iₓ'. -/
 @[simp]
-theorem inv_i : i⁻¹ = -i := by simp [inv_eq_one_div]
-#align complex.inv_I Complex.inv_i
+theorem inv_I : I⁻¹ = -I := by simp [inv_eq_one_div]
+#align complex.inv_I Complex.inv_I
 
+/- warning: complex.norm_sq_inv -> Complex.normSq_inv is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (Inv.inv.{0} Complex Complex.hasInv z)) (Inv.inv.{0} Real Real.hasInv (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (Inv.inv.{0} Complex Complex.instInvComplex z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (Inv.inv.{0} Complex Complex.instInvComplex z)) (Inv.inv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instInvReal (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_inv Complex.normSq_invₓ'. -/
 @[simp]
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
 #align complex.norm_sq_inv Complex.normSq_inv
 
+/- warning: complex.norm_sq_div -> Complex.normSq_div is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (w : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z w)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq w))
+but is expected to have type
+  forall (z : Complex) (w : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) z w)) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) w) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) z) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq w))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_div Complex.normSq_divₓ'. -/
 @[simp]
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
@@ -721,41 +1389,95 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 /-! ### Cast lemmas -/
 
 
+/- warning: complex.of_real_nat_cast -> Complex.ofReal_nat_cast is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Complex (Complex.ofReal' (Nat.cast.{0} Real Real.natCast n)) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_nat_cast Complex.ofReal_nat_castₓ'. -/
 @[simp, norm_cast]
-theorem of_real_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
   map_natCast ofReal n
-#align complex.of_real_nat_cast Complex.of_real_nat_cast
-
+#align complex.of_real_nat_cast Complex.ofReal_nat_cast
+
+/- warning: complex.nat_cast_re -> Complex.nat_cast_re is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (Complex.re ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} Real (Complex.re (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} Real Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align complex.nat_cast_re Complex.nat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← of_real_nat_cast, of_real_re]
 #align complex.nat_cast_re Complex.nat_cast_re
 
+/- warning: complex.nat_cast_im -> Complex.nat_cast_im is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall (n : Nat), Eq.{1} Real (Complex.im (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.nat_cast_im Complex.nat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← of_real_nat_cast, of_real_im]
 #align complex.nat_cast_im Complex.nat_cast_im
 
+/- warning: complex.of_real_int_cast -> Complex.ofReal_int_cast is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)
+but is expected to have type
+  forall (n : Int), Eq.{1} Complex (Complex.ofReal' (Int.cast.{0} Real Real.intCast n)) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_int_cast Complex.ofReal_int_castₓ'. -/
 @[simp, norm_cast]
-theorem of_real_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
   map_intCast ofReal n
-#align complex.of_real_int_cast Complex.of_real_int_cast
-
+#align complex.of_real_int_cast Complex.ofReal_int_cast
+
+/- warning: complex.int_cast_re -> Complex.int_cast_re is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Real (Complex.re ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) n)
+but is expected to have type
+  forall (n : Int), Eq.{1} Real (Complex.re (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Int.cast.{0} Real Real.intCast n)
+Case conversion may be inaccurate. Consider using '#align complex.int_cast_re Complex.int_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← of_real_int_cast, of_real_re]
 #align complex.int_cast_re Complex.int_cast_re
 
+/- warning: complex.int_cast_im -> Complex.int_cast_im is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall (n : Int), Eq.{1} Real (Complex.im (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))
+Case conversion may be inaccurate. Consider using '#align complex.int_cast_im Complex.int_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← of_real_int_cast, of_real_im]
 #align complex.int_cast_im Complex.int_cast_im
 
+/- warning: complex.of_real_rat_cast -> Complex.ofReal_rat_cast is a dubious translation:
+lean 3 declaration is
+  forall (n : Rat), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) n)
+but is expected to have type
+  forall (n : Rat), Eq.{1} Complex (Complex.ofReal' (RatCast.ratCast.{0} Real Real.ratCast n)) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) n)
+Case conversion may be inaccurate. Consider using '#align complex.of_real_rat_cast Complex.ofReal_rat_castₓ'. -/
 @[simp, norm_cast]
-theorem of_real_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
+theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = n :=
   map_ratCast ofReal n
-#align complex.of_real_rat_cast Complex.of_real_rat_cast
-
+#align complex.of_real_rat_cast Complex.ofReal_rat_cast
+
+/- warning: complex.rat_cast_re -> Complex.rat_cast_re is a dubious translation:
+lean 3 declaration is
+  forall (q : Rat), Eq.{1} Real (Complex.re ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) q)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Real (HasLiftT.mk.{1, 1} Rat Real (CoeTCₓ.coe.{1, 1} Rat Real (Rat.castCoe.{0} Real Real.hasRatCast))) q)
+but is expected to have type
+  forall (q : Rat), Eq.{1} Complex (Complex.ofReal' (Complex.re (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q))) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q)
+Case conversion may be inaccurate. Consider using '#align complex.rat_cast_re Complex.rat_cast_reₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_re (q : ℚ) : (q : ℂ).re = q := by rw [← of_real_rat_cast, of_real_re]
 #align complex.rat_cast_re Complex.rat_cast_re
 
+/- warning: complex.rat_cast_im -> Complex.rat_cast_im is a dubious translation:
+lean 3 declaration is
+  forall (q : Rat), Eq.{1} Real (Complex.im ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Rat Complex (HasLiftT.mk.{1, 1} Rat Complex (CoeTCₓ.coe.{1, 1} Rat Complex (Rat.castCoe.{0} Complex (DivisionRing.toHasRatCast.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field))))) q)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
+  forall (q : Rat), Eq.{1} Complex (Complex.ofReal' (Complex.im (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) q))) (RatCast.ratCast.{0} Complex (Field.toRatCast.{0} Complex Complex.instFieldComplex) (OfNat.ofNat.{0} Rat 0 (Rat.instOfNatRat 0)))
+Case conversion may be inaccurate. Consider using '#align complex.rat_cast_im Complex.rat_cast_imₓ'. -/
 @[simp, norm_cast]
 theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast, of_real_im]
 #align complex.rat_cast_im Complex.rat_cast_im
@@ -763,19 +1485,37 @@ theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by rw [← of_real_rat_cast,
 /-! ### Characteristic zero -/
 
 
+/- warning: complex.char_zero_complex -> Complex.charZero_complex is a dubious translation:
+lean 3 declaration is
+  CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne)
+but is expected to have type
+  CharZero.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.Complex.addGroupWithOne)
+Case conversion may be inaccurate. Consider using '#align complex.char_zero_complex Complex.charZero_complexₓ'. -/
 instance charZero_complex : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← of_real_nat_cast, of_real_eq_zero, Nat.cast_eq_zero] at h
 #align complex.char_zero_complex Complex.charZero_complex
 
+/- warning: complex.re_eq_add_conj -> Complex.re_eq_add_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.re z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HAdd.hAdd.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align complex.re_eq_add_conj Complex.re_eq_add_conjₓ'. -/
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   simp only [add_conj, of_real_mul, of_real_one, of_real_bit0,
     mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 
+/- warning: complex.im_eq_sub_conj -> Complex.im_eq_sub_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (DivInvMonoid.toHasDiv.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) z (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne)))) Complex.I))
+but is expected to have type
+  forall (z : Complex), Eq.{1} Complex (Complex.ofReal' (Complex.im z)) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (HSub.hSub.{0, 0, 0} Complex ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) z) Complex (instHSub.{0} Complex Complex.instSubComplex) 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Complex.I))
+Case conversion may be inaccurate. Consider using '#align complex.im_eq_sub_conj Complex.im_eq_sub_conjₓ'. -/
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
-theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * i) := by
+theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   simp only [sub_conj, of_real_mul, of_real_one, of_real_bit0, mul_right_comm,
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
@@ -798,6 +1538,12 @@ private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
   Real.sqrt_nonneg _
 #align complex.abs_theory.abs_nonneg' complex.abs_theory.abs_nonneg'
 
+/- warning: complex.abs_theory.abs_conj -> Complex.AbsTheory.abs_conj is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) 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(Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conjₓ'. -/
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
 
@@ -824,138 +1570,300 @@ private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
     exact re_le_abs (z * conj w)
 #align complex.abs_theory.abs_add complex.abs_theory.abs_add
 
+#print Complex.AbsTheory.Complex.abs /-
 /-- The complex absolute value function, defined as the square root of the norm squared. -/
-noncomputable def Complex.abs : AbsoluteValue ℂ ℝ
+noncomputable def Complex.AbsTheory.Complex.abs : AbsoluteValue ℂ ℝ
     where
   toFun x := abs x
   map_mul' := abs_mul
   nonneg' := abs_nonneg'
   eq_zero' _ := (Real.sqrt_eq_zero <| normSq_nonneg _).trans normSq_eq_zero
   add_le' := abs_add
-#align complex.abs Complex.abs
+#align complex.abs Complex.AbsTheory.Complex.abs
+-/
 
 end AbsTheory
 
-theorem abs_def : (abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
+/- warning: complex.abs_def -> Complex.abs_def is a dubious translation:
+lean 3 declaration is
+  Eq.{1} ((fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) Complex.AbsTheory.Complex.abs) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (z : Complex) => Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align complex.abs_def Complex.abs_defₓ'. -/
+theorem abs_def : (Complex.AbsTheory.Complex.abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
 #align complex.abs_def Complex.abs_def
 
-theorem abs_apply {z : ℂ} : abs z = (normSq z).sqrt :=
+/- warning: complex.abs_apply -> Complex.abs_apply is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (Real.sqrt (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z))
+but is expected to have type
+  forall {z : Complex}, Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (Real.sqrt (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z))
+Case conversion may be inaccurate. Consider using '#align complex.abs_apply Complex.abs_applyₓ'. -/
+theorem abs_apply {z : ℂ} : Complex.AbsTheory.Complex.abs z = (normSq z).sqrt :=
   rfl
 #align complex.abs_apply Complex.abs_apply
 
+/- warning: complex.abs_of_real -> Complex.abs_ofReal is a dubious translation:
+lean 3 declaration is
+  forall (r : Real), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) r)
+but is expected to have type
+  forall (r : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) r)
+Case conversion may be inaccurate. Consider using '#align complex.abs_of_real Complex.abs_ofRealₓ'. -/
 @[simp, norm_cast]
-theorem abs_of_real (r : ℝ) : abs r = |r| := by
+theorem abs_ofReal (r : ℝ) : Complex.AbsTheory.Complex.abs r = |r| := by
   simp [abs, norm_sq_of_real, Real.sqrt_mul_self_eq_abs]
-#align complex.abs_of_real Complex.abs_of_real
-
-theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : abs r = r :=
-  (abs_of_real _).trans (abs_of_nonneg h)
+#align complex.abs_of_real Complex.abs_ofReal
+
+/- warning: complex.abs_of_nonneg -> Complex.abs_of_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {r : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r)) r)
+but is expected to have type
+  forall {r : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Complex.ofReal' r)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Complex.ofReal' r)) r)
+Case conversion may be inaccurate. Consider using '#align complex.abs_of_nonneg Complex.abs_of_nonnegₓ'. -/
+theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.AbsTheory.Complex.abs r = r :=
+  (abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 
-theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
+/- warning: complex.abs_of_nat -> Complex.abs_of_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align complex.abs_of_nat Complex.abs_of_natₓ'. -/
+theorem abs_of_nat (n : ℕ) : Complex.AbsTheory.Complex.abs n = n :=
   calc
-    Complex.abs n = Complex.abs (n : ℝ) := by rw [of_real_nat_cast]
+    Complex.AbsTheory.Complex.abs n = Complex.AbsTheory.Complex.abs (n : ℝ) := by
+      rw [of_real_nat_cast]
     _ = _ := abs_of_nonneg (Nat.cast_nonneg n)
     
 #align complex.abs_of_nat Complex.abs_of_nat
 
-theorem mul_self_abs (z : ℂ) : abs z * abs z = normSq z :=
+/- warning: complex.mul_self_abs -> Complex.mul_self_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMulReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) 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(NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq z)
+Case conversion may be inaccurate. Consider using '#align complex.mul_self_abs Complex.mul_self_absₓ'. -/
+theorem mul_self_abs (z : ℂ) :
+    Complex.AbsTheory.Complex.abs z * Complex.AbsTheory.Complex.abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
 #align complex.mul_self_abs Complex.mul_self_abs
 
-theorem sq_abs (z : ℂ) : abs z ^ 2 = normSq z :=
+/- warning: complex.sq_abs -> Complex.sq_abs is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align complex.sq_abs Complex.sq_absₓ'. -/
+theorem sq_abs (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 = normSq z :=
   Real.sq_sqrt (normSq_nonneg _)
 #align complex.sq_abs Complex.sq_abs
 
+/- warning: complex.sq_abs_sub_sq_re -> Complex.sq_abs_sub_sq_re is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_reₓ'. -/
 @[simp]
-theorem sq_abs_sub_sq_re (z : ℂ) : abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
+theorem sq_abs_sub_sq_re (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
   rw [sq_abs, norm_sq_apply, ← sq, ← sq, add_sub_cancel']
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
 
+/- warning: complex.sq_abs_sub_sq_im -> Complex.sq_abs_sub_sq_im is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_imₓ'. -/
 @[simp]
-theorem sq_abs_sub_sq_im (z : ℂ) : abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
+theorem sq_abs_sub_sq_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
   rw [← sq_abs_sub_sq_re, sub_sub_cancel]
 #align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
 
+/- warning: complex.abs_I -> Complex.abs_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs Complex.I) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) Complex.I) Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.abs_I Complex.abs_Iₓ'. -/
 @[simp]
-theorem abs_i : abs i = 1 := by simp [abs]
-#align complex.abs_I Complex.abs_i
+theorem abs_I : Complex.AbsTheory.Complex.abs I = 1 := by simp [abs]
+#align complex.abs_I Complex.abs_I
 
+/- warning: complex.abs_two -> Complex.abs_two is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (OfNat.ofNat.{0} Complex 2 (instOfNat.{0} Complex 2 (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align complex.abs_two Complex.abs_twoₓ'. -/
 @[simp]
-theorem abs_two : abs 2 = 2 :=
+theorem abs_two : Complex.AbsTheory.Complex.abs 2 = 2 :=
   calc
-    abs 2 = abs (2 : ℝ) := by rw [of_real_bit0, of_real_one]
+    Complex.AbsTheory.Complex.abs 2 = Complex.AbsTheory.Complex.abs (2 : ℝ) := by
+      rw [of_real_bit0, of_real_one]
     _ = (2 : ℝ) := abs_of_nonneg (by norm_num)
     
 #align complex.abs_two Complex.abs_two
 
+/- warning: complex.range_abs -> Complex.range_abs is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  Eq.{1} (Set.{0} Real) (Set.range.{0, 1} Real Complex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (Set.Ici.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.range_abs Complex.range_absₓ'. -/
 @[simp]
-theorem range_abs : range abs = Ici 0 :=
-  Subset.antisymm (range_subset_iff.2 abs.NonNeg) fun x hx => ⟨x, abs_of_nonneg hx⟩
+theorem range_abs : range Complex.AbsTheory.Complex.abs = Ici 0 :=
+  Subset.antisymm (range_subset_iff.2 Complex.AbsTheory.Complex.abs.NonNeg) fun x hx =>
+    ⟨x, abs_of_nonneg hx⟩
 #align complex.range_abs Complex.range_abs
 
+/- warning: complex.abs_conj -> Complex.abs_conj is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (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 (a : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) a) (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 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(Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.abs_conj Complex.abs_conjₓ'. -/
 @[simp]
-theorem abs_conj (z : ℂ) : abs (conj z) = abs z :=
+theorem abs_conj (z : ℂ) :
+    Complex.AbsTheory.Complex.abs (conj z) = Complex.AbsTheory.Complex.abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
 
+/- warning: complex.abs_prod -> Complex.abs_prod is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.commMonoid s (fun (i : ι) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (f i)))
+but is expected to have type
+  forall {ι : Type.{u1}} (s : Finset.{u1} ι) (f : ι -> Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Finset.prod.{0, u1} Complex ι (CommRing.toCommMonoid.{0} Complex Complex.commRing) s f)) (Finset.prod.{0, u1} Real ι Real.instCommMonoidReal s (fun (i : ι) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (f i)))
+Case conversion may be inaccurate. Consider using '#align complex.abs_prod Complex.abs_prodₓ'. -/
 @[simp]
 theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
-    abs (s.Prod f) = s.Prod fun i => abs (f i) :=
-  map_prod abs _ _
+    Complex.AbsTheory.Complex.abs (s.Prod f) =
+      s.Prod fun i => Complex.AbsTheory.Complex.abs (f i) :=
+  map_prod Complex.AbsTheory.Complex.abs _ _
 #align complex.abs_prod Complex.abs_prod
 
+/- warning: complex.abs_pow -> Complex.abs_pow is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z n)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
+but is expected to have type
+  forall (z : Complex) (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (MonoidWithZero.toMonoid.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+Case conversion may be inaccurate. Consider using '#align complex.abs_pow Complex.abs_powₓ'. -/
 @[simp]
-theorem abs_pow (z : ℂ) (n : ℕ) : abs (z ^ n) = abs z ^ n :=
-  map_pow abs z n
+theorem abs_pow (z : ℂ) (n : ℕ) :
+    Complex.AbsTheory.Complex.abs (z ^ n) = Complex.AbsTheory.Complex.abs z ^ n :=
+  map_pow Complex.AbsTheory.Complex.abs z n
 #align complex.abs_pow Complex.abs_pow
 
+/- warning: complex.abs_zpow -> Complex.abs_zpow is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex) (n : Int), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.field)))) z n)) (HPow.hPow.{0, 0, 0} Real Int Real (instHPow.{0, 0} Real Int (DivInvMonoid.Pow.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) n)
+but is expected to have type
+  forall (z : Complex) (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (HPow.hPow.{0, 0, 0} Complex Int Complex (instHPow.{0, 0} Complex Int (DivInvMonoid.Pow.{0} Complex (DivisionRing.toDivInvMonoid.{0} Complex (Field.toDivisionRing.{0} Complex Complex.instFieldComplex)))) z n)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Int ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Int (DivInvMonoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (DivisionRing.toDivInvMonoid.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instDivisionRingReal))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) n)
+Case conversion may be inaccurate. Consider using '#align complex.abs_zpow Complex.abs_zpowₓ'. -/
 @[simp]
-theorem abs_zpow (z : ℂ) (n : ℤ) : abs (z ^ n) = abs z ^ n :=
-  map_zpow₀ abs z n
+theorem abs_zpow (z : ℂ) (n : ℤ) :
+    Complex.AbsTheory.Complex.abs (z ^ n) = Complex.AbsTheory.Complex.abs z ^ n :=
+  map_zpow₀ Complex.AbsTheory.Complex.abs z n
 #align complex.abs_zpow Complex.abs_zpow
 
-theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z :=
+/- warning: complex.abs_re_le_abs -> Complex.abs_re_le_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.abs_re_le_abs Complex.abs_re_le_absₓ'. -/
+theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.AbsTheory.Complex.abs z :=
   Real.abs_le_sqrt <| by
     rw [norm_sq_apply, ← sq]
     exact le_add_of_nonneg_right (mul_self_nonneg _)
 #align complex.abs_re_le_abs Complex.abs_re_le_abs
 
-theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ abs z :=
+/- warning: complex.abs_im_le_abs -> Complex.abs_im_le_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.abs_im_le_abs Complex.abs_im_le_absₓ'. -/
+theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.AbsTheory.Complex.abs z :=
   Real.abs_le_sqrt <| by
     rw [norm_sq_apply, ← sq, ← sq]
     exact le_add_of_nonneg_left (sq_nonneg _)
 #align complex.abs_im_le_abs Complex.abs_im_le_abs
 
-theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
+/- warning: complex.re_le_abs -> Complex.re_le_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.re_le_abs Complex.re_le_absₓ'. -/
+theorem re_le_abs (z : ℂ) : z.re ≤ Complex.AbsTheory.Complex.abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
 #align complex.re_le_abs Complex.re_le_abs
 
-theorem im_le_abs (z : ℂ) : z.im ≤ abs z :=
+/- warning: complex.im_le_abs -> Complex.im_le_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.im_le_abs Complex.im_le_absₓ'. -/
+theorem im_le_abs (z : ℂ) : z.im ≤ Complex.AbsTheory.Complex.abs z :=
   (abs_le.1 (abs_im_le_abs _)).2
 #align complex.im_le_abs Complex.im_le_abs
 
+/- warning: complex.abs_re_lt_abs -> Complex.abs_re_lt_abs is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.abs_re_lt_abs Complex.abs_re_lt_absₓ'. -/
 @[simp]
-theorem abs_re_lt_abs {z : ℂ} : |z.re| < abs z ↔ z.im ≠ 0 := by
+theorem abs_re_lt_abs {z : ℂ} : |z.re| < Complex.AbsTheory.Complex.abs z ↔ z.im ≠ 0 := by
   rw [abs, AbsoluteValue.coe_mk, MulHom.coe_mk, Real.lt_sqrt (abs_nonneg _), norm_sq_apply,
     _root_.sq_abs, ← sq, lt_add_iff_pos_right, mul_self_pos]
 #align complex.abs_re_lt_abs Complex.abs_re_lt_abs
 
+/- warning: complex.abs_im_lt_abs -> Complex.abs_im_lt_abs is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.hasLt (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {z : Complex}, Iff (LT.lt.{0} Real Real.instLTReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (Ne.{1} Real (Complex.re z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align complex.abs_im_lt_abs Complex.abs_im_lt_absₓ'. -/
 @[simp]
-theorem abs_im_lt_abs {z : ℂ} : |z.im| < abs z ↔ z.re ≠ 0 := by simpa using @abs_re_lt_abs (z * I)
+theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.AbsTheory.Complex.abs z ↔ z.re ≠ 0 := by
+  simpa using @abs_re_lt_abs (z * I)
 #align complex.abs_im_lt_abs Complex.abs_im_lt_abs
 
+/- warning: complex.abs_abs -> Complex.abs_abs is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} Real (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z)
+but is expected to have type
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instNegReal Real.instSupReal) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z)
+Case conversion may be inaccurate. Consider using '#align complex.abs_abs Complex.abs_absₓ'. -/
 @[simp]
-theorem abs_abs (z : ℂ) : |abs z| = abs z :=
-  abs_of_nonneg (abs.NonNeg _)
+theorem abs_abs (z : ℂ) : |Complex.AbsTheory.Complex.abs z| = Complex.AbsTheory.Complex.abs z :=
+  abs_of_nonneg (Complex.AbsTheory.Complex.abs.NonNeg _)
 #align complex.abs_abs Complex.abs_abs
 
-theorem abs_le_abs_re_add_abs_im (z : ℂ) : abs z ≤ |z.re| + |z.im| := by
+/- warning: complex.abs_le_abs_re_add_abs_im -> Complex.abs_le_abs_re_add_abs_im is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z)))
+but is expected to have type
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_imₓ'. -/
+theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.AbsTheory.Complex.abs z ≤ |z.re| + |z.im| := by
   simpa [re_add_im] using abs.add_le z.re (z.im * I)
 #align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
 
-theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
+/- warning: complex.abs_le_sqrt_two_mul_max -> Complex.abs_le_sqrt_two_mul_max is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Real.sqrt (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (LinearOrder.max.{0} Real Real.linearOrder (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (Complex.im z))))
+but is expected to have type
+  forall (z : Complex), LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real.instLEReal (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Real.sqrt (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (Max.max.{0} Real (LinearOrderedRing.toMax.{0} Real Real.instLinearOrderedRingReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.re z)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (Complex.im z))))
+Case conversion may be inaccurate. Consider using '#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_maxₓ'. -/
+theorem abs_le_sqrt_two_mul_max (z : ℂ) :
+    Complex.AbsTheory.Complex.abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) :=
   by
   cases' z with x y
   simp only [abs_apply, norm_sq_mk, ← sq]
@@ -970,30 +1878,61 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : abs z ≤ Real.sqrt 2 * max (|z.re|)
     
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 
+/- warning: complex.abs_re_div_abs_le_one -> Complex.abs_re_div_abs_le_one is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.re z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.re z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_oneₓ'. -/
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_re_le_abs]
 #align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_one
 
+/- warning: complex.abs_im_div_abs_le_one -> Complex.abs_im_div_abs_le_one is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Complex.im z) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+  forall (z : Complex), LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HDiv.hDiv.{0, 0, 0} Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) z) Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Complex.im z) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs z))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_oneₓ'. -/
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / z.abs| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs, div_le_iff (abs.pos hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
+/- warning: complex.abs_cast_nat -> Complex.abs_cast_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{1} Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Complex (HasLiftT.mk.{1, 1} Nat Complex (CoeTCₓ.coe.{1, 1} Nat Complex (Nat.castCoe.{0} Complex (AddMonoidWithOne.toNatCast.{0} Complex (AddGroupWithOne.toAddMonoidWithOne.{0} Complex Complex.addGroupWithOne))))) n)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)
+but is expected to have type
+  forall (n : Nat), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n)) Real.natCast n)
+Case conversion may be inaccurate. Consider using '#align complex.abs_cast_nat Complex.abs_cast_natₓ'. -/
 @[simp, norm_cast]
-theorem abs_cast_nat (n : ℕ) : abs (n : ℂ) = n := by
+theorem abs_cast_nat (n : ℕ) : Complex.AbsTheory.Complex.abs (n : ℂ) = n := by
   rw [← of_real_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
 #align complex.abs_cast_nat Complex.abs_cast_nat
 
+/- warning: complex.int_cast_abs -> Complex.int_cast_abs is a dubious translation:
+lean 3 declaration is
+  forall (n : Int), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (Abs.abs.{0} Int (Neg.toHasAbs.{0} Int Int.hasNeg (SemilatticeSup.toHasSup.{0} Int (Lattice.toSemilatticeSup.{0} Int (LinearOrder.toLattice.{0} Int Int.linearOrder)))) n)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Complex (HasLiftT.mk.{1, 1} Int Complex (CoeTCₓ.coe.{1, 1} Int Complex (Int.castCoe.{0} Complex (AddGroupWithOne.toHasIntCast.{0} Complex Complex.addGroupWithOne)))) n))
+but is expected to have type
+  forall (n : Int), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Abs.abs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) (Neg.toHasAbs.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.instNegReal Real.instSupReal) (Int.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n)) Real.intCast n)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (Int.cast.{0} Complex (Ring.toIntCast.{0} Complex Complex.instRingComplex) n))
+Case conversion may be inaccurate. Consider using '#align complex.int_cast_abs Complex.int_cast_absₓ'. -/
 @[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : ↑(|n|) = abs n := by
+theorem int_cast_abs (n : ℤ) : ↑(|n|) = Complex.AbsTheory.Complex.abs n := by
   rw [← of_real_int_cast, abs_of_real, Int.cast_abs]
 #align complex.int_cast_abs Complex.int_cast_abs
 
-theorem normSq_eq_abs (x : ℂ) : normSq x = abs x ^ 2 := by
+/- warning: complex.norm_sq_eq_abs -> Complex.normSq_eq_abs is a dubious translation:
+lean 3 declaration is
+  forall (x : Complex), Eq.{1} Real (coeFn.{1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) (fun (_x : MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) => Complex -> Real) (MonoidWithZeroHom.hasCoeToFun.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.ring)))) Complex.normSq x) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall (x : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) x) (FunLike.coe.{1, 1, 1} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) _x) (MulHomClass.toFunLike.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulOneClass.toMul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (MulOneClass.toMul.{0} Real (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))) (MonoidHomClass.toMulHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (MulZeroOneClass.toMulOneClass.{0} Real (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (MonoidWithZeroHomClass.toMonoidHomClass.{0, 0, 0} (MonoidWithZeroHom.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (MonoidWithZeroHom.monoidWithZeroHomClass.{0, 0} Complex Real (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonAssocSemiring.toMulZeroOneClass.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))))))) Complex.normSq x) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Real) x) (instHPow.{0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Nat (Monoid.Pow.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) x) Real.instMonoidReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) 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(DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align complex.norm_sq_eq_abs Complex.normSq_eq_absₓ'. -/
+theorem normSq_eq_abs (x : ℂ) : normSq x = Complex.AbsTheory.Complex.abs x ^ 2 := by
   simp [abs, sq, Real.mul_self_sqrt (norm_sq_nonneg _)]
 #align complex.norm_sq_eq_abs Complex.normSq_eq_abs
 
+#print Complex.partialOrder /-
 /-- We put a partial order on ℂ so that `z ≤ w` exactly if `w - z` is real and nonnegative.
 Complex numbers with different imaginary parts are incomparable.
 -/
@@ -1009,78 +1948,148 @@ protected def partialOrder : PartialOrder ℂ
   le_trans x y z h₁ h₂ := ⟨h₁.1.trans h₂.1, h₁.2.trans h₂.2⟩
   le_antisymm z w h₁ h₂ := ext (h₁.1.antisymm h₂.1) h₁.2
 #align complex.partial_order Complex.partialOrder
+-/
 
 section ComplexOrder
 
 scoped[ComplexOrder] attribute [instance] Complex.partialOrder
 
-theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
+/- warning: complex.le_def -> Complex.ComplexOrder.le_def is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.hasLe (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LE.le.{0} Real Real.instLEReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.le_def Complex.ComplexOrder.le_defₓ'. -/
+theorem Complex.ComplexOrder.le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.le_def Complex.le_def
-
-theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
+#align complex.le_def Complex.ComplexOrder.le_def
+
+/- warning: complex.lt_def -> Complex.ComplexOrder.lt_def is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.hasLt (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w) (And (LT.lt.{0} Real Real.instLTReal (Complex.re z) (Complex.re w)) (Eq.{1} Real (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.lt_def Complex.ComplexOrder.lt_defₓ'. -/
+theorem Complex.ComplexOrder.lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.lt_def Complex.lt_def
-
+#align complex.lt_def Complex.ComplexOrder.lt_def
+
+/- warning: complex.real_le_real -> Complex.ComplexOrder.real_le_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LE.le.{0} Real Real.hasLe x y)
+but is expected to have type
+  forall {x : Real} {y : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LE.le.{0} Real Real.instLEReal x y)
+Case conversion may be inaccurate. Consider using '#align complex.real_le_real Complex.ComplexOrder.real_le_realₓ'. -/
 @[simp, norm_cast]
-theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
-#align complex.real_le_real Complex.real_le_real
-
+theorem Complex.ComplexOrder.real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def]
+#align complex.real_le_real Complex.ComplexOrder.real_le_real
+
+/- warning: complex.real_lt_real -> Complex.ComplexOrder.real_lt_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) y)) (LT.lt.{0} Real Real.hasLt x y)
+but is expected to have type
+  forall {x : Real} {y : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' x) (Complex.ofReal' y)) (LT.lt.{0} Real Real.instLTReal x y)
+Case conversion may be inaccurate. Consider using '#align complex.real_lt_real Complex.ComplexOrder.real_lt_realₓ'. -/
 @[simp, norm_cast]
-theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
-#align complex.real_lt_real Complex.real_lt_real
-
+theorem Complex.ComplexOrder.real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def]
+#align complex.real_lt_real Complex.ComplexOrder.real_lt_real
+
+/- warning: complex.zero_le_real -> Complex.ComplexOrder.zero_le_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+but is expected to have type
+  forall {x : Real}, Iff (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
+Case conversion may be inaccurate. Consider using '#align complex.zero_le_real Complex.ComplexOrder.zero_le_realₓ'. -/
 @[simp, norm_cast]
-theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
-  real_le_real
-#align complex.zero_le_real Complex.zero_le_real
-
+theorem Complex.ComplexOrder.zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
+  Complex.ComplexOrder.real_le_real
+#align complex.zero_le_real Complex.ComplexOrder.zero_le_real
+
+/- warning: complex.zero_lt_real -> Complex.ComplexOrder.zero_lt_real is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x)) (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x)
+but is expected to have type
+  forall {x : Real}, Iff (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)) (Complex.ofReal' x)) (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x)
+Case conversion may be inaccurate. Consider using '#align complex.zero_lt_real Complex.ComplexOrder.zero_lt_realₓ'. -/
 @[simp, norm_cast]
-theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
-  real_lt_real
-#align complex.zero_lt_real Complex.zero_lt_real
-
-theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
+theorem Complex.ComplexOrder.zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
+  Complex.ComplexOrder.real_lt_real
+#align complex.zero_lt_real Complex.ComplexOrder.zero_lt_real
+
+/- warning: complex.not_le_iff -> Complex.ComplexOrder.not_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.hasLt (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LT.lt.{0} Real Real.instLTReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.not_le_iff Complex.ComplexOrder.not_le_iffₓ'. -/
+theorem Complex.ComplexOrder.not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
   rw [le_def, not_and_or, not_le]
-#align complex.not_le_iff Complex.not_le_iff
-
-theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
+#align complex.not_le_iff Complex.ComplexOrder.not_le_iff
+
+/- warning: complex.not_lt_iff -> Complex.ComplexOrder.not_lt_iff is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.hasLe (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+but is expected to have type
+  forall {z : Complex} {w : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z w)) (Or (LE.le.{0} Real Real.instLEReal (Complex.re w) (Complex.re z)) (Ne.{1} Real (Complex.im z) (Complex.im w)))
+Case conversion may be inaccurate. Consider using '#align complex.not_lt_iff Complex.ComplexOrder.not_lt_iffₓ'. -/
+theorem Complex.ComplexOrder.not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
   rw [lt_def, not_and_or, not_lt]
-#align complex.not_lt_iff Complex.not_lt_iff
-
-theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
-  not_le_iff
-#align complex.not_le_zero_iff Complex.not_le_zero_iff
-
-theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
-  not_lt_iff
-#align complex.not_lt_zero_iff Complex.not_lt_zero_iff
-
-theorem eq_re_of_real_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
+#align complex.not_lt_iff Complex.ComplexOrder.not_lt_iff
+
+/- warning: complex.not_le_zero_iff -> Complex.ComplexOrder.not_le_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {z : Complex}, Iff (Not (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align complex.not_le_zero_iff Complex.ComplexOrder.not_le_zero_iffₓ'. -/
+theorem Complex.ComplexOrder.not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
+  Complex.ComplexOrder.not_le_iff
+#align complex.not_le_zero_iff Complex.ComplexOrder.not_le_zero_iff
+
+/- warning: complex.not_lt_zero_iff -> Complex.ComplexOrder.not_lt_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero))))) (Or (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))
+but is expected to have type
+  forall {z : Complex}, Iff (Not (LT.lt.{0} Complex (Preorder.toLT.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) z (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex)))) (Or (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Complex.re z)) (Ne.{1} Real (Complex.im z) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))
+Case conversion may be inaccurate. Consider using '#align complex.not_lt_zero_iff Complex.ComplexOrder.not_lt_zero_iffₓ'. -/
+theorem Complex.ComplexOrder.not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
+  Complex.ComplexOrder.not_lt_iff
+#align complex.not_lt_zero_iff Complex.ComplexOrder.not_lt_zero_iff
+
+/- warning: complex.eq_re_of_real_le -> Complex.ComplexOrder.eq_re_ofReal_le is a dubious translation:
+lean 3 declaration is
+  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) r) z) -> (Eq.{1} Complex z ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Complex.re z)))
+but is expected to have type
+  forall {r : Real} {z : Complex}, (LE.le.{0} Complex (Preorder.toLE.{0} Complex (PartialOrder.toPreorder.{0} Complex Complex.partialOrder)) (Complex.ofReal' r) z) -> (Eq.{1} Complex z (Complex.ofReal' (Complex.re z)))
+Case conversion may be inaccurate. Consider using '#align complex.eq_re_of_real_le Complex.ComplexOrder.eq_re_ofReal_leₓ'. -/
+theorem Complex.ComplexOrder.eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
   by
   ext
   rfl
-  simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.of_real_im]
-#align complex.eq_re_of_real_le Complex.eq_re_of_real_le
+  simp only [← (Complex.ComplexOrder.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
+#align complex.eq_re_of_real_le Complex.ComplexOrder.eq_re_ofReal_le
 
+#print Complex.ComplexOrder.strictOrderedCommRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
 -/
-protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
+protected def Complex.ComplexOrder.strictOrderedCommRing : StrictOrderedCommRing ℂ :=
   { Complex.partialOrder, Complex.commRing,
     Complex.nontrivial with
     zero_le_one := ⟨zero_le_one, rfl⟩
     add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
     mul_pos := fun z w hz hw => by
       simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1] }
-#align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
+#align complex.strict_ordered_comm_ring Complex.ComplexOrder.strictOrderedCommRing
+-/
 
-scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
+scoped[ComplexOrder] attribute [instance] Complex.ComplexOrder.strictOrderedCommRing
 
+#print Complex.ComplexOrder.starOrderedRing /-
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a star ordered ring.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
-protected def starOrderedRing : StarOrderedRing ℂ :=
-  { Complex.strictOrderedCommRing with
+protected def Complex.ComplexOrder.starOrderedRing : StarOrderedRing ℂ :=
+  { Complex.ComplexOrder.strictOrderedCommRing with
     nonneg_iff := fun r =>
       by
       refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
@@ -1099,9 +2108,10 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
             neg_zero]
       · obtain ⟨s, rfl⟩ := h
         simp only [← norm_sq_eq_conj_mul_self, norm_sq_nonneg, zero_le_real, star_def] }
-#align complex.star_ordered_ring Complex.starOrderedRing
+#align complex.star_ordered_ring Complex.ComplexOrder.starOrderedRing
+-/
 
-scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing
+scoped[ComplexOrder] attribute [instance] Complex.ComplexOrder.starOrderedRing
 
 end ComplexOrder
 
@@ -1111,37 +2121,84 @@ end ComplexOrder
 -- mathport name: exprabs'
 local notation "abs'" => Abs.abs
 
-theorem isCauSeq_re (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
+/- warning: complex.is_cau_seq_re -> Complex.isCauSeq_re is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.re (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.re (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_re Complex.isCauSeq_reₓ'. -/
+theorem isCauSeq_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_re Complex.isCauSeq_re
 
-theorem isCauSeq_im (f : CauSeq ℂ abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
+/- warning: complex.is_cau_seq_im -> Complex.isCauSeq_im is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Complex.im (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Complex.im (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_im Complex.isCauSeq_imₓ'. -/
+theorem isCauSeq_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
   (f.Cauchy ε0).imp fun i H j ij =>
     lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
 #align complex.is_cau_seq_im Complex.isCauSeq_im
 
+/- warning: complex.cau_seq_re -> Complex.cauSeqRe is a dubious translation:
+lean 3 declaration is
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+but is expected to have type
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+Case conversion may be inaccurate. Consider using '#align complex.cau_seq_re Complex.cauSeqReₓ'. -/
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqRe (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqRe (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_re f⟩
 #align complex.cau_seq_re Complex.cauSeqRe
 
+/- warning: complex.cau_seq_im -> Complex.cauSeqIm is a dubious translation:
+lean 3 declaration is
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+but is expected to have type
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+Case conversion may be inaccurate. Consider using '#align complex.cau_seq_im Complex.cauSeqImₓ'. -/
 /-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqIm (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqIm (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_im f⟩
 #align complex.cau_seq_im Complex.cauSeqIm
 
-theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq abs f) : IsCauSeq abs' (abs ∘ f) := fun ε ε0 =>
+/- warning: complex.is_cau_seq_abs -> Complex.isCauSeq_abs is a dubious translation:
+lean 3 declaration is
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (Function.comp.{1, 1, 1} Nat Complex Real (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) f))
+but is expected to have type
+  forall {f : Nat -> Complex}, (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) -> (IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (Function.comp.{1, 1, 1} Nat Complex Real (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f))
+Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_abs Complex.isCauSeq_absₓ'. -/
+theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.AbsTheory.Complex.abs f) :
+    IsCauSeq abs' (Complex.AbsTheory.Complex.abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
-  ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
+  ⟨i, fun j hj =>
+    lt_of_le_of_lt (Complex.AbsTheory.Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.is_cau_seq_abs Complex.isCauSeq_abs
 
+/- warning: complex.lim_aux -> Complex.limAux is a dubious translation:
+lean 3 declaration is
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> Complex
+but is expected to have type
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> Complex
+Case conversion may be inaccurate. Consider using '#align complex.lim_aux Complex.limAuxₓ'. -/
 /-- The limit of a Cauchy sequence of complex numbers. -/
-noncomputable def limAux (f : CauSeq ℂ abs) : ℂ :=
+noncomputable def limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : ℂ :=
   ⟨CauSeq.lim (cauSeqRe f), CauSeq.lim (cauSeqIm f)⟩
 #align complex.lim_aux Complex.limAux
 
-theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) := fun ε ε0 =>
+/- warning: complex.equiv_lim_aux -> Complex.equiv_limAux is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), HasEquivₓ.Equiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (setoidHasEquiv.{1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), HasEquiv.Equiv.{1, 0} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (instHasEquiv.{1} (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) (CauSeq.equiv.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex 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(Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs))) f (CauSeq.const.{0, 0} Real Complex Real.instLinearOrderedFieldReal Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real 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Complex.instRingComplex) Complex.AbsTheory.Complex.abs) (Complex.limAux f))
+Case conversion may be inaccurate. Consider using '#align complex.equiv_lim_aux Complex.equiv_limAuxₓ'. -/
+theorem equiv_limAux (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    f ≈ CauSeq.const Complex.AbsTheory.Complex.abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
         (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
     fun i H j ij => by
@@ -1152,77 +2209,148 @@ theorem equiv_limAux (f : CauSeq ℂ abs) : f ≈ CauSeq.const abs (limAux f) :=
     rwa [add_halves] at this
 #align complex.equiv_lim_aux Complex.equiv_limAux
 
-instance : CauSeq.IsComplete ℂ abs :=
+instance : CauSeq.IsComplete ℂ Complex.AbsTheory.Complex.abs :=
   ⟨fun f => ⟨limAux f, equiv_limAux f⟩⟩
 
 open CauSeq
 
-theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ abs) :
-    limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * i :=
+/- warning: complex.lim_eq_lim_im_add_lim_re -> Complex.lim_eq_lim_im_add_lim_re is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f))) Complex.I))
+but is expected to have type
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(AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f))) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f))) Complex.I))
+Case conversion may be inaccurate. Consider using '#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_reₓ'. -/
+theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    limUnder f = ↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I :=
   lim_eq_of_equiv_const <|
     calc
       f ≈ _ := equiv_limAux f
-      _ = CauSeq.const abs (↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * i) :=
+      _ =
+          CauSeq.const Complex.AbsTheory.Complex.abs
+            (↑(limUnder (cauSeqRe f)) + ↑(limUnder (cauSeqIm f)) * I) :=
         CauSeq.ext fun _ =>
           Complex.ext (by simp [lim_aux, cau_seq_re]) (by simp [lim_aux, cau_seq_im])
       
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
 
-theorem lim_re (f : CauSeq ℂ abs) : limUnder (cauSeqRe f) = (limUnder f).re := by
-  rw [lim_eq_lim_im_add_lim_re] <;> simp
+/- warning: complex.lim_re -> Complex.lim_re is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqRe f)) (Complex.re (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+Case conversion may be inaccurate. Consider using '#align complex.lim_re Complex.lim_reₓ'. -/
+theorem lim_re (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    limUnder (cauSeqRe f) = (limUnder f).re := by rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_re Complex.lim_re
 
-theorem lim_im (f : CauSeq ℂ abs) : limUnder (cauSeqIm f) = (limUnder f).im := by
-  rw [lim_eq_lim_im_add_lim_re] <;> simp
+/- warning: complex.lim_im -> Complex.lim_im is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqIm f)) (Complex.im (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+Case conversion may be inaccurate. Consider using '#align complex.lim_im Complex.lim_imₓ'. -/
+theorem lim_im (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    limUnder (cauSeqIm f) = (limUnder f).im := by rw [lim_eq_lim_im_add_lim_re] <;> simp
 #align complex.lim_im Complex.lim_im
 
-theorem isCauSeq_conj (f : CauSeq ℂ abs) : IsCauSeq abs fun n => conj (f n) := fun ε ε0 =>
+/- warning: complex.is_cau_seq_conj -> Complex.isCauSeq_conj is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), IsCauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (coeFn.{1, 1} (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) (fun (_x : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) => Nat -> Complex) (CauSeq.hasCoeToFun.{0, 0} Real Complex Real.linearOrderedField Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) f n))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) 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=> Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (fun (n : Nat) => 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.2372 : 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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (Subtype.val.{1} (Nat -> Complex) (fun (f : Nat -> Complex) => IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (a : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) a) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) f) f n))
+Case conversion may be inaccurate. Consider using '#align complex.is_cau_seq_conj Complex.isCauSeq_conjₓ'. -/
+theorem isCauSeq_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    IsCauSeq Complex.AbsTheory.Complex.abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by rw [← RingHom.map_sub, abs_conj] <;> exact hi j hj⟩
 #align complex.is_cau_seq_conj Complex.isCauSeq_conj
 
+/- warning: complex.cau_seq_conj -> Complex.cauSeqConj is a dubious translation:
+lean 3 declaration is
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs))
+but is expected to have type
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs))
+Case conversion may be inaccurate. Consider using '#align complex.cau_seq_conj Complex.cauSeqConjₓ'. -/
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
-noncomputable def cauSeqConj (f : CauSeq ℂ abs) : CauSeq ℂ abs :=
+noncomputable def cauSeqConj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    CauSeq ℂ Complex.AbsTheory.Complex.abs :=
   ⟨_, isCauSeq_conj f⟩
 #align complex.cau_seq_conj Complex.cauSeqConj
 
-theorem lim_conj (f : CauSeq ℂ abs) : limUnder (cauSeqConj f) = conj (limUnder f) :=
+/- warning: complex.lim_conj -> Complex.lim_conj is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete (Complex.cauSeqConj f)) (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Complex (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring (Complex.cauSeqConj f)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex 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(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.instStarRingComplexToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing) (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} 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+Case conversion may be inaccurate. Consider using '#align complex.lim_conj Complex.lim_conjₓ'. -/
+theorem lim_conj (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    limUnder (cauSeqConj f) = conj (limUnder f) :=
   Complex.ext (by simp [cau_seq_conj, (lim_re _).symm, cau_seq_re])
     (by simp [cau_seq_conj, (lim_im _).symm, cau_seq_im, (lim_neg _).symm] <;> rfl)
 #align complex.lim_conj Complex.lim_conj
 
+/- warning: complex.cau_seq_abs -> Complex.cauSeqAbs is a dubious translation:
+lean 3 declaration is
+  (CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)))
+but is expected to have type
+  (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)) -> (CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)))
+Case conversion may be inaccurate. Consider using '#align complex.cau_seq_abs Complex.cauSeqAbsₓ'. -/
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqAbs (f : CauSeq ℂ abs) : CauSeq ℝ abs' :=
+noncomputable def cauSeqAbs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) : CauSeq ℝ abs' :=
   ⟨_, isCauSeq_abs f.2⟩
 #align complex.cau_seq_abs Complex.cauSeqAbs
 
-theorem lim_abs (f : CauSeq ℂ abs) : limUnder (cauSeqAbs f) = abs (limUnder f) :=
+/- warning: complex.lim_abs -> Complex.lim_abs is a dubious translation:
+lean 3 declaration is
+  forall (f : CauSeq.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.linearOrderedRing) Real.HasAbs.Abs.CauSeq.isComplete (Complex.cauSeqAbs f)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.linearOrderedField Complex Complex.ring (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) => Complex -> Real) (AbsoluteValue.hasCoeToFun.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (StrictOrderedSemiring.toOrderedSemiring.{0} Real (StrictOrderedRing.toStrictOrderedSemiring.{0} Real (LinearOrderedRing.toStrictOrderedRing.{0} Real (LinearOrderedCommRing.toLinearOrderedRing.{0} Real (LinearOrderedField.toLinearOrderedCommRing.{0} Real Real.linearOrderedField))))) Complex (Ring.toSemiring.{0} Complex Complex.ring) Complex.AbsTheory.Complex.abs) Complex.AbsTheory.Complex.abs.CauSeq.isComplete f))
+but is expected to have type
+  forall (f : CauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs)), Eq.{1} Real (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (IsAbsoluteValue.abs_isAbsoluteValue.{0} Real Real.instLinearOrderedRingReal) Real.instIsCompleteRealInstLinearOrderedFieldRealInstRingRealAbsToHasAbsInstNegRealInstSupRealAbs_isAbsoluteValueInstLinearOrderedRingReal (Complex.cauSeqAbs f)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs (CauSeq.lim.{0, 0} Real Real.instLinearOrderedFieldReal Complex Complex.instRingComplex (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.98 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.orderedSemiring))) (AbsoluteValue.subadditiveHomClass.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring)) Complex.AbsTheory.Complex.abs) (AbsoluteValue.isAbsoluteValue.{0, 0} Real (OrderedCommSemiring.toOrderedSemiring.{0} Real (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Real (LinearOrderedCommSemiring.toStrictOrderedCommSemiring.{0} Real (LinearOrderedSemifield.toLinearOrderedCommSemiring.{0} Real (LinearOrderedField.toLinearOrderedSemifield.{0} Real Real.instLinearOrderedFieldReal))))) Complex (Ring.toSemiring.{0} Complex Complex.instRingComplex) Complex.AbsTheory.Complex.abs) Complex.instIsCompleteRealInstLinearOrderedFieldRealComplexInstRingComplexCoeAbsoluteValueToSemiringToDivisionSemiringToSemifieldInstFieldComplexOrderedSemiringToFunLikeToAddToDistribToNonUnitalNonAssocSemiringToNonAssocSemiringToSemiringToLEToPreorderToPartialOrderSubadditiveHomClassAbsIsAbsoluteValueToOrderedSemiringToOrderedCommSemiringToStrictOrderedCommSemiringToLinearOrderedCommSemiringToLinearOrderedSemifieldToSemiring f))
+Case conversion may be inaccurate. Consider using '#align complex.lim_abs Complex.lim_absₓ'. -/
+theorem lim_abs (f : CauSeq ℂ Complex.AbsTheory.Complex.abs) :
+    limUnder (cauSeqAbs f) = Complex.AbsTheory.Complex.abs (limUnder f) :=
   lim_eq_of_equiv_const fun ε ε0 =>
     let ⟨i, hi⟩ := equiv_lim f ε ε0
-    ⟨i, fun j hj => lt_of_le_of_lt (abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
+    ⟨i, fun j hj =>
+      lt_of_le_of_lt (Complex.AbsTheory.Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.lim_abs Complex.lim_abs
 
 variable {α : Type _} (s : Finset α)
 
+/- warning: complex.of_real_prod -> Complex.ofReal_prod is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Finset.prod.{0, u1} Real α Real.commMonoid s (fun (i : α) => f i))) (Finset.prod.{0, u1} Complex α (CommRing.toCommMonoid.{0} Complex Complex.commRing) s (fun (i : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f i)))
+but is expected to have type
+  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (Finset.prod.{0, u1} Real α Real.instCommMonoidReal s (fun (i : α) => f i))) (Finset.prod.{0, u1} Complex α (CommRing.toCommMonoid.{0} Complex Complex.commRing) s (fun (i : α) => Complex.ofReal' (f i)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_prod Complex.ofReal_prodₓ'. -/
 @[simp, norm_cast]
-theorem of_real_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
+theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
   RingHom.map_prod ofReal _ _
-#align complex.of_real_prod Complex.of_real_prod
-
+#align complex.of_real_prod Complex.ofReal_prod
+
+/- warning: complex.of_real_sum -> Complex.ofReal_sum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (Finset.sum.{0, u1} Real α Real.addCommMonoid s (fun (i : α) => f i))) (Finset.sum.{0, u1} Complex α (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) s (fun (i : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) (f i)))
+but is expected to have type
+  forall {α : Type.{u1}} (s : Finset.{u1} α) (f : α -> Real), Eq.{1} Complex (Complex.ofReal' (Finset.sum.{0, u1} Real α Real.instAddCommMonoidReal s (fun (i : α) => f i))) (Finset.sum.{0, u1} Complex α (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) s (fun (i : α) => Complex.ofReal' (f i)))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_sum Complex.ofReal_sumₓ'. -/
 @[simp, norm_cast]
-theorem of_real_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
+theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
   RingHom.map_sum ofReal _ _
-#align complex.of_real_sum Complex.of_real_sum
+#align complex.of_real_sum Complex.ofReal_sum
 
+#print Complex.re_sum /-
 @[simp]
 theorem re_sum (f : α → ℂ) : (∑ i in s, f i).re = ∑ i in s, (f i).re :=
   reAddGroupHom.map_sum f s
 #align complex.re_sum Complex.re_sum
+-/
 
+#print Complex.im_sum /-
 @[simp]
 theorem im_sum (f : α → ℂ) : (∑ i in s, f i).im = ∑ i in s, (f i).im :=
   imAddGroupHom.map_sum f s
 #align complex.im_sum Complex.im_sum
+-/
 
 end Complex
 

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

Adds a representation for Complex numbers and DualNumber so they can be used in #eval statements.

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

@@ -941,6 +941,16 @@ theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
     mul_div_cancel_left₀ _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 
+/-- Show the imaginary number ⟨x, y⟩ as an "x + y*I" string
+
+Note that the Real numbers used for x and y will show as cauchy sequences due to the way Real
+numbers are represented.
+-/
+unsafe instance instRepr : Repr ℂ where
+  reprPrec f p :=
+    (if p > 65 then (Std.Format.bracket "(" . ")") else (·)) <|
+      reprPrec f.re 65 ++ " + " ++ reprPrec f.im 70 ++ "*I"
+
 end Complex
 
 assert_not_exists Multiset

• consistently use the YYYY-MM-DD format
• when easily possible, put the date on the same line as the deprecated attribute
• when easily possible, format the entire declaration on the same line

Why these changes?

• consistency makes it easier for tools to parse this information
• compactness: I don't see a good reason for these declarations taking up more space than needed; as I understand it, deprecated lemmas are not supposed to be used in mathlib anyway
• putting the date on the same line as the attribute makes it easier to discover un-dated deprecations; they also ease writing a tool to replace these by a machine-readable version using leanprover/lean4#3968

@@ -243,8 +243,8 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
 @[simp, norm_cast] lemma abs_intCast (n : ℤ) : abs n = |↑n| := by rw [← ofReal_intCast, abs_ofReal]
 #align complex.int_cast_abs Complex.abs_intCast
 
--- 2024-02-14
-@[deprecated] lemma int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := (abs_intCast _).symm
+@[deprecated] -- 2024-02-14
+lemma int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := (abs_intCast _).symm
 
 theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by
   simp [abs, sq, abs_def, Real.mul_self_sqrt (normSq_nonneg _)]

Define the canonical coercion from the nonnegative rationals to any division semiring.

From LeanAPAP

@@ -495,6 +495,7 @@ end
 
 /-! ### Cast lemmas -/
 
+noncomputable instance instNNRatCast : NNRatCast ℂ where nnratCast q := ofReal' q
 noncomputable instance instRatCast : RatCast ℂ where ratCast q := ofReal' q
 
 -- See note [no_index around OfNat.ofNat]
@@ -502,6 +503,7 @@ noncomputable instance instRatCast : RatCast ℂ where ratCast q := ofReal' q
     ofReal' (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
 @[simp, norm_cast] lemma ofReal_natCast (n : ℕ) : ofReal' n = n := rfl
 @[simp, norm_cast] lemma ofReal_intCast (n : ℤ) : ofReal' n = n := rfl
+@[simp, norm_cast] lemma ofReal_nnratCast (q : ℚ≥0) : ofReal' q = q := rfl
 @[simp, norm_cast] lemma ofReal_ratCast (q : ℚ) : ofReal' q = q := rfl
 #align complex.of_real_nat_cast Complex.ofReal_natCast
 #align complex.of_real_int_cast Complex.ofReal_intCast
@@ -515,6 +517,8 @@ lemma re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re =
 @[simp, norm_cast] lemma natCast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
 @[simp, norm_cast] lemma intCast_re (n : ℤ) : (n : ℂ).re = n := rfl
 @[simp, norm_cast] lemma intCast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma re_nnratCast (q : ℚ≥0) : (q : ℂ).re = q := rfl
+@[simp, norm_cast] lemma im_nnratCast (q : ℚ≥0) : (q : ℂ).im = 0 := rfl
 @[simp, norm_cast] lemma ratCast_re (q : ℚ) : (q : ℂ).re = q := rfl
 @[simp, norm_cast] lemma ratCast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
 #align complex.nat_cast_re Complex.natCast_re
@@ -818,11 +822,17 @@ lemma div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / n
 noncomputable instance instField : Field ℂ where
   mul_inv_cancel := @Complex.mul_inv_cancel
   inv_zero := Complex.inv_zero
+  nnqsmul := (· • ·)
   qsmul := (· • ·)
+  nnratCast_def q := by ext <;> simp [NNRat.cast_def, div_re, div_im, mul_div_mul_comm]
   ratCast_def q := by ext <;> simp [Rat.cast_def, div_re, div_im, mul_div_mul_comm]
+  nnqsmul_def n z := ext_iff.2 <| by simp [NNRat.smul_def, smul_re, smul_im]
   qsmul_def n z := ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
 #align complex.field Complex.instField
 
+@[simp, norm_cast]
+lemma ofReal_nnqsmul (q : ℚ≥0) (r : ℝ) : ofReal' (q • r) = q • r := by simp [NNRat.smul_def]
+
 @[simp, norm_cast]
 lemma ofReal_qsmul (q : ℚ) (r : ℝ) : ofReal' (q • r) = q • r := by simp [Rat.smul_def]
 

This is the parts of the diff of #11203 which don't mention NNRat.cast.

• Use more where notation.
• Write qsmul := _ instead of qsmul := qsmulRec _ to make the instances more robust to definition changes.
• Delete qsmulRec.
• Move qsmul before ratCast_def in instance declarations.
• Name more instances.
• Rename rat_smul to qsmul.

@@ -818,8 +818,8 @@ lemma div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / n
 noncomputable instance instField : Field ℂ where
   mul_inv_cancel := @Complex.mul_inv_cancel
   inv_zero := Complex.inv_zero
-  ratCast_def q := by ext <;> simp [Rat.cast_def, div_re, div_im, mul_div_mul_comm]
   qsmul := (· • ·)
+  ratCast_def q := by ext <;> simp [Rat.cast_def, div_re, div_im, mul_div_mul_comm]
   qsmul_def n z := ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
 #align complex.field Complex.instField
 

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

@@ -500,29 +500,29 @@ noncomputable instance instRatCast : RatCast ℂ where ratCast q := ofReal' q
 -- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast] lemma ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
     ofReal' (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
-@[simp, norm_cast] lemma ofReal_nat_cast (n : ℕ) : ofReal' n = n := rfl
-@[simp, norm_cast] lemma ofReal_int_cast (n : ℤ) : ofReal' n = n := rfl
-@[simp, norm_cast] lemma ofReal_rat_cast (q : ℚ) : ofReal' q = q := rfl
-#align complex.of_real_nat_cast Complex.ofReal_nat_cast
-#align complex.of_real_int_cast Complex.ofReal_int_cast
-#align complex.of_real_rat_cast Complex.ofReal_rat_cast
+@[simp, norm_cast] lemma ofReal_natCast (n : ℕ) : ofReal' n = n := rfl
+@[simp, norm_cast] lemma ofReal_intCast (n : ℤ) : ofReal' n = n := rfl
+@[simp, norm_cast] lemma ofReal_ratCast (q : ℚ) : ofReal' q = q := rfl
+#align complex.of_real_nat_cast Complex.ofReal_natCast
+#align complex.of_real_int_cast Complex.ofReal_intCast
+#align complex.of_real_rat_cast Complex.ofReal_ratCast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 lemma re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re = OfNat.ofNat n := rfl
 @[simp] lemma im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 := rfl
-@[simp, norm_cast] lemma nat_cast_re (n : ℕ) : (n : ℂ).re = n := rfl
-@[simp, norm_cast] lemma nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
-@[simp, norm_cast] lemma int_cast_re (n : ℤ) : (n : ℂ).re = n := rfl
-@[simp, norm_cast] lemma int_cast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
-@[simp, norm_cast] lemma rat_cast_re (q : ℚ) : (q : ℂ).re = q := rfl
-@[simp, norm_cast] lemma rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
-#align complex.nat_cast_re Complex.nat_cast_re
-#align complex.nat_cast_im Complex.nat_cast_im
-#align complex.int_cast_re Complex.int_cast_re
-#align complex.int_cast_im Complex.int_cast_im
-#align complex.rat_cast_re Complex.rat_cast_re
-#align complex.rat_cast_im Complex.rat_cast_im
+@[simp, norm_cast] lemma natCast_re (n : ℕ) : (n : ℂ).re = n := rfl
+@[simp, norm_cast] lemma natCast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma intCast_re (n : ℤ) : (n : ℂ).re = n := rfl
+@[simp, norm_cast] lemma intCast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma ratCast_re (q : ℚ) : (q : ℂ).re = q := rfl
+@[simp, norm_cast] lemma ratCast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
+#align complex.nat_cast_re Complex.natCast_re
+#align complex.nat_cast_im Complex.natCast_im
+#align complex.int_cast_re Complex.intCast_re
+#align complex.int_cast_im Complex.intCast_im
+#align complex.rat_cast_re Complex.ratCast_re
+#align complex.rat_cast_im Complex.ratCast_im
 
 @[norm_cast] lemma ofReal_nsmul (n : ℕ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
 @[norm_cast] lemma ofReal_zsmul (n : ℤ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
@@ -562,7 +562,7 @@ theorem conj_I : conj I = -I :=
 #noalign complex.conj_bit0
 #noalign complex.conj_bit1
 
-theorem conj_nat_cast (n : ℕ) : conj (n : ℂ) = n := map_natCast _ _
+theorem conj_natCast (n : ℕ) : conj (n : ℂ) = n := map_natCast _ _
 
 -- See note [no_index around OfNat.ofNat]
 theorem conj_ofNat (n : ℕ) [n.AtLeastTwo] : conj (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n :=
@@ -624,19 +624,19 @@ theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by
 #align complex.norm_sq_of_real Complex.normSq_ofReal
 
 @[simp]
-theorem normSq_nat_cast (n : ℕ) : normSq n = n * n := normSq_ofReal _
+theorem normSq_natCast (n : ℕ) : normSq n = n * n := normSq_ofReal _
 
 @[simp]
-theorem normSq_int_cast (z : ℤ) : normSq z = z * z := normSq_ofReal _
+theorem normSq_intCast (z : ℤ) : normSq z = z * z := normSq_ofReal _
 
 @[simp]
-theorem normSq_rat_cast (q : ℚ) : normSq q = q * q := normSq_ofReal _
+theorem normSq_ratCast (q : ℚ) : normSq q = q * q := normSq_ofReal _
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem normSq_ofNat (n : ℕ) [n.AtLeastTwo] :
     normSq (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n * OfNat.ofNat n :=
-  normSq_nat_cast _
+  normSq_natCast _
 
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
@@ -883,43 +883,42 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 lemma div_ofReal (z : ℂ) (x : ℝ) : z / x = ⟨z.re / x, z.im / x⟩ := by
   simp_rw [div_eq_inv_mul, ← ofReal_inv, ofReal_mul']
 
-lemma div_nat_cast (z : ℂ) (n : ℕ) : z / n = ⟨z.re / n, z.im / n⟩ :=
+lemma div_natCast (z : ℂ) (n : ℕ) : z / n = ⟨z.re / n, z.im / n⟩ :=
   mod_cast div_ofReal z n
 
-lemma div_int_cast (z : ℂ) (n : ℤ) : z / n = ⟨z.re / n, z.im / n⟩ :=
+lemma div_intCast (z : ℂ) (n : ℤ) : z / n = ⟨z.re / n, z.im / n⟩ :=
   mod_cast div_ofReal z n
 
-lemma div_rat_cast (z : ℂ) (x : ℚ) : z / x = ⟨z.re / x, z.im / x⟩ :=
+lemma div_ratCast (z : ℂ) (x : ℚ) : z / x = ⟨z.re / x, z.im / x⟩ :=
   mod_cast div_ofReal z x
 
 lemma div_ofNat (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
     z / OfNat.ofNat n = ⟨z.re / OfNat.ofNat n, z.im / OfNat.ofNat n⟩ :=
-  div_nat_cast z n
+  div_natCast z n
 
 @[simp] lemma div_ofReal_re (z : ℂ) (x : ℝ) : (z / x).re = z.re / x := by rw [div_ofReal]
 @[simp] lemma div_ofReal_im (z : ℂ) (x : ℝ) : (z / x).im = z.im / x := by rw [div_ofReal]
-@[simp] lemma div_nat_cast_re (z : ℂ) (n : ℕ) : (z / n).re = z.re / n := by rw [div_nat_cast]
-@[simp] lemma div_nat_cast_im (z : ℂ) (n : ℕ) : (z / n).im = z.im / n := by rw [div_nat_cast]
-@[simp] lemma div_int_cast_re (z : ℂ) (n : ℤ) : (z / n).re = z.re / n := by rw [div_int_cast]
-@[simp] lemma div_int_cast_im (z : ℂ) (n : ℤ) : (z / n).im = z.im / n := by rw [div_int_cast]
-@[simp] lemma div_rat_cast_re (z : ℂ) (x : ℚ) : (z / x).re = z.re / x := by rw [div_rat_cast]
-@[simp] lemma div_rat_cast_im (z : ℂ) (x : ℚ) : (z / x).im = z.im / x := by rw [div_rat_cast]
+@[simp] lemma div_natCast_re (z : ℂ) (n : ℕ) : (z / n).re = z.re / n := by rw [div_natCast]
+@[simp] lemma div_natCast_im (z : ℂ) (n : ℕ) : (z / n).im = z.im / n := by rw [div_natCast]
+@[simp] lemma div_intCast_re (z : ℂ) (n : ℤ) : (z / n).re = z.re / n := by rw [div_intCast]
+@[simp] lemma div_intCast_im (z : ℂ) (n : ℤ) : (z / n).im = z.im / n := by rw [div_intCast]
+@[simp] lemma div_ratCast_re (z : ℂ) (x : ℚ) : (z / x).re = z.re / x := by rw [div_ratCast]
+@[simp] lemma div_ratCast_im (z : ℂ) (x : ℚ) : (z / x).im = z.im / x := by rw [div_ratCast]
 
 @[simp]
 lemma div_ofNat_re (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
-    (z / no_index (OfNat.ofNat n)).re = z.re / OfNat.ofNat n := div_nat_cast_re z n
+    (z / no_index (OfNat.ofNat n)).re = z.re / OfNat.ofNat n := div_natCast_re z n
 
 @[simp]
 lemma div_ofNat_im (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
-    (z / no_index (OfNat.ofNat n)).im = z.im / OfNat.ofNat n := div_nat_cast_im z n
+    (z / no_index (OfNat.ofNat n)).im = z.im / OfNat.ofNat n := div_natCast_im z n
 
 /-! ### Characteristic zero -/
 
 
-instance charZero : CharZero ℂ :=
-  charZero_of_inj_zero fun n h => by
-    rwa [← ofReal_nat_cast, ofReal_eq_zero, Nat.cast_eq_zero] at h
-#align complex.char_zero_complex Complex.charZero
+instance instCharZero : CharZero ℂ :=
+  charZero_of_inj_zero fun n h => by rwa [← ofReal_natCast, ofReal_eq_zero, Nat.cast_eq_zero] at h
+#align complex.char_zero_complex Complex.instCharZero
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by

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

@@ -240,7 +240,7 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
     div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
-@[simp, norm_cast] lemma abs_intCast (n : ℤ) : abs n = |↑n| := by rw [← ofReal_int_cast, abs_ofReal]
+@[simp, norm_cast] lemma abs_intCast (n : ℤ) : abs n = |↑n| := by rw [← ofReal_intCast, abs_ofReal]
 #align complex.int_cast_abs Complex.abs_intCast
 
 -- 2024-02-14

This scopes and moves to Complex.SMul the instance instSMulRealComplex. Rationale: This instance is used in Data.Complex.{Basic|Module} to bootstrap SMul instances from the reals, but afterwards, instances SMul R ℂ should not need to rely on that (rather be obtained via Algebra R ℂ, for example). This speeds up the two mentioned files a bit (in fact, it reverts a slow-down caused by reducing the instance priority in #12070) and does not seem to have any adverse effects.

I think this is a cleaner solution compared to just reducing the instance priority.

See here on Zulip.

@@ -125,6 +125,7 @@ def Set.reProdIm (s t : Set ℝ) : Set ℂ :=
   re ⁻¹' s ∩ im ⁻¹' t
 #align set.re_prod_im Complex.Set.reProdIm
 
+@[inherit_doc]
 infixl:72 " ×ℂ " => Set.reProdIm
 
 theorem mem_reProdIm {z : ℂ} {s t : Set ℝ} : z ∈ s ×ℂ t ↔ z.re ∈ s ∧ z.im ∈ t :=
@@ -346,18 +347,26 @@ instance : Nontrivial ℂ :=
   pullback_nonzero re rfl rfl
 
 -- Porting note: moved from `Module/Data/Complex/Basic.lean`
-section SMul
-
-variable {R : Type*} [SMul R ℝ]
+namespace SMul
 
-/- The useless `0` multiplication in `smul` is to make sure that
-`RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally. -/
--- priority manually adjusted in #12070, to avoid situations like instance synthesis
+-- The useless `0` multiplication in `smul` is to make sure that
+-- `RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally.
+-- instance made scoped to avoid situations like instance synthesis
 -- of `SMul ℂ ℂ` trying to proceed via `SMul ℂ ℝ`.
--- See issue #11692.
-instance (priority := 90) instSMulRealComplex : SMul R ℂ where
+/-- Scalar multiplication by `R` on `ℝ` extends to `ℂ`. This is used here and in
+`Matlib.Data.Complex.Module` to transfer instances from `ℝ` to `ℂ`, but is not
+needed outside, so we make it scoped. -/
+scoped instance instSMulRealComplex {R : Type*} [SMul R ℝ] : SMul R ℂ where
   smul r x := ⟨r • x.re - 0 * x.im, r • x.im + 0 * x.re⟩
 
+end SMul
+
+open scoped SMul
+
+section SMul
+
+variable {R : Type*} [SMul R ℝ]
+
 theorem smul_re (r : R) (z : ℂ) : (r • z).re = r • z.re := by simp [(· • ·), SMul.smul]
 #align complex.smul_re Complex.smul_re
 

See here on Zulip.

We reduce the instance priority of Complex.instSMulRealComplex to 90. This leads to a very significant speed-up in two Modular Forms files (and still noticeable speed-ups in some other files).

@@ -352,7 +352,10 @@ variable {R : Type*} [SMul R ℝ]
 
 /- The useless `0` multiplication in `smul` is to make sure that
 `RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally. -/
-instance instSMulRealComplex : SMul R ℂ where
+-- priority manually adjusted in #12070, to avoid situations like instance synthesis
+-- of `SMul ℂ ℂ` trying to proceed via `SMul ℂ ℝ`.
+-- See issue #11692.
+instance (priority := 90) instSMulRealComplex : SMul R ℂ where
   smul r x := ⟨r • x.re - 0 * x.im, r • x.im + 0 * x.re⟩
 
 theorem smul_re (r : R) (z : ℂ) : (r • z).re = r • z.re := by simp [(· • ·), SMul.smul]

Soon, there will be NNRat analogs of the Rat fields in the definition of Field. NNRat is less nicely a structure than Rat, hence there is a need to reduce the dependency of Field on the internals of Rat.

This PR achieves this by restating Field.ratCast_mk' in terms of Rat.num, Rat.den. This requires fixing a few downstream instances.

Reduce the diff of #11203.

Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -479,27 +479,41 @@ theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1 : ℂ) ^ n * I := by rw [pow_bit
 set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit1 Complex.I_pow_bit1
 
--- Porting note (#10756): new theorem
--- See note [no_index around OfNat.ofNat]
-@[simp, norm_cast]
-theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
-    ((no_index (OfNat.ofNat n) : ℝ) : ℂ) = OfNat.ofNat n :=
-  rfl
+end
+
+/-! ### Cast lemmas -/
+
+noncomputable instance instRatCast : RatCast ℂ where ratCast q := ofReal' q
 
 -- See note [no_index around OfNat.ofNat]
-@[simp]
-theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re = OfNat.ofNat n :=
-  rfl
+@[simp, norm_cast] lemma ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
+    ofReal' (no_index (OfNat.ofNat n)) = OfNat.ofNat n := rfl
+@[simp, norm_cast] lemma ofReal_nat_cast (n : ℕ) : ofReal' n = n := rfl
+@[simp, norm_cast] lemma ofReal_int_cast (n : ℤ) : ofReal' n = n := rfl
+@[simp, norm_cast] lemma ofReal_rat_cast (q : ℚ) : ofReal' q = q := rfl
+#align complex.of_real_nat_cast Complex.ofReal_nat_cast
+#align complex.of_real_int_cast Complex.ofReal_int_cast
+#align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
 -- See note [no_index around OfNat.ofNat]
 @[simp]
-theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 :=
-  rfl
-
-noncomputable instance : RatCast ℂ where
-  ratCast q := ofReal' q
+lemma re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re = OfNat.ofNat n := rfl
+@[simp] lemma im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma nat_cast_re (n : ℕ) : (n : ℂ).re = n := rfl
+@[simp, norm_cast] lemma nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma int_cast_re (n : ℤ) : (n : ℂ).re = n := rfl
+@[simp, norm_cast] lemma int_cast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
+@[simp, norm_cast] lemma rat_cast_re (q : ℚ) : (q : ℂ).re = q := rfl
+@[simp, norm_cast] lemma rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
+#align complex.nat_cast_re Complex.nat_cast_re
+#align complex.nat_cast_im Complex.nat_cast_im
+#align complex.int_cast_re Complex.int_cast_re
+#align complex.int_cast_im Complex.int_cast_im
+#align complex.rat_cast_re Complex.rat_cast_re
+#align complex.rat_cast_im Complex.rat_cast_im
 
-end
+@[norm_cast] lemma ofReal_nsmul (n : ℕ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
+@[norm_cast] lemma ofReal_zsmul (n : ℤ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
 
 /-! ### Complex conjugation -/
 
@@ -777,58 +791,29 @@ protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
     ofReal_one]
 #align complex.mul_inv_cancel Complex.mul_inv_cancel
 
-/-! ### Cast lemmas -/
-
-@[simp, norm_cast]
-theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n := rfl
-#align complex.of_real_nat_cast Complex.ofReal_nat_cast
-
-@[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := rfl
-#align complex.nat_cast_re Complex.nat_cast_re
-
-@[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
-#align complex.nat_cast_im Complex.nat_cast_im
-
-@[simp, norm_cast]
-theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n := rfl
-#align complex.of_real_int_cast Complex.ofReal_int_cast
-
-@[simp, norm_cast]
-theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := rfl
-#align complex.int_cast_re Complex.int_cast_re
-
-@[simp, norm_cast]
-theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
-#align complex.int_cast_im Complex.int_cast_im
-
-@[simp, norm_cast]
-theorem ofReal_rat_cast (q : ℚ) : ((q : ℝ) : ℂ) = q := rfl
-#align complex.of_real_rat_cast Complex.ofReal_rat_cast
-
-@[simp, norm_cast]
-theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℝ) := rfl
-#align complex.rat_cast_re Complex.rat_cast_re
+noncomputable instance instDivInvMonoid : DivInvMonoid ℂ where
 
-@[simp, norm_cast]
-theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
-#align complex.rat_cast_im Complex.rat_cast_im
+lemma div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
+  simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
+#align complex.div_re Complex.div_re
 
-@[norm_cast] lemma ofReal_nsmul (n : ℕ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
-@[norm_cast] lemma ofReal_zsmul (n : ℤ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
+lemma div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
+  simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
+#align complex.div_im Complex.div_im
 
 /-! ### Field instance and lemmas -/
 
-noncomputable instance instField : Field ℂ :=
-{ qsmul := fun n z => n • z
-  qsmul_eq_mul' := fun n z => ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
-  ratCast_mk := fun n d hd h2 => by ext <;> simp [Field.ratCast_mk]
-  inv := Inv.inv
+noncomputable instance instField : Field ℂ where
   mul_inv_cancel := @Complex.mul_inv_cancel
-  inv_zero := Complex.inv_zero }
+  inv_zero := Complex.inv_zero
+  ratCast_def q := by ext <;> simp [Rat.cast_def, div_re, div_im, mul_div_mul_comm]
+  qsmul := (· • ·)
+  qsmul_def n z := ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
 #align complex.field Complex.instField
 
+@[simp, norm_cast]
+lemma ofReal_qsmul (q : ℚ) (r : ℝ) : ofReal' (q • r) = q • r := by simp [Rat.smul_def]
+
 section
 set_option linter.deprecated false
 @[simp]
@@ -843,14 +828,6 @@ set_option linter.uppercaseLean3 false in
 
 end
 
-theorem div_re (z w : ℂ) : (z / w).re = z.re * w.re / normSq w + z.im * w.im / normSq w := by
-  simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg]
-#align complex.div_re Complex.div_re
-
-theorem div_im (z w : ℂ) : (z / w).im = z.im * w.re / normSq w - z.re * w.im / normSq w := by
-  simp [div_eq_mul_inv, mul_assoc, sub_eq_add_neg, add_comm]
-#align complex.div_im Complex.div_im
-
 theorem conj_inv (x : ℂ) : conj x⁻¹ = (conj x)⁻¹ :=
   star_inv' _
 #align complex.conj_inv Complex.conj_inv

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

@@ -201,44 +201,21 @@ theorem add_im (z w : ℂ) : (z + w).im = z.im + w.im :=
   rfl
 #align complex.add_im Complex.add_im
 
-section
-set_option linter.deprecated false
-@[simp]
-theorem bit0_re (z : ℂ) : (bit0 z).re = bit0 z.re :=
-  rfl
-#align complex.bit0_re Complex.bit0_re
-
-@[simp]
-theorem bit1_re (z : ℂ) : (bit1 z).re = bit1 z.re :=
-  rfl
-#align complex.bit1_re Complex.bit1_re
-
-@[simp]
-theorem bit0_im (z : ℂ) : (bit0 z).im = bit0 z.im :=
-  Eq.refl _
-#align complex.bit0_im Complex.bit0_im
-
-@[simp]
-theorem bit1_im (z : ℂ) : (bit1 z).im = bit0 z.im :=
-  add_zero _
-#align complex.bit1_im Complex.bit1_im
+-- replaced by `re_ofNat`
+#noalign complex.bit0_re
+#noalign complex.bit1_re
+-- replaced by `im_ofNat`
+#noalign complex.bit0_im
+#noalign complex.bit1_im
 
 @[simp, norm_cast]
 theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
   ext_iff.2 <| by simp [ofReal']
 #align complex.of_real_add Complex.ofReal_add
 
-@[simp, norm_cast]
-theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 (r : ℂ) :=
-  ext_iff.2 <| by simp [bit0]
-#align complex.of_real_bit0 Complex.ofReal_bit0
-
-@[simp, norm_cast]
-theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 (r : ℂ) :=
-  ext_iff.2 <| by simp [bit1]
-#align complex.of_real_bit1 Complex.ofReal_bit1
-
-end
+-- replaced by `Complex.ofReal_ofNat`
+#noalign complex.of_real_bit0
+#noalign complex.of_real_bit1
 
 instance : Neg ℂ :=
   ⟨fun z => ⟨-z.re, -z.im⟩⟩
@@ -556,17 +533,15 @@ theorem conj_I : conj I = -I :=
   set_option linter.uppercaseLean3 false in
 #align complex.conj_I Complex.conj_I
 
+#noalign complex.conj_bit0
+#noalign complex.conj_bit1
 
-section
-set_option linter.deprecated false
-theorem conj_bit0 (z : ℂ) : conj (bit0 z) = bit0 (conj z) :=
-  ext_iff.2 <| by simp [bit0]
-#align complex.conj_bit0 Complex.conj_bit0
+theorem conj_nat_cast (n : ℕ) : conj (n : ℂ) = n := map_natCast _ _
+
+-- See note [no_index around OfNat.ofNat]
+theorem conj_ofNat (n : ℕ) [n.AtLeastTwo] : conj (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n :=
+  map_ofNat _ _
 
-theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
-  ext_iff.2 <| by simp [bit0]
-#align complex.conj_bit1 Complex.conj_bit1
-end
 -- @[simp]
 /- Porting note (#11119): `simp` attribute removed as the result could be proved
 by `simp only [@map_neg, Complex.conj_i, @neg_neg]`

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

@@ -590,7 +590,7 @@ theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
 #align complex.conj_eq_iff_im Complex.conj_eq_iff_im
 
--- `simpNF` complains about this being provable by `IsROrC.star_def` even
+-- `simpNF` complains about this being provable by `RCLike.star_def` even
 -- though it's not imported by this file.
 -- Porting note: linter `simpNF` not found
 @[simp]

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

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

| Statement | New name | Old name | |

@@ -959,13 +959,13 @@ instance charZero : CharZero ℂ :=
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
-  simp only [add_conj, ofReal_mul, ofReal_ofNat, mul_div_cancel_left (z.re : ℂ) two_ne_zero]
+  simp only [add_conj, ofReal_mul, ofReal_ofNat, mul_div_cancel_left₀ (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   simp only [sub_conj, ofReal_mul, ofReal_ofNat, mul_right_comm,
-    mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
+    mul_div_cancel_left₀ _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 
 end Complex

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

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

| Statement | New name | Old name | |

@@ -102,7 +102,7 @@ theorem sq_abs (z : ℂ) : Complex.abs z ^ 2 = normSq z :=
 
 @[simp]
 theorem sq_abs_sub_sq_re (z : ℂ) : Complex.abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
-  rw [sq_abs, normSq_apply, ← sq, ← sq, add_sub_cancel']
+  rw [sq_abs, normSq_apply, ← sq, ← sq, add_sub_cancel_left]
 #align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
 
 @[simp]

Classifies by adding issue number #10618 to porting notes claiming

@[simp] can prove

@@ -136,7 +136,7 @@ theorem abs_conj (z : ℂ) : Complex.abs (conj z) = Complex.abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
 
--- Porting note: @[simp] can prove it now
+-- Porting note (#10618): @[simp] can prove it now
 theorem abs_prod {ι : Type*} (s : Finset ι) (f : ι → ℂ) :
     Complex.abs (s.prod f) = s.prod fun I => Complex.abs (f I) :=
   map_prod Complex.abs _ _

Classifies by adding issue number #10756 to porting notes claiming anything equivalent to:

• "added theorem"
• "added theorems"
• "new theorem"
• "new theorems"
• "added lemma"
• "new lemma"
• "new lemmas"

@@ -502,7 +502,7 @@ theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1 : ℂ) ^ n * I := by rw [pow_bit
 set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit1 Complex.I_pow_bit1
 
--- Porting note: new theorem
+-- Porting note (#10756): new theorem
 -- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :

@@ -959,15 +959,12 @@ instance charZero : CharZero ℂ :=
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
-  have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := rfl
-  simp only [add_conj, ofReal_mul, ofReal_one, ofReal_bit0, this,
-    mul_div_cancel_left (z.re : ℂ) two_ne_zero]
+  simp only [add_conj, ofReal_mul, ofReal_ofNat, mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
-  have : (↑2 : ℝ ) * I = 2 * I := rfl
-  simp only [sub_conj, ofReal_mul, ofReal_one, ofReal_bit0, mul_right_comm, this,
+  simp only [sub_conj, ofReal_mul, ofReal_ofNat, mul_right_comm,
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -368,7 +368,7 @@ defined in `Data.Complex.Module`. -/
 instance : Nontrivial ℂ :=
   pullback_nonzero re rfl rfl
 
--- porting note: moved from `Module/Data/Complex/Basic.lean`
+-- Porting note: moved from `Module/Data/Complex/Basic.lean`
 section SMul
 
 variable {R : Type*} [SMul R ℝ]
@@ -460,7 +460,7 @@ instance : Ring ℂ := by infer_instance
 instance : CommSemiring ℂ :=
   inferInstance
 
--- porting note: added due to changes in typeclass search order
+-- Porting note: added due to changes in typeclass search order
 /-- This shortcut instance ensures we do not find `Semiring` via the noncomputable
 `Complex.field` instance. -/
 instance : Semiring ℂ :=
@@ -502,7 +502,7 @@ theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1 : ℂ) ^ n * I := by rw [pow_bit
 set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit1 Complex.I_pow_bit1
 
---Porting note: new theorem
+-- Porting note: new theorem
 -- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :

Classifies by adding issue number #11119 to porting notes claiming anything semantically equivalent to:

• "@[simp] removed [...]"
• "@[simp] removed [...]"
• "removed @[simp]"

@@ -568,7 +568,7 @@ theorem conj_bit1 (z : ℂ) : conj (bit1 z) = bit1 (conj z) :=
 #align complex.conj_bit1 Complex.conj_bit1
 end
 -- @[simp]
-/- Porting note: `simp` attribute removed as the result could be proved
+/- Porting note (#11119): `simp` attribute removed as the result could be proved
 by `simp only [@map_neg, Complex.conj_i, @neg_neg]`
 -/
 theorem conj_neg_I : conj (-I) = I :=
@@ -652,14 +652,14 @@ theorem normSq_eq_conj_mul_self {z : ℂ} : (normSq z : ℂ) = conj z * z := by
 #align complex.norm_sq_eq_conj_mul_self Complex.normSq_eq_conj_mul_self
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_zero]` -/
 theorem normSq_zero : normSq 0 = 0 :=
   normSq.map_zero
 #align complex.norm_sq_zero Complex.normSq_zero
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_one]` -/
 theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
@@ -903,14 +903,14 @@ set_option linter.uppercaseLean3 false in
 #align complex.inv_I Complex.inv_I
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_inv₀]` -/
 theorem normSq_inv (z : ℂ) : normSq z⁻¹ = (normSq z)⁻¹ :=
   map_inv₀ normSq z
 #align complex.norm_sq_inv Complex.normSq_inv
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_div₀]` -/
 theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w

Classifies by adding issue number #11119 to porting notes claiming anything semantically equivalent to:

• "@[simp] removed [...]"
• "@[simp] removed [...]"
• "removed @[simp]"

@@ -143,14 +143,14 @@ theorem abs_prod {ι : Type*} (s : Finset ι) (f : ι → ℂ) :
 #align complex.abs_prod Complex.abs_prod
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_pow]` -/
 theorem abs_pow (z : ℂ) (n : ℕ) : Complex.abs (z ^ n) = Complex.abs z ^ n :=
   map_pow Complex.abs z n
 #align complex.abs_pow Complex.abs_pow
 
 -- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
+/- Porting note (#11119): `simp` attribute removed as linter reports this can be proved
 by `simp only [@map_zpow₀]` -/
 theorem abs_zpow (z : ℂ) (n : ℤ) : Complex.abs (z ^ n) = Complex.abs z ^ n :=
   map_zpow₀ Complex.abs z n

From https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Bounds.20on.20alternating.20convergent.20series/near/418770183

@@ -113,6 +113,9 @@ theorem sq_abs_sub_sq_im (z : ℂ) : Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 :=
 lemma abs_add_mul_I (x y : ℝ) : abs (x + y * I) = (x ^ 2 + y ^ 2).sqrt := by
   rw [← normSq_add_mul_I]; rfl
 
+lemma abs_eq_sqrt_sq_add_sq (z : ℂ) : abs z = (z.re ^ 2 + z.im ^ 2).sqrt := by
+  rw [abs_apply, normSq_apply, sq, sq]
+
 @[simp]
 theorem abs_I : Complex.abs I = 1 := by simp [Complex.abs]
 set_option linter.uppercaseLean3 false in

@@ -416,7 +416,7 @@ instance addCommGroup : AddCommGroup ℂ :=
     add_left_neg := by intros; ext <;> simp }
 
 
-instance Complex.addGroupWithOne : AddGroupWithOne ℂ :=
+instance addGroupWithOne : AddGroupWithOne ℂ :=
   { Complex.addCommGroup with
     natCast := fun n => ⟨n, 0⟩
     natCast_zero := by
@@ -436,7 +436,7 @@ instance Complex.addGroupWithOne : AddGroupWithOne ℂ :=
 
 -- Porting note: proof needed modifications and rewritten fields
 instance commRing : CommRing ℂ :=
-  { Complex.addGroupWithOne with
+  { addGroupWithOne with
     mul := (· * ·)
     npow := @npowRec _ ⟨(1 : ℂ)⟩ ⟨(· * ·)⟩
     add_comm := by intros; ext <;> simp [add_comm]

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

@@ -237,10 +237,11 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
     div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
-@[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := by
-  rw [← ofReal_int_cast, abs_ofReal]
-#align complex.int_cast_abs Complex.int_cast_abs
+@[simp, norm_cast] lemma abs_intCast (n : ℤ) : abs n = |↑n| := by rw [← ofReal_int_cast, abs_ofReal]
+#align complex.int_cast_abs Complex.abs_intCast
+
+-- 2024-02-14
+@[deprecated] lemma int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := (abs_intCast _).symm
 
 theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by
   simp [abs, sq, abs_def, Real.mul_self_sqrt (normSq_nonneg _)]

... to avoid conflict with _root_.map_nonneg, see Zulip.

@@ -124,7 +124,7 @@ theorem abs_two : Complex.abs 2 = 2 := abs_ofNat 2
 @[simp]
 theorem range_abs : range Complex.abs = Ici 0 :=
   Subset.antisymm
-    (by simp only [range_subset_iff, Ici, mem_setOf_eq, map_nonneg, forall_const])
+    (by simp only [range_subset_iff, Ici, mem_setOf_eq, apply_nonneg, forall_const])
     (fun x hx => ⟨x, Complex.abs_of_nonneg hx⟩)
 #align complex.range_abs Complex.range_abs
 

• Add import Mathlib.Tactic.GCongr.Core to Algebra/Order/Ring/Lemmas.
• Move most @[gcongr] tags next to the lemmas.

See Zulip thread

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

@@ -3,6 +3,7 @@ Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 -/
+import Mathlib.Algebra.CharZero.Lemmas
 import Mathlib.Algebra.GroupPower.Ring
 import Mathlib.Algebra.GroupWithZero.Bitwise
 import Mathlib.Data.Real.Basic

• depends on: #9830
• depends on: #9772
• depends on: #9996

This checks files for unused imports. The output here is piped through gh-problem-matcher-wrap so that it will show up as annotations.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -3,8 +3,9 @@ Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 -/
-import Mathlib.Data.Real.Basic
+import Mathlib.Algebra.GroupPower.Ring
 import Mathlib.Algebra.GroupWithZero.Bitwise
+import Mathlib.Data.Real.Basic
 import Mathlib.Data.Set.Image
 
 #align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"

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

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

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

@@ -24,12 +24,13 @@ open Set Function
 
 /-- Complex numbers consist of two `Real`s: a real part `re` and an imaginary part `im`. -/
 structure Complex : Type where
+  /-- The real part of a complex number. -/
   re : ℝ
+  /-- The imaginary part of a complex number. -/
   im : ℝ
 #align complex Complex
 
-
-notation "ℂ" => Complex
+@[inherit_doc] notation "ℂ" => Complex
 
 namespace Complex
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,6 +5,7 @@ Authors: Kevin Buzzard, Mario Carneiro
 -/
 import Mathlib.Data.Real.Basic
 import Mathlib.Algebra.GroupWithZero.Bitwise
+import Mathlib.Data.Set.Image
 
 #align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
 

Add a more general version of the Jacobi theta function with a second variable, and prove the transformation law for this more general function rather than just for the one-variable version. Preparatory to functional equations for Dirichlet L-functions.

@@ -733,6 +733,9 @@ theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
 set_option linter.uppercaseLean3 false in
 #align complex.I_sq Complex.I_sq
 
+@[simp]
+theorem I_pow_four : I ^ 4 = 1 := by rw [(by norm_num : 4 = 2 * 2), pow_mul, I_sq, neg_one_sq]
+
 @[simp]
 theorem sub_re (z w : ℂ) : (z - w).re = z.re - w.re :=
   rfl

The current design for abs is flawed:

• The Abs notation typeclass has exactly two instances: one for [Neg α] [Sup α], one for [Inv α] [Sup α]. This means that:
  • We can't write a meaningful hover for Abs.abs
  • Fields have two Abs instances!
• We have the multiplicative definition but:
  • All the lemmas in Algebra.Order.Group.Abs are about the additive version.
  • The only lemmas about the multiplicative version are in Algebra.Order.Group.PosPart, and they get additivised to duplicates of the lemmas in Algebra.Order.Group.Abs!

This PR changes the notation typeclass with two new definitions (related through to_additive): mabs and abs. abs inherits the |a| notation and mabs gets |a|ₘ instead.

The first half of Algebra.Order.Group.Abs gets multiplicativised. A later PR will multiplicativise the second half, and another one will deduplicate the lemmas in Algebra.Order.Group.PosPart.

Part of #9411.

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

@@ -254,7 +254,7 @@ theorem range_normSq : range normSq = Ici 0 :=
 
 /-! ### Cauchy sequences -/
 
-local notation "abs'" => Abs.abs
+local notation "abs'" => _root_.abs
 
 theorem isCauSeq_re (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
   (f.cauchy ε0).imp fun i H j ij =>
@@ -262,8 +262,8 @@ theorem isCauSeq_re (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).
 #align complex.is_cau_seq_re Complex.isCauSeq_re
 
 theorem isCauSeq_im (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
-  (f.cauchy ε0).imp fun i H j ij =>
-    lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
+  (f.cauchy ε0).imp fun i H j ij ↦ by
+    simpa only [← ofReal_sub, abs_ofReal, sub_re] using (abs_im_le_abs _).trans_lt $ H _ ij
 #align complex.is_cau_seq_im Complex.isCauSeq_im
 
 /-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/

and rename ofReal_mul_re → re_mul_ofReal, ofReal_mul_im → im_mul_ofReal.

From LeanAPAP

@@ -275,14 +275,17 @@ theorem ofReal_mul (r s : ℝ) : ((r * s : ℝ) : ℂ) = r * s :=
   ext_iff.2 <| by simp [ofReal']
 #align complex.of_real_mul Complex.ofReal_mul
 
-theorem ofReal_mul_re (r : ℝ) (z : ℂ) : (↑r * z).re = r * z.re := by simp [ofReal']
-#align complex.of_real_mul_re Complex.ofReal_mul_re
+theorem re_ofReal_mul (r : ℝ) (z : ℂ) : (r * z).re = r * z.re := by simp [ofReal']
+#align complex.of_real_mul_re Complex.re_ofReal_mul
 
-theorem ofReal_mul_im (r : ℝ) (z : ℂ) : (↑r * z).im = r * z.im := by simp [ofReal']
-#align complex.of_real_mul_im Complex.ofReal_mul_im
+theorem im_ofReal_mul (r : ℝ) (z : ℂ) : (r * z).im = r * z.im := by simp [ofReal']
+#align complex.of_real_mul_im Complex.im_ofReal_mul
+
+lemma re_mul_ofReal (z : ℂ) (r : ℝ) : (z * r).re = z.re *  r := by simp [ofReal']
+lemma im_mul_ofReal (z : ℂ) (r : ℝ) : (z * r).im = z.im *  r := by simp [ofReal']
 
 theorem ofReal_mul' (r : ℝ) (z : ℂ) : ↑r * z = ⟨r * z.re, r * z.im⟩ :=
-  ext (ofReal_mul_re _ _) (ofReal_mul_im _ _)
+  ext (re_ofReal_mul _ _) (im_ofReal_mul _ _)
 #align complex.of_real_mul' Complex.ofReal_mul'
 
 /-! ### The imaginary unit, `I` -/
@@ -317,8 +320,7 @@ theorem I_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
 set_option linter.uppercaseLean3 false in
 #align complex.I_mul Complex.I_mul
 
-theorem I_ne_zero : (I : ℂ) ≠ 0 :=
-  mt (congr_arg im) zero_ne_one.symm
+@[simp] lemma I_ne_zero : (I : ℂ) ≠ 0 := mt (congr_arg im) zero_ne_one.symm
 set_option linter.uppercaseLean3 false in
 #align complex.I_ne_zero Complex.I_ne_zero
 
@@ -831,6 +833,9 @@ theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℝ) := rfl
 theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
 #align complex.rat_cast_im Complex.rat_cast_im
 
+@[norm_cast] lemma ofReal_nsmul (n : ℕ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
+@[norm_cast] lemma ofReal_zsmul (n : ℤ) (r : ℝ) : ↑(n • r) = n • (r : ℂ) := by simp
+
 /-! ### Field instance and lemmas -/
 
 noncomputable instance instField : Field ℂ :=

and rename ofReal_mul_re → re_mul_ofReal, ofReal_mul_im → im_mul_ofReal.

From LeanAPAP

@@ -110,6 +110,9 @@ theorem sq_abs_sub_sq_im (z : ℂ) : Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 :=
   rw [← sq_abs_sub_sq_re, sub_sub_cancel]
 #align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
 
+lemma abs_add_mul_I (x y : ℝ) : abs (x + y * I) = (x ^ 2 + y ^ 2).sqrt := by
+  rw [← normSq_add_mul_I]; rfl
+
 @[simp]
 theorem abs_I : Complex.abs I = 1 := by simp [Complex.abs]
 set_option linter.uppercaseLean3 false in

In accordance with this Zulip thread, this remove Complex.ext from the global ext attribute list and only enables it locally in certain files.

@@ -51,11 +51,13 @@ theorem eta : ∀ z : ℂ, Complex.mk z.re z.im = z
   | ⟨_, _⟩ => rfl
 #align complex.eta Complex.eta
 
-@[ext]
+-- We only mark this lemma with `ext` *locally* to avoid it applying whenever terms of `ℂ` appear.
 theorem ext : ∀ {z w : ℂ}, z.re = w.re → z.im = w.im → z = w
   | ⟨_, _⟩, ⟨_, _⟩, rfl, rfl => rfl
 #align complex.ext Complex.ext
 
+attribute [local ext] Complex.ext
+
 theorem ext_iff {z w : ℂ} : z = w ↔ z.re = w.re ∧ z.im = w.im :=
   ⟨fun H => by simp [H], fun h => ext h.1 h.2⟩
 #align complex.ext_iff Complex.ext_iff

This adds proofs of the Euler product formula for the Riemann zeta function and Dirichlet L-series.

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

@@ -348,3 +348,9 @@ theorem lim_abs (f : CauSeq ℂ Complex.abs) : lim (cauSeqAbs f) = Complex.abs (
     let ⟨i, hi⟩ := equiv_lim f ε ε0
     ⟨i, fun j hj => lt_of_le_of_lt (Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.lim_abs Complex.lim_abs
+
+lemma ne_zero_of_one_lt_re {s : ℂ} (hs : 1 < s.re) : s ≠ 0 :=
+  fun h ↦ ((zero_re ▸ h ▸ hs).trans zero_lt_one).false
+
+lemma re_neg_ne_zero_of_one_lt_re {s : ℂ} (hs : 1 < s.re) : (-s).re ≠ 0 :=
+  ne_iff_lt_or_gt.mpr <| Or.inl <| neg_re s ▸ by linarith

@@ -31,12 +31,12 @@ theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in
 
 @[simp]
 theorem re_sum (f : α → ℂ) : (∑ i in s, f i).re = ∑ i in s, (f i).re :=
-  reAddGroupHom.map_sum f s
+  map_sum reAddGroupHom f s
 #align complex.re_sum Complex.re_sum
 
 @[simp]
 theorem im_sum (f : α → ℂ) : (∑ i in s, f i).im = ∑ i in s, (f i).im :=
-  imAddGroupHom.map_sum f s
+  map_sum imAddGroupHom f s
 #align complex.im_sum Complex.im_sum
 
 end Complex

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -905,14 +905,14 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
 lemma div_ofReal (z : ℂ) (x : ℝ) : z / x = ⟨z.re / x, z.im / x⟩ := by
   simp_rw [div_eq_inv_mul, ← ofReal_inv, ofReal_mul']
 
-lemma div_nat_cast (z : ℂ) (n : ℕ) : z / n = ⟨z.re / n, z.im / n⟩ := by
-  exact_mod_cast div_ofReal z n
+lemma div_nat_cast (z : ℂ) (n : ℕ) : z / n = ⟨z.re / n, z.im / n⟩ :=
+  mod_cast div_ofReal z n
 
-lemma div_int_cast (z : ℂ) (n : ℤ) : z / n = ⟨z.re / n, z.im / n⟩ := by
-  exact_mod_cast div_ofReal z n
+lemma div_int_cast (z : ℂ) (n : ℤ) : z / n = ⟨z.re / n, z.im / n⟩ :=
+  mod_cast div_ofReal z n
 
-lemma div_rat_cast (z : ℂ) (x : ℚ) : z / x = ⟨z.re / x, z.im / x⟩ := by
-  exact_mod_cast div_ofReal z x
+lemma div_rat_cast (z : ℂ) (x : ℚ) : z / x = ⟨z.re / x, z.im / x⟩ :=
+  mod_cast div_ofReal z x
 
 lemma div_ofNat (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
     z / OfNat.ofNat n = ⟨z.re / OfNat.ofNat n, z.im / OfNat.ofNat n⟩ :=

@@ -16,8 +16,6 @@ of characteristic zero. The result that the complex numbers are algebraically cl
 `FieldTheory.AlgebraicClosure`.
 -/
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open Set Function
 
 /-! ### Definition and basic arithmetic -/

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -3,7 +3,7 @@ Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 -/
-import Mathlib.Data.Real.Sqrt
+import Mathlib.Data.Real.Basic
 import Mathlib.Algebra.GroupWithZero.Bitwise
 
 #align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
@@ -18,8 +18,6 @@ of characteristic zero. The result that the complex numbers are algebraically cl
 
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
-open BigOperators
-
 open Set Function
 
 /-! ### Definition and basic arithmetic -/
@@ -670,12 +668,6 @@ theorem normSq_nonneg (z : ℂ) : 0 ≤ normSq z :=
   add_nonneg (mul_self_nonneg _) (mul_self_nonneg _)
 #align complex.norm_sq_nonneg Complex.normSq_nonneg
 
-@[simp]
-theorem range_normSq : range normSq = Ici 0 :=
-  Subset.antisymm (range_subset_iff.2 normSq_nonneg) fun x hx =>
-    ⟨Real.sqrt x, by rw [normSq_ofReal, Real.mul_self_sqrt hx]⟩
-#align complex.range_norm_sq Complex.range_normSq
-
 theorem normSq_eq_zero {z : ℂ} : normSq z = 0 ↔ z = 0 :=
   ⟨fun h =>
     ext (eq_zero_of_mul_self_add_mul_self_eq_zero h)
@@ -953,9 +945,6 @@ instance charZero : CharZero ℂ :=
     rwa [← ofReal_nat_cast, ofReal_eq_zero, Nat.cast_eq_zero] at h
 #align complex.char_zero_complex Complex.charZero
 
--- Test if the `ℚ` smul instance is correct.
-example : (Complex.instSMulRealComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := rfl
-
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := rfl
@@ -970,353 +959,7 @@ theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 
-/-! ### Absolute value -/
-
-
-namespace AbsTheory
-
--- We develop enough theory to bundle `abs` into an `AbsoluteValue` before making things public;
--- this is so there's not two versions of it hanging around.
-local notation "abs" z => Real.sqrt (normSq z)
-
-private theorem mul_self_abs (z : ℂ) : ((abs z) * abs z) = normSq z :=
-  Real.mul_self_sqrt (normSq_nonneg _)
-
-private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
-  Real.sqrt_nonneg _
-
-theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
-#align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
-
-private theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z := by
-  rw [mul_self_le_mul_self_iff (abs_nonneg z.re) (abs_nonneg' _), abs_mul_abs_self, mul_self_abs]
-  apply re_sq_le_normSq
-
-private theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
-  (abs_le.1 (abs_re_le_abs _)).2
-
-private theorem abs_mul (z w : ℂ) : (abs z * w) = (abs z) * abs w := by
-  rw [normSq_mul, Real.sqrt_mul (normSq_nonneg _)]
-
-private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
-  (mul_self_le_mul_self_iff (abs_nonneg' (z + w))
-      (add_nonneg (abs_nonneg' z) (abs_nonneg' w))).2 <| by
-    rw [mul_self_abs, add_mul_self_eq, mul_self_abs, mul_self_abs, add_right_comm, normSq_add,
-      add_le_add_iff_left, mul_assoc, mul_le_mul_left (zero_lt_two' ℝ), ←
-      Real.sqrt_mul <| normSq_nonneg z, ← normSq_conj w, ← map_mul]
-    exact re_le_abs (z * conj w)
-
-/-- The complex absolute value function, defined as the square root of the norm squared. -/
-noncomputable def _root_.Complex.abs : AbsoluteValue ℂ ℝ where
-  toFun x := abs x
-  map_mul' := abs_mul
-  nonneg' := abs_nonneg'
-  eq_zero' _ := (Real.sqrt_eq_zero <| normSq_nonneg _).trans normSq_eq_zero
-  add_le' := abs_add
-#align complex.abs Complex.abs
-
-end AbsTheory
-
-theorem abs_def : (Complex.abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
-  rfl
-#align complex.abs_def Complex.abs_def
-
-theorem abs_apply {z : ℂ} : Complex.abs z = (normSq z).sqrt :=
-  rfl
-#align complex.abs_apply Complex.abs_apply
-
-@[simp, norm_cast]
-theorem abs_ofReal (r : ℝ) : Complex.abs r = |r| := by
-  simp [Complex.abs, normSq_ofReal, Real.sqrt_mul_self_eq_abs]
-#align complex.abs_of_real Complex.abs_ofReal
-
-nonrec theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.abs r = r :=
-  (Complex.abs_ofReal _).trans (abs_of_nonneg h)
-#align complex.abs_of_nonneg Complex.abs_of_nonneg
-
--- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
-@[simp]
-theorem abs_natCast (n : ℕ) : Complex.abs n = n := Complex.abs_of_nonneg (Nat.cast_nonneg n)
-#align complex.abs_of_nat Complex.abs_natCast
-#align complex.abs_cast_nat Complex.abs_natCast
-
--- See note [no_index around OfNat.ofNat]
-@[simp]
-theorem abs_ofNat (n : ℕ) [n.AtLeastTwo] :
-    Complex.abs (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n :=
-  abs_natCast n
-
-theorem mul_self_abs (z : ℂ) : Complex.abs z * Complex.abs z = normSq z :=
-  Real.mul_self_sqrt (normSq_nonneg _)
-#align complex.mul_self_abs Complex.mul_self_abs
-
-theorem sq_abs (z : ℂ) : Complex.abs z ^ 2 = normSq z :=
-  Real.sq_sqrt (normSq_nonneg _)
-#align complex.sq_abs Complex.sq_abs
-
-@[simp]
-theorem sq_abs_sub_sq_re (z : ℂ) : Complex.abs z ^ 2 - z.re ^ 2 = z.im ^ 2 := by
-  rw [sq_abs, normSq_apply, ← sq, ← sq, add_sub_cancel']
-#align complex.sq_abs_sub_sq_re Complex.sq_abs_sub_sq_re
-
-@[simp]
-theorem sq_abs_sub_sq_im (z : ℂ) : Complex.abs z ^ 2 - z.im ^ 2 = z.re ^ 2 := by
-  rw [← sq_abs_sub_sq_re, sub_sub_cancel]
-#align complex.sq_abs_sub_sq_im Complex.sq_abs_sub_sq_im
-
-@[simp]
-theorem abs_I : Complex.abs I = 1 := by simp [Complex.abs]
-set_option linter.uppercaseLean3 false in
-#align complex.abs_I Complex.abs_I
-
-theorem abs_two : Complex.abs 2 = 2 := abs_ofNat 2
-#align complex.abs_two Complex.abs_two
-
-@[simp]
-theorem range_abs : range Complex.abs = Ici 0 :=
-  Subset.antisymm
-    (by simp only [range_subset_iff, Ici, mem_setOf_eq, map_nonneg, forall_const])
-    (fun x hx => ⟨x, Complex.abs_of_nonneg hx⟩)
-#align complex.range_abs Complex.range_abs
-
-@[simp]
-theorem abs_conj (z : ℂ) : Complex.abs (conj z) = Complex.abs z :=
-  AbsTheory.abs_conj z
-#align complex.abs_conj Complex.abs_conj
-
--- Porting note: @[simp] can prove it now
-theorem abs_prod {ι : Type*} (s : Finset ι) (f : ι → ℂ) :
-    Complex.abs (s.prod f) = s.prod fun I => Complex.abs (f I) :=
-  map_prod Complex.abs _ _
-#align complex.abs_prod Complex.abs_prod
-
--- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
-by `simp only [@map_pow]` -/
-theorem abs_pow (z : ℂ) (n : ℕ) : Complex.abs (z ^ n) = Complex.abs z ^ n :=
-  map_pow Complex.abs z n
-#align complex.abs_pow Complex.abs_pow
-
--- @[simp]
-/- Porting note: `simp` attribute removed as linter reports this can be proved
-by `simp only [@map_zpow₀]` -/
-theorem abs_zpow (z : ℂ) (n : ℤ) : Complex.abs (z ^ n) = Complex.abs z ^ n :=
-  map_zpow₀ Complex.abs z n
-#align complex.abs_zpow Complex.abs_zpow
-
-theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ Complex.abs z :=
-  Real.abs_le_sqrt <| by
-    rw [normSq_apply, ← sq]
-    exact le_add_of_nonneg_right (mul_self_nonneg _)
-#align complex.abs_re_le_abs Complex.abs_re_le_abs
-
-theorem abs_im_le_abs (z : ℂ) : |z.im| ≤ Complex.abs z :=
-  Real.abs_le_sqrt <| by
-    rw [normSq_apply, ← sq, ← sq]
-    exact le_add_of_nonneg_left (sq_nonneg _)
-#align complex.abs_im_le_abs Complex.abs_im_le_abs
-
-theorem re_le_abs (z : ℂ) : z.re ≤ Complex.abs z :=
-  (abs_le.1 (abs_re_le_abs _)).2
-#align complex.re_le_abs Complex.re_le_abs
-
-theorem im_le_abs (z : ℂ) : z.im ≤ Complex.abs z :=
-  (abs_le.1 (abs_im_le_abs _)).2
-#align complex.im_le_abs Complex.im_le_abs
-
-@[simp]
-theorem abs_re_lt_abs {z : ℂ} : |z.re| < Complex.abs z ↔ z.im ≠ 0 := by
-  rw [Complex.abs, AbsoluteValue.coe_mk, MulHom.coe_mk, Real.lt_sqrt (abs_nonneg _), normSq_apply,
-    _root_.sq_abs, ← sq, lt_add_iff_pos_right, mul_self_pos]
-#align complex.abs_re_lt_abs Complex.abs_re_lt_abs
-
-@[simp]
-theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.abs z ↔ z.re ≠ 0 := by
-  simpa using @abs_re_lt_abs (z * I)
-#align complex.abs_im_lt_abs Complex.abs_im_lt_abs
-
-@[simp]
-lemma abs_re_eq_abs {z : ℂ} : |z.re| = abs z ↔ z.im = 0 :=
-  not_iff_not.1 <| (abs_re_le_abs z).lt_iff_ne.symm.trans abs_re_lt_abs
-
-@[simp]
-lemma abs_im_eq_abs {z : ℂ} : |z.im| = abs z ↔ z.re = 0 :=
-  not_iff_not.1 <| (abs_im_le_abs z).lt_iff_ne.symm.trans abs_im_lt_abs
-
-@[simp]
-theorem abs_abs (z : ℂ) : |Complex.abs z| = Complex.abs z :=
-  _root_.abs_of_nonneg (AbsoluteValue.nonneg _ z)
-#align complex.abs_abs Complex.abs_abs
-
--- Porting note: probably should be golfed
-theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.abs z ≤ |z.re| + |z.im| := by
-  simpa [re_add_im] using Complex.abs.add_le z.re (z.im * I)
-#align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
-
--- Porting note: added so `two_pos` in the next proof works
--- TODO: move somewhere else
-instance : NeZero (1 : ℝ) :=
- ⟨by apply one_ne_zero⟩
-
-theorem abs_le_sqrt_two_mul_max (z : ℂ) : Complex.abs z ≤ Real.sqrt 2 * max |z.re| |z.im| := by
-  cases' z with x y
-  simp only [abs_apply, normSq_mk, ← sq]
-  by_cases hle : |x| ≤ |y|
-  · calc
-      Real.sqrt (x ^ 2 + y ^ 2) ≤ Real.sqrt (y ^ 2 + y ^ 2) :=
-        Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
-      _ = Real.sqrt 2 * max |x| |y| := by
-        rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
-  · have hle' := le_of_not_le hle
-    rw [add_comm]
-    calc
-      Real.sqrt (y ^ 2 + x ^ 2) ≤ Real.sqrt (x ^ 2 + x ^ 2) :=
-        Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle') _)
-      _ = Real.sqrt 2 * max |x| |y| := by
-        rw [max_eq_left hle', ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
-#align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
-
-theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / Complex.abs z| ≤ 1 :=
-  if hz : z = 0 then by simp [hz, zero_le_one]
-  else by simp_rw [_root_.abs_div, abs_abs,
-    div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_re_le_abs]
-#align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_one
-
-theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
-  if hz : z = 0 then by simp [hz, zero_le_one]
-  else by simp_rw [_root_.abs_div, abs_abs,
-    div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs]
-#align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
-
-@[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := by
-  rw [← ofReal_int_cast, abs_ofReal]
-#align complex.int_cast_abs Complex.int_cast_abs
-
-theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by
-  simp [abs, sq, abs_def, Real.mul_self_sqrt (normSq_nonneg _)]
-#align complex.norm_sq_eq_abs Complex.normSq_eq_abs
-
-/-! ### Cauchy sequences -/
-
-local notation "abs'" => Abs.abs
-
-theorem isCauSeq_re (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>
-  (f.cauchy ε0).imp fun i H j ij =>
-    lt_of_le_of_lt (by simpa using abs_re_le_abs (f j - f i)) (H _ ij)
-#align complex.is_cau_seq_re Complex.isCauSeq_re
-
-theorem isCauSeq_im (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).im := fun ε ε0 =>
-  (f.cauchy ε0).imp fun i H j ij =>
-    lt_of_le_of_lt (by simpa using abs_im_le_abs (f j - f i)) (H _ ij)
-#align complex.is_cau_seq_im Complex.isCauSeq_im
-
-/-- The real part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqRe (f : CauSeq ℂ Complex.abs) : CauSeq ℝ abs' :=
-  ⟨_, isCauSeq_re f⟩
-#align complex.cau_seq_re Complex.cauSeqRe
-
-/-- The imaginary part of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqIm (f : CauSeq ℂ Complex.abs) : CauSeq ℝ abs' :=
-  ⟨_, isCauSeq_im f⟩
-#align complex.cau_seq_im Complex.cauSeqIm
-
-theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.abs f) :
-    IsCauSeq abs' (Complex.abs ∘ f) := fun ε ε0 =>
-  let ⟨i, hi⟩ := hf ε ε0
-  ⟨i, fun j hj => lt_of_le_of_lt
-    (Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
-#align complex.is_cau_seq_abs Complex.isCauSeq_abs
-
-/-- The limit of a Cauchy sequence of complex numbers. -/
-noncomputable def limAux (f : CauSeq ℂ Complex.abs) : ℂ :=
-  ⟨CauSeq.lim (cauSeqRe f), CauSeq.lim (cauSeqIm f)⟩
-#align complex.lim_aux Complex.limAux
-
-theorem equiv_limAux (f : CauSeq ℂ Complex.abs) :
-    f ≈ CauSeq.const Complex.abs (limAux f) := fun ε ε0 =>
-  (exists_forall_ge_and
-  (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
-        (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
-    fun i H j ij => by
-    cases' H _ ij with H₁ H₂
-    apply lt_of_le_of_lt (abs_le_abs_re_add_abs_im _)
-    dsimp [limAux] at *
-    have := add_lt_add H₁ H₂
-    rwa [add_halves] at this
-#align complex.equiv_lim_aux Complex.equiv_limAux
-
-instance instIsComplete : CauSeq.IsComplete ℂ Complex.abs :=
-  ⟨fun f => ⟨limAux f, equiv_limAux f⟩⟩
-
-open CauSeq
-
-theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.abs) :
-    lim f = ↑(lim (cauSeqRe f)) + ↑(lim (cauSeqIm f)) * I :=
-  lim_eq_of_equiv_const <|
-    calc
-      f ≈ _ := equiv_limAux f
-      _ = CauSeq.const Complex.abs (↑(lim (cauSeqRe f)) + ↑(lim (cauSeqIm f)) * I) :=
-        CauSeq.ext fun _ =>
-          Complex.ext (by simp [limAux, cauSeqRe, ofReal']) (by simp [limAux, cauSeqIm, ofReal'])
-#align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
-
-theorem lim_re (f : CauSeq ℂ Complex.abs) : lim (cauSeqRe f) = (lim f).re := by
-  rw [lim_eq_lim_im_add_lim_re]; simp [ofReal']
-#align complex.lim_re Complex.lim_re
-
-theorem lim_im (f : CauSeq ℂ Complex.abs) : lim (cauSeqIm f) = (lim f).im := by
-  rw [lim_eq_lim_im_add_lim_re]; simp [ofReal']
-#align complex.lim_im Complex.lim_im
-
-theorem isCauSeq_conj (f : CauSeq ℂ Complex.abs) :
-    IsCauSeq Complex.abs fun n => conj (f n) := fun ε ε0 =>
-  let ⟨i, hi⟩ := f.2 ε ε0
-  ⟨i, fun j hj => by
-    rw [← RingHom.map_sub, abs_conj]; exact hi j hj⟩
-#align complex.is_cau_seq_conj Complex.isCauSeq_conj
-
-/-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
-noncomputable def cauSeqConj (f : CauSeq ℂ Complex.abs) : CauSeq ℂ Complex.abs :=
-  ⟨_, isCauSeq_conj f⟩
-#align complex.cau_seq_conj Complex.cauSeqConj
-
-theorem lim_conj (f : CauSeq ℂ Complex.abs) : lim (cauSeqConj f) = conj (lim f) :=
-  Complex.ext (by simp [cauSeqConj, (lim_re _).symm, cauSeqRe])
-    (by simp [cauSeqConj, (lim_im _).symm, cauSeqIm, (lim_neg _).symm]; rfl)
-#align complex.lim_conj Complex.lim_conj
-
-/-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/
-noncomputable def cauSeqAbs (f : CauSeq ℂ Complex.abs) : CauSeq ℝ abs' :=
-  ⟨_, isCauSeq_abs f.2⟩
-#align complex.cau_seq_abs Complex.cauSeqAbs
-
-theorem lim_abs (f : CauSeq ℂ Complex.abs) : lim (cauSeqAbs f) = Complex.abs (lim f) :=
-  lim_eq_of_equiv_const fun ε ε0 =>
-    let ⟨i, hi⟩ := equiv_lim f ε ε0
-    ⟨i, fun j hj => lt_of_le_of_lt (Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
-#align complex.lim_abs Complex.lim_abs
-
-variable {α : Type*} (s : Finset α)
-
-@[simp, norm_cast]
-theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=
-  map_prod ofReal _ _
-#align complex.of_real_prod Complex.ofReal_prod
-
-@[simp, norm_cast]
-theorem ofReal_sum (f : α → ℝ) : ((∑ i in s, f i : ℝ) : ℂ) = ∑ i in s, (f i : ℂ) :=
-  map_sum ofReal _ _
-#align complex.of_real_sum Complex.ofReal_sum
-
-@[simp]
-theorem re_sum (f : α → ℂ) : (∑ i in s, f i).re = ∑ i in s, (f i).re :=
-  reAddGroupHom.map_sum f s
-#align complex.re_sum Complex.re_sum
-
-@[simp]
-theorem im_sum (f : α → ℂ) : (∑ i in s, f i).im = ∑ i in s, (f i).im :=
-  imAddGroupHom.map_sum f s
-#align complex.im_sum Complex.im_sum
-
 end Complex
+
+assert_not_exists Multiset
+assert_not_exists Algebra

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

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

@@ -499,15 +499,18 @@ set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit1 Complex.I_pow_bit1
 
 --Porting note: new theorem
+-- See note [no_index around OfNat.ofNat]
 @[simp, norm_cast]
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
     ((no_index (OfNat.ofNat n) : ℝ) : ℂ) = OfNat.ofNat n :=
   rfl
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re = OfNat.ofNat n :=
   rfl
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 :=
   rfl
@@ -624,6 +627,7 @@ theorem normSq_int_cast (z : ℤ) : normSq z = z * z := normSq_ofReal _
 @[simp]
 theorem normSq_rat_cast (q : ℚ) : normSq q = q * q := normSq_ofReal _
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem normSq_ofNat (n : ℕ) [n.AtLeastTwo] :
     normSq (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n * OfNat.ofNat n :=
@@ -657,7 +661,6 @@ theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
 
-
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [normSq]
 set_option linter.uppercaseLean3 false in
@@ -1037,6 +1040,7 @@ theorem abs_natCast (n : ℕ) : Complex.abs n = n := Complex.abs_of_nonneg (Nat.
 #align complex.abs_of_nat Complex.abs_natCast
 #align complex.abs_cast_nat Complex.abs_natCast
 
+-- See note [no_index around OfNat.ofNat]
 @[simp]
 theorem abs_ofNat (n : ℕ) [n.AtLeastTwo] :
     Complex.abs (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n :=

One Nat lemma was duplicated

@@ -16,6 +16,7 @@ of characteristic zero. The result that the complex numbers are algebraically cl
 `FieldTheory.AlgebraicClosure`.
 -/
 
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open BigOperators
 
@@ -488,12 +489,12 @@ theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
 section
 set_option linter.deprecated false
 @[simp]
-theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', Complex.I_mul_I]
+theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1 : ℂ) ^ n := by rw [pow_bit0', Complex.I_mul_I]
 set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit0 Complex.I_pow_bit0
 
 @[simp]
-theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', Complex.I_mul_I]
+theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1 : ℂ) ^ n * I := by rw [pow_bit1', Complex.I_mul_I]
 set_option linter.uppercaseLean3 false in
 #align complex.I_pow_bit1 Complex.I_pow_bit1
 
@@ -511,7 +512,11 @@ theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re
 theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 :=
   rfl
 
+noncomputable instance : RatCast ℂ where
+  ratCast q := ofReal' q
+
 end
+
 /-! ### Complex conjugation -/
 
 
@@ -610,6 +615,20 @@ theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by
   simp [normSq, ofReal']
 #align complex.norm_sq_of_real Complex.normSq_ofReal
 
+@[simp]
+theorem normSq_nat_cast (n : ℕ) : normSq n = n * n := normSq_ofReal _
+
+@[simp]
+theorem normSq_int_cast (z : ℤ) : normSq z = z * z := normSq_ofReal _
+
+@[simp]
+theorem normSq_rat_cast (q : ℚ) : normSq q = q * q := normSq_ofReal _
+
+@[simp]
+theorem normSq_ofNat (n : ℕ) [n.AtLeastTwo] :
+    normSq (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n * OfNat.ofNat n :=
+  normSq_nat_cast _
+
 @[simp]
 theorem normSq_mk (x y : ℝ) : normSq ⟨x, y⟩ = x * x + y * y :=
   rfl
@@ -638,10 +657,6 @@ theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
 
-@[simp]
-theorem normSq_ofNat (n : ℕ) [n.AtLeastTwo] :
-    normSq (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n * OfNat.ofNat n := by
-  simp [normSq]
 
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [normSq]
@@ -783,56 +798,50 @@ protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
     ofReal_one]
 #align complex.mul_inv_cancel Complex.mul_inv_cancel
 
-noncomputable instance : RatCast ℂ where
-  ratCast := Rat.castRec
-
 /-! ### Cast lemmas -/
 
 @[simp, norm_cast]
-theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
-  map_natCast ofReal n
+theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n := rfl
 #align complex.of_real_nat_cast Complex.ofReal_nat_cast
 
 @[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← ofReal_nat_cast, ofReal_re]
+theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := rfl
 #align complex.nat_cast_re Complex.nat_cast_re
 
 @[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← ofReal_nat_cast, ofReal_im]
+theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := rfl
 #align complex.nat_cast_im Complex.nat_cast_im
 
 @[simp, norm_cast]
-theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
-  map_intCast ofReal n
+theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n := rfl
 #align complex.of_real_int_cast Complex.ofReal_int_cast
 
 @[simp, norm_cast]
-theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← ofReal_int_cast, ofReal_re]
+theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := rfl
 #align complex.int_cast_re Complex.int_cast_re
 
 @[simp, norm_cast]
-theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← ofReal_int_cast, ofReal_im]
+theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := rfl
 #align complex.int_cast_im Complex.int_cast_im
 
 @[simp, norm_cast]
-theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by
-  show (Rat.castRec q : ℂ).im = 0
-  cases q
-  simp [Rat.castRec]
-#align complex.rat_cast_im Complex.rat_cast_im
+theorem ofReal_rat_cast (q : ℚ) : ((q : ℝ) : ℂ) = q := rfl
+#align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
 @[simp, norm_cast]
-theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℝ) := by
-  show (Rat.castRec q : ℂ).re = _
-  cases q
-  simp [Rat.castRec, normSq, Rat.mk_eq_divInt, Rat.mkRat_eq_div, div_eq_mul_inv, *]
+theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℝ) := rfl
 #align complex.rat_cast_re Complex.rat_cast_re
 
+@[simp, norm_cast]
+theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := rfl
+#align complex.rat_cast_im Complex.rat_cast_im
+
 /-! ### Field instance and lemmas -/
 
 noncomputable instance instField : Field ℂ :=
 { qsmul := fun n z => n • z
   qsmul_eq_mul' := fun n z => ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
+  ratCast_mk := fun n d hd h2 => by ext <;> simp [Field.ratCast_mk]
   inv := Inv.inv
   mul_inv_cancel := @Complex.mul_inv_cancel
   inv_zero := Complex.inv_zero }
@@ -841,12 +850,12 @@ noncomputable instance instField : Field ℂ :=
 section
 set_option linter.deprecated false
 @[simp]
-theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
+theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1 : ℂ) ^ n := by rw [zpow_bit0', I_mul_I]
 set_option linter.uppercaseLean3 false in
 #align complex.I_zpow_bit0 Complex.I_zpow_bit0
 
 @[simp]
-theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
+theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1 : ℂ) ^ n * I := by rw [zpow_bit1', I_mul_I]
 set_option linter.uppercaseLean3 false in
 #align complex.I_zpow_bit1 Complex.I_zpow_bit1
 
@@ -900,11 +909,6 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
 #align complex.norm_sq_div Complex.normSq_div
 
-@[simp, norm_cast]
-theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = (n : ℂ) :=
-  map_ratCast ofReal n
-#align complex.of_real_rat_cast Complex.ofReal_rat_cast
-
 lemma div_ofReal (z : ℂ) (x : ℝ) : z / x = ⟨z.re / x, z.im / x⟩ := by
   simp_rw [div_eq_inv_mul, ← ofReal_inv, ofReal_mul']
 
@@ -1027,8 +1031,11 @@ nonrec theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.abs r = r :=
   (Complex.abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 
+-- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
+@[simp]
 theorem abs_natCast (n : ℕ) : Complex.abs n = n := Complex.abs_of_nonneg (Nat.cast_nonneg n)
 #align complex.abs_of_nat Complex.abs_natCast
+#align complex.abs_cast_nat Complex.abs_natCast
 
 @[simp]
 theorem abs_ofNat (n : ℕ) [n.AtLeastTwo] :
@@ -1177,12 +1184,6 @@ theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
     div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
--- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
-@[simp]
-theorem abs_cast_nat (n : ℕ) : Complex.abs (n : ℂ) = n := by
-  rw [← ofReal_nat_cast, abs_of_nonneg (Nat.cast_nonneg n)]
-#align complex.abs_cast_nat Complex.abs_cast_nat
-
 @[simp, norm_cast]
 theorem int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := by
   rw [← ofReal_int_cast, abs_ofReal]

@@ -1124,6 +1124,14 @@ theorem abs_im_lt_abs {z : ℂ} : |z.im| < Complex.abs z ↔ z.re ≠ 0 := by
   simpa using @abs_re_lt_abs (z * I)
 #align complex.abs_im_lt_abs Complex.abs_im_lt_abs
 
+@[simp]
+lemma abs_re_eq_abs {z : ℂ} : |z.re| = abs z ↔ z.im = 0 :=
+  not_iff_not.1 <| (abs_re_le_abs z).lt_iff_ne.symm.trans abs_re_lt_abs
+
+@[simp]
+lemma abs_im_eq_abs {z : ℂ} : |z.im| = abs z ↔ z.re = 0 :=
+  not_iff_not.1 <| (abs_im_le_abs z).lt_iff_ne.symm.trans abs_im_lt_abs
+
 @[simp]
 theorem abs_abs (z : ℂ) : |Complex.abs z| = Complex.abs z :=
   _root_.abs_of_nonneg (AbsoluteValue.nonneg _ z)

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -226,7 +226,7 @@ theorem ofReal_add (r s : ℝ) : ((r + s : ℝ) : ℂ) = r + s :=
 #align complex.of_real_add Complex.ofReal_add
 
 @[simp, norm_cast]
-theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 (r : ℂ)  :=
+theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 (r : ℂ) :=
   ext_iff.2 <| by simp [bit0]
 #align complex.of_real_bit0 Complex.ofReal_bit0
 

@@ -905,6 +905,38 @@ theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = (n : ℂ) :=
   map_ratCast ofReal n
 #align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
+lemma div_ofReal (z : ℂ) (x : ℝ) : z / x = ⟨z.re / x, z.im / x⟩ := by
+  simp_rw [div_eq_inv_mul, ← ofReal_inv, ofReal_mul']
+
+lemma div_nat_cast (z : ℂ) (n : ℕ) : z / n = ⟨z.re / n, z.im / n⟩ := by
+  exact_mod_cast div_ofReal z n
+
+lemma div_int_cast (z : ℂ) (n : ℤ) : z / n = ⟨z.re / n, z.im / n⟩ := by
+  exact_mod_cast div_ofReal z n
+
+lemma div_rat_cast (z : ℂ) (x : ℚ) : z / x = ⟨z.re / x, z.im / x⟩ := by
+  exact_mod_cast div_ofReal z x
+
+lemma div_ofNat (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
+    z / OfNat.ofNat n = ⟨z.re / OfNat.ofNat n, z.im / OfNat.ofNat n⟩ :=
+  div_nat_cast z n
+
+@[simp] lemma div_ofReal_re (z : ℂ) (x : ℝ) : (z / x).re = z.re / x := by rw [div_ofReal]
+@[simp] lemma div_ofReal_im (z : ℂ) (x : ℝ) : (z / x).im = z.im / x := by rw [div_ofReal]
+@[simp] lemma div_nat_cast_re (z : ℂ) (n : ℕ) : (z / n).re = z.re / n := by rw [div_nat_cast]
+@[simp] lemma div_nat_cast_im (z : ℂ) (n : ℕ) : (z / n).im = z.im / n := by rw [div_nat_cast]
+@[simp] lemma div_int_cast_re (z : ℂ) (n : ℤ) : (z / n).re = z.re / n := by rw [div_int_cast]
+@[simp] lemma div_int_cast_im (z : ℂ) (n : ℤ) : (z / n).im = z.im / n := by rw [div_int_cast]
+@[simp] lemma div_rat_cast_re (z : ℂ) (x : ℚ) : (z / x).re = z.re / x := by rw [div_rat_cast]
+@[simp] lemma div_rat_cast_im (z : ℂ) (x : ℚ) : (z / x).im = z.im / x := by rw [div_rat_cast]
+
+@[simp]
+lemma div_ofNat_re (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
+    (z / no_index (OfNat.ofNat n)).re = z.re / OfNat.ofNat n := div_nat_cast_re z n
+
+@[simp]
+lemma div_ofNat_im (z : ℂ) (n : ℕ) [n.AtLeastTwo] :
+    (z / no_index (OfNat.ofNat n)).im = z.im / OfNat.ofNat n := div_nat_cast_im z n
 
 /-! ### Characteristic zero -/
 

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

@@ -638,6 +638,11 @@ theorem normSq_one : normSq 1 = 1 :=
   normSq.map_one
 #align complex.norm_sq_one Complex.normSq_one
 
+@[simp]
+theorem normSq_ofNat (n : ℕ) [n.AtLeastTwo] :
+    normSq (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n * OfNat.ofNat n := by
+  simp [normSq]
+
 @[simp]
 theorem normSq_I : normSq I = 1 := by simp [normSq]
 set_option linter.uppercaseLean3 false in
@@ -990,11 +995,13 @@ nonrec theorem abs_of_nonneg {r : ℝ} (h : 0 ≤ r) : Complex.abs r = r :=
   (Complex.abs_ofReal _).trans (abs_of_nonneg h)
 #align complex.abs_of_nonneg Complex.abs_of_nonneg
 
-theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
-  calc
-    Complex.abs n = Complex.abs (n : ℝ) := by rw [ofReal_nat_cast]
-    _ = _ := Complex.abs_of_nonneg (Nat.cast_nonneg n)
-#align complex.abs_of_nat Complex.abs_of_nat
+theorem abs_natCast (n : ℕ) : Complex.abs n = n := Complex.abs_of_nonneg (Nat.cast_nonneg n)
+#align complex.abs_of_nat Complex.abs_natCast
+
+@[simp]
+theorem abs_ofNat (n : ℕ) [n.AtLeastTwo] :
+    Complex.abs (no_index (OfNat.ofNat n : ℂ)) = OfNat.ofNat n :=
+  abs_natCast n
 
 theorem mul_self_abs (z : ℂ) : Complex.abs z * Complex.abs z = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
@@ -1019,11 +1026,7 @@ theorem abs_I : Complex.abs I = 1 := by simp [Complex.abs]
 set_option linter.uppercaseLean3 false in
 #align complex.abs_I Complex.abs_I
 
-@[simp]
-theorem abs_two : Complex.abs 2 = 2 :=
-  calc
-    Complex.abs 2 = Complex.abs (2 : ℝ) := rfl
-    _ = (2 : ℝ) := Complex.abs_of_nonneg (by norm_num)
+theorem abs_two : Complex.abs 2 = 2 := abs_ofNat 2
 #align complex.abs_two Complex.abs_two
 
 @[simp]

@@ -1038,7 +1038,7 @@ theorem abs_conj (z : ℂ) : Complex.abs (conj z) = Complex.abs z :=
   AbsTheory.abs_conj z
 #align complex.abs_conj Complex.abs_conj
 
-@[simp]
+-- Porting note: @[simp] can prove it now
 theorem abs_prod {ι : Type*} (s : Finset ι) (f : ι → ℂ) :
     Complex.abs (s.prod f) = s.prod fun I => Complex.abs (f I) :=
   map_prod Complex.abs _ _

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -1174,7 +1174,7 @@ noncomputable def cauSeqIm (f : CauSeq ℂ Complex.abs) : CauSeq ℝ abs' :=
 #align complex.cau_seq_im Complex.cauSeqIm
 
 theorem isCauSeq_abs {f : ℕ → ℂ} (hf : IsCauSeq Complex.abs f) :
-  IsCauSeq abs' (Complex.abs ∘ f) := fun ε ε0 =>
+    IsCauSeq abs' (Complex.abs ∘ f) := fun ε ε0 =>
   let ⟨i, hi⟩ := hf ε ε0
   ⟨i, fun j hj => lt_of_le_of_lt
     (Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
@@ -1186,7 +1186,7 @@ noncomputable def limAux (f : CauSeq ℂ Complex.abs) : ℂ :=
 #align complex.lim_aux Complex.limAux
 
 theorem equiv_limAux (f : CauSeq ℂ Complex.abs) :
-  f ≈ CauSeq.const Complex.abs (limAux f) := fun ε ε0 =>
+    f ≈ CauSeq.const Complex.abs (limAux f) := fun ε ε0 =>
   (exists_forall_ge_and
   (CauSeq.equiv_lim ⟨_, isCauSeq_re f⟩ _ (half_pos ε0))
         (CauSeq.equiv_lim ⟨_, isCauSeq_im f⟩ _ (half_pos ε0))).imp
@@ -1222,7 +1222,7 @@ theorem lim_im (f : CauSeq ℂ Complex.abs) : lim (cauSeqIm f) = (lim f).im := b
 #align complex.lim_im Complex.lim_im
 
 theorem isCauSeq_conj (f : CauSeq ℂ Complex.abs) :
-  IsCauSeq Complex.abs fun n => conj (f n) := fun ε ε0 =>
+    IsCauSeq Complex.abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by
     rw [← RingHom.map_sub, abs_conj]; exact hi j hj⟩

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

@@ -432,9 +432,6 @@ instance Complex.addGroupWithOne : AddGroupWithOne ℂ :=
 -- Porting note: proof needed modifications and rewritten fields
 instance commRing : CommRing ℂ :=
   { Complex.addGroupWithOne with
-    zero := (0 : ℂ)
-    add := (· + ·)
-    one := 1
     mul := (· * ·)
     npow := @npowRec _ ⟨(1 : ℂ)⟩ ⟨(· * ·)⟩
     add_comm := by intros; ext <;> simp [add_comm]

Removing further unnecessary imports on the path to major tactics.

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

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 -/
 import Mathlib.Data.Real.Sqrt
+import Mathlib.Algebra.GroupWithZero.Bitwise
 
 #align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
 

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -916,14 +916,14 @@ example : (Complex.instSMulRealComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
-  have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := by rfl
+  have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := rfl
   simp only [add_conj, ofReal_mul, ofReal_one, ofReal_bit0, this,
     mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj
 
 /-- A complex number `z` minus its conjugate `conj z` is `2i` times its imaginary part. -/
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
-  have : (↑2 : ℝ ) * I = 2 * I := by rfl
+  have : (↑2 : ℝ ) * I = 2 * I := rfl
   simp only [sub_conj, ofReal_mul, ofReal_one, ofReal_bit0, mul_right_comm, this,
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
@@ -1024,7 +1024,7 @@ set_option linter.uppercaseLean3 false in
 @[simp]
 theorem abs_two : Complex.abs 2 = 2 :=
   calc
-    Complex.abs 2 = Complex.abs (2 : ℝ) := by rfl
+    Complex.abs 2 = Complex.abs (2 : ℝ) := rfl
     _ = (2 : ℝ) := Complex.abs_of_nonneg (by norm_num)
 #align complex.abs_two Complex.abs_two
 

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

This has nice performance benefits.

@@ -365,7 +365,7 @@ instance : Nontrivial ℂ :=
 -- porting note: moved from `Module/Data/Complex/Basic.lean`
 section SMul
 
-variable {R : Type _} [SMul R ℝ]
+variable {R : Type*} [SMul R ℝ]
 
 /- The useless `0` multiplication in `smul` is to make sure that
 `RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally. -/
@@ -1041,7 +1041,7 @@ theorem abs_conj (z : ℂ) : Complex.abs (conj z) = Complex.abs z :=
 #align complex.abs_conj Complex.abs_conj
 
 @[simp]
-theorem abs_prod {ι : Type _} (s : Finset ι) (f : ι → ℂ) :
+theorem abs_prod {ι : Type*} (s : Finset ι) (f : ι → ℂ) :
     Complex.abs (s.prod f) = s.prod fun I => Complex.abs (f I) :=
   map_prod Complex.abs _ _
 #align complex.abs_prod Complex.abs_prod
@@ -1251,7 +1251,7 @@ theorem lim_abs (f : CauSeq ℂ Complex.abs) : lim (cauSeqAbs f) = Complex.abs (
     ⟨i, fun j hj => lt_of_le_of_lt (Complex.abs.abs_abv_sub_le_abv_sub _ _) (hi j hj)⟩
 #align complex.lim_abs Complex.lim_abs
 
-variable {α : Type _} (s : Finset α)
+variable {α : Type*} (s : Finset α)
 
 @[simp, norm_cast]
 theorem ofReal_prod (f : α → ℝ) : ((∏ i in s, f i : ℝ) : ℂ) = ∏ i in s, (f i : ℂ) :=

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

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

@@ -369,7 +369,7 @@ variable {R : Type _} [SMul R ℝ]
 
 /- The useless `0` multiplication in `smul` is to make sure that
 `RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally. -/
-instance : SMul R ℂ where
+instance instSMulRealComplex : SMul R ℂ where
   smul r x := ⟨r • x.re - 0 * x.im, r • x.im + 0 * x.re⟩
 
 theorem smul_re (r : R) (z : ℂ) : (r • z).re = r • z.re := by simp [(· • ·), SMul.smul]
@@ -912,7 +912,7 @@ instance charZero : CharZero ℂ :=
 #align complex.char_zero_complex Complex.charZero
 
 -- Test if the `ℚ` smul instance is correct.
-example : (Complex.instSMulComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := rfl
+example : (Complex.instSMulRealComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := rfl
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by

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

@@ -1151,119 +1151,6 @@ theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by
   simp [abs, sq, abs_def, Real.mul_self_sqrt (normSq_nonneg _)]
 #align complex.norm_sq_eq_abs Complex.normSq_eq_abs
 
-/-- We put a partial order on ℂ so that `z ≤ w` exactly if `w - z` is real and nonnegative.
-Complex numbers with different imaginary parts are incomparable.
--/
-protected def partialOrder : PartialOrder ℂ where
-  le z w := z.re ≤ w.re ∧ z.im = w.im
-  lt z w := z.re < w.re ∧ z.im = w.im
-  lt_iff_le_not_le z w := by
-    dsimp
-    rw [lt_iff_le_not_le]
-    tauto
-  le_refl x := ⟨le_rfl, rfl⟩
-  le_trans x y z h₁ h₂ := ⟨h₁.1.trans h₂.1, h₁.2.trans h₂.2⟩
-  le_antisymm z w h₁ h₂ := ext (h₁.1.antisymm h₂.1) h₁.2
-#align complex.partial_order Complex.partialOrder
-
-namespace _root_.ComplexOrder
-
--- Porting note: made section into namespace to allow scoping
-scoped[ComplexOrder] attribute [instance] Complex.partialOrder
-
-end _root_.ComplexOrder
-
-section ComplexOrder
-
-open ComplexOrder
-
-theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
-  Iff.rfl
-#align complex.le_def Complex.le_def
-
-theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
-  Iff.rfl
-#align complex.lt_def Complex.lt_def
-
-
-@[simp, norm_cast]
-theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def, ofReal']
-#align complex.real_le_real Complex.real_le_real
-
-@[simp, norm_cast]
-theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def, ofReal']
-#align complex.real_lt_real Complex.real_lt_real
-
-
-@[simp, norm_cast]
-theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
-  real_le_real
-#align complex.zero_le_real Complex.zero_le_real
-
-@[simp, norm_cast]
-theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
-  real_lt_real
-#align complex.zero_lt_real Complex.zero_lt_real
-
-theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
-  rw [le_def, not_and_or, not_le]
-#align complex.not_le_iff Complex.not_le_iff
-
-theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
-  rw [lt_def, not_and_or, not_lt]
-#align complex.not_lt_iff Complex.not_lt_iff
-
-theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
-  not_le_iff
-#align complex.not_le_zero_iff Complex.not_le_zero_iff
-
-theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
-  not_lt_iff
-#align complex.not_lt_zero_iff Complex.not_lt_zero_iff
-
-theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by
-  ext
-  rfl
-  simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
-#align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
-
-/-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
--/
-protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
-  { zero_le_one := ⟨zero_le_one, rfl⟩
-    add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
-    mul_pos := fun z w hz hw => by
-      simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
-    mul_comm := by intros; ext <;> ring_nf }
-#align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
-
-scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
-
-/-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a star ordered ring.
-(That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
--/
-protected def starOrderedRing : StarOrderedRing ℂ :=
-  StarOrderedRing.ofNonnegIff' add_le_add_left fun r => by
-    refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-    · have h₁ : 0 ≤ r.re := by
-        rw [le_def] at hr
-        exact hr.1
-      have h₂ : r.im = 0 := by
-        rw [le_def] at hr
-        exact hr.2.symm
-      ext
-      · simp only [ofReal_im, star_def, ofReal_re, sub_zero, conj_re, mul_re, mul_zero,
-          ← Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
-      · simp only [h₂, add_zero, ofReal_im, star_def, zero_mul, conj_im, mul_im, mul_zero,
-          neg_zero]
-    · obtain ⟨s, rfl⟩ := h
-      simp only [← normSq_eq_conj_mul_self, normSq_nonneg, zero_le_real, star_def]
-#align complex.star_ordered_ring Complex.starOrderedRing
-
-scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing
-
-end ComplexOrder
-
 /-! ### Cauchy sequences -/
 
 local notation "abs'" => Abs.abs

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2017 Kevin Buzzard. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
-
-! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Real.Sqrt
 
+#align_import data.complex.basic from "leanprover-community/mathlib"@"31c24aa72e7b3e5ed97a8412470e904f82b81004"
+
 /-!
 # The complex numbers
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

@@ -232,7 +232,7 @@ theorem ofReal_bit0 (r : ℝ) : ((bit0 r : ℝ) : ℂ) = bit0 (r : ℂ)  :=
   ext_iff.2 <| by simp [bit0]
 #align complex.of_real_bit0 Complex.ofReal_bit0
 
-@[simp,  norm_cast]
+@[simp, norm_cast]
 theorem ofReal_bit1 (r : ℝ) : ((bit1 r : ℝ) : ℂ) = bit1 (r : ℂ) :=
   ext_iff.2 <| by simp [bit1]
 #align complex.of_real_bit1 Complex.ofReal_bit1
@@ -919,7 +919,7 @@ example : (Complex.instSMulComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
-  have : (↑(↑2 : ℝ) : ℂ)  = (2 : ℂ) := by rfl
+  have : (↑(↑2 : ℝ) : ℂ) = (2 : ℂ) := by rfl
   simp only [add_conj, ofReal_mul, ofReal_one, ofReal_bit0, this,
     mul_div_cancel_left (z.re : ℂ) two_ne_zero]
 #align complex.re_eq_add_conj Complex.re_eq_add_conj

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

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

@@ -504,15 +504,16 @@ set_option linter.uppercaseLean3 false in
 
 --Porting note: new theorem
 @[simp, norm_cast]
-theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ) : ℂ) = OfNat.ofNat n :=
+theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] :
+    ((no_index (OfNat.ofNat n) : ℝ) : ℂ) = OfNat.ofNat n :=
   rfl
 
 @[simp]
-theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : ℂ).re = OfNat.ofNat n :=
+theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).re = OfNat.ofNat n :=
   rfl
 
 @[simp]
-theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : ℂ).im = 0 :=
+theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (no_index (OfNat.ofNat n) : ℂ).im = 0 :=
   rfl
 
 end

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

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

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

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

@@ -449,7 +449,7 @@ instance commRing : CommRing ℂ :=
     mul_assoc := by intros; ext <;> simp [mul_assoc] <;> ring
     one_mul := by intros; ext <;> simp [one_mul]
     mul_one := by intros; ext <;> simp [mul_one]
-    mul_comm := by intros; ext <;> simp [mul_comm] ; ring }
+    mul_comm := by intros; ext <;> simp [mul_comm]; ring }
 
 /-- This shortcut instance ensures we do not find `Ring` via the noncomputable `Complex.field`
 instance. -/
@@ -574,7 +574,7 @@ theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
 #align complex.conj_eq_iff_real Complex.conj_eq_iff_real
 
 theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
-  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ ; simp [ofReal'], fun h => ⟨_, h.symm⟩⟩
+  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩; simp [ofReal'], fun h => ⟨_, h.symm⟩⟩
 #align complex.conj_eq_iff_re Complex.conj_eq_iff_re
 
 theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
@@ -682,7 +682,7 @@ theorem normSq_mul (z w : ℂ) : normSq (z * w) = normSq z * normSq w :=
 #align complex.norm_sq_mul Complex.normSq_mul
 
 theorem normSq_add (z w : ℂ) : normSq (z + w) = normSq z + normSq w + 2 * (z * conj w).re := by
-  dsimp [normSq] ; ring
+  dsimp [normSq]; ring
 #align complex.norm_sq_add Complex.normSq_add
 
 theorem re_sq_le_normSq (z : ℂ) : z.re * z.re ≤ normSq z :=
@@ -1331,18 +1331,18 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.abs) :
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
 
 theorem lim_re (f : CauSeq ℂ Complex.abs) : lim (cauSeqRe f) = (lim f).re := by
-  rw [lim_eq_lim_im_add_lim_re] ; simp [ofReal']
+  rw [lim_eq_lim_im_add_lim_re]; simp [ofReal']
 #align complex.lim_re Complex.lim_re
 
 theorem lim_im (f : CauSeq ℂ Complex.abs) : lim (cauSeqIm f) = (lim f).im := by
-  rw [lim_eq_lim_im_add_lim_re] ; simp [ofReal']
+  rw [lim_eq_lim_im_add_lim_re]; simp [ofReal']
 #align complex.lim_im Complex.lim_im
 
 theorem isCauSeq_conj (f : CauSeq ℂ Complex.abs) :
   IsCauSeq Complex.abs fun n => conj (f n) := fun ε ε0 =>
   let ⟨i, hi⟩ := f.2 ε ε0
   ⟨i, fun j hj => by
-    rw [← RingHom.map_sub, abs_conj] ; exact hi j hj⟩
+    rw [← RingHom.map_sub, abs_conj]; exact hi j hj⟩
 #align complex.is_cau_seq_conj Complex.isCauSeq_conj
 
 /-- The complex conjugate of a complex Cauchy sequence, as a complex Cauchy sequence. -/
@@ -1352,7 +1352,7 @@ noncomputable def cauSeqConj (f : CauSeq ℂ Complex.abs) : CauSeq ℂ Complex.a
 
 theorem lim_conj (f : CauSeq ℂ Complex.abs) : lim (cauSeqConj f) = conj (lim f) :=
   Complex.ext (by simp [cauSeqConj, (lim_re _).symm, cauSeqRe])
-    (by simp [cauSeqConj, (lim_im _).symm, cauSeqIm, (lim_neg _).symm] ; rfl)
+    (by simp [cauSeqConj, (lim_im _).symm, cauSeqIm, (lim_neg _).symm]; rfl)
 #align complex.lim_conj Complex.lim_conj
 
 /-- The absolute value of a complex Cauchy sequence, as a real Cauchy sequence. -/

@@ -1108,21 +1108,21 @@ theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.abs z ≤ |z.re| + |z.im| :
 instance : NeZero (1 : ℝ) :=
  ⟨by apply one_ne_zero⟩
 
-theorem abs_le_sqrt_two_mul_max (z : ℂ) : Complex.abs z ≤ Real.sqrt 2 * max (|z.re|) (|z.im|) := by
+theorem abs_le_sqrt_two_mul_max (z : ℂ) : Complex.abs z ≤ Real.sqrt 2 * max |z.re| |z.im| := by
   cases' z with x y
   simp only [abs_apply, normSq_mk, ← sq]
   by_cases hle : |x| ≤ |y|
   · calc
       Real.sqrt (x ^ 2 + y ^ 2) ≤ Real.sqrt (y ^ 2 + y ^ 2) :=
         Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
-      _ = Real.sqrt 2 * max (|x|) (|y|) := by
+      _ = Real.sqrt 2 * max |x| |y| := by
         rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
   · have hle' := le_of_not_le hle
     rw [add_comm]
     calc
       Real.sqrt (y ^ 2 + x ^ 2) ≤ Real.sqrt (x ^ 2 + x ^ 2) :=
         Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle') _)
-      _ = Real.sqrt 2 * max (|x|) (|y|) := by
+      _ = Real.sqrt 2 * max |x| |y| := by
         rw [max_eq_left hle', ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 
@@ -1145,7 +1145,7 @@ theorem abs_cast_nat (n : ℕ) : Complex.abs (n : ℂ) = n := by
 #align complex.abs_cast_nat Complex.abs_cast_nat
 
 @[simp, norm_cast]
-theorem int_cast_abs (n : ℤ) : (|↑n|) = Complex.abs n := by
+theorem int_cast_abs (n : ℤ) : |↑n| = Complex.abs n := by
   rw [← ofReal_int_cast, abs_ofReal]
 #align complex.int_cast_abs Complex.int_cast_abs
 

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com>

@@ -365,22 +365,47 @@ defined in `Data.Complex.Module`. -/
 instance : Nontrivial ℂ :=
   pullback_nonzero re rfl rfl
 
+-- porting note: moved from `Module/Data/Complex/Basic.lean`
+section SMul
+
+variable {R : Type _} [SMul R ℝ]
+
+/- The useless `0` multiplication in `smul` is to make sure that
+`RestrictScalars.module ℝ ℂ ℂ = Complex.module` definitionally. -/
+instance : SMul R ℂ where
+  smul r x := ⟨r • x.re - 0 * x.im, r • x.im + 0 * x.re⟩
+
+theorem smul_re (r : R) (z : ℂ) : (r • z).re = r • z.re := by simp [(· • ·), SMul.smul]
+#align complex.smul_re Complex.smul_re
+
+theorem smul_im (r : R) (z : ℂ) : (r • z).im = r • z.im := by simp [(· • ·), SMul.smul]
+#align complex.smul_im Complex.smul_im
+
+@[simp]
+theorem real_smul {x : ℝ} {z : ℂ} : x • z = x * z :=
+  rfl
+#align complex.real_smul Complex.real_smul
+
+end SMul
+
 -- Porting note: proof needed modifications and rewritten fields
 instance addCommGroup : AddCommGroup ℂ :=
   { zero := (0 : ℂ)
     add := (· + ·)
     neg := Neg.neg
     sub := Sub.sub
-    nsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
-    zsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
-    zsmul_zero' := by intros; ext <;> simp
-    nsmul_zero := by intros; ext <;> simp
+    nsmul := fun n z => n • z
+    zsmul := fun n z => n • z
+    zsmul_zero' := by intros; ext <;> simp [smul_re, smul_im]
+    nsmul_zero := by intros; ext <;> simp [smul_re, smul_im]
     nsmul_succ := by
-      intros; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm]
+      intros; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm,
+        smul_re, smul_im]
     zsmul_succ' := by
-      intros; ext <;> simp [SubNegMonoid.zsmul_succ', add_mul, add_comm]
+      intros; ext <;> simp [SubNegMonoid.zsmul_succ', add_mul, add_comm,
+        smul_re, smul_im]
     zsmul_neg' := by
-      intros; ext <;> simp [zsmul_neg', add_mul]
+      intros; ext <;> simp [zsmul_neg', add_mul, smul_re, smul_im]
     add_assoc := by intros; ext <;> simp [add_assoc]
     zero_add := by intros; ext <;> simp
     add_zero := by intros; ext <;> simp
@@ -757,11 +782,57 @@ protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
     ofReal_one]
 #align complex.mul_inv_cancel Complex.mul_inv_cancel
 
-/-! ### Field instance and lemmas -/
+noncomputable instance : RatCast ℂ where
+  ratCast := Rat.castRec
+
+/-! ### Cast lemmas -/
+
+@[simp, norm_cast]
+theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
+  map_natCast ofReal n
+#align complex.of_real_nat_cast Complex.ofReal_nat_cast
+
+@[simp, norm_cast]
+theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← ofReal_nat_cast, ofReal_re]
+#align complex.nat_cast_re Complex.nat_cast_re
+
+@[simp, norm_cast]
+theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← ofReal_nat_cast, ofReal_im]
+#align complex.nat_cast_im Complex.nat_cast_im
+
+@[simp, norm_cast]
+theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
+  map_intCast ofReal n
+#align complex.of_real_int_cast Complex.ofReal_int_cast
+
+@[simp, norm_cast]
+theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← ofReal_int_cast, ofReal_re]
+#align complex.int_cast_re Complex.int_cast_re
+
+@[simp, norm_cast]
+theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← ofReal_int_cast, ofReal_im]
+#align complex.int_cast_im Complex.int_cast_im
+
+@[simp, norm_cast]
+theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by
+  show (Rat.castRec q : ℂ).im = 0
+  cases q
+  simp [Rat.castRec]
+#align complex.rat_cast_im Complex.rat_cast_im
 
+@[simp, norm_cast]
+theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℝ) := by
+  show (Rat.castRec q : ℂ).re = _
+  cases q
+  simp [Rat.castRec, normSq, Rat.mk_eq_divInt, Rat.mkRat_eq_div, div_eq_mul_inv, *]
+#align complex.rat_cast_re Complex.rat_cast_re
+
+/-! ### Field instance and lemmas -/
 
 noncomputable instance instField : Field ℂ :=
-{ inv := Inv.inv
+{ qsmul := fun n z => n • z
+  qsmul_eq_mul' := fun n z => ext_iff.2 <| by simp [Rat.smul_def, smul_re, smul_im]
+  inv := Inv.inv
   mul_inv_cancel := @Complex.mul_inv_cancel
   inv_zero := Complex.inv_zero }
 #align complex.field Complex.instField
@@ -828,51 +899,11 @@ theorem normSq_div (z w : ℂ) : normSq (z / w) = normSq z / normSq w :=
   map_div₀ normSq z w
 #align complex.norm_sq_div Complex.normSq_div
 
-/-! ### Cast lemmas -/
-
-
-@[simp, norm_cast]
-theorem ofReal_nat_cast (n : ℕ) : ((n : ℝ) : ℂ) = n :=
-  map_natCast ofReal n
-#align complex.of_real_nat_cast Complex.ofReal_nat_cast
-
-@[simp, norm_cast]
-theorem nat_cast_re (n : ℕ) : (n : ℂ).re = n := by rw [← ofReal_nat_cast, ofReal_re]
-#align complex.nat_cast_re Complex.nat_cast_re
-
-@[simp, norm_cast]
-theorem nat_cast_im (n : ℕ) : (n : ℂ).im = 0 := by rw [← ofReal_nat_cast, ofReal_im]
-#align complex.nat_cast_im Complex.nat_cast_im
-
-@[simp, norm_cast]
-theorem ofReal_int_cast (n : ℤ) : ((n : ℝ) : ℂ) = n :=
-  map_intCast ofReal n
-#align complex.of_real_int_cast Complex.ofReal_int_cast
-
-@[simp, norm_cast]
-theorem int_cast_re (n : ℤ) : (n : ℂ).re = n := by rw [← ofReal_int_cast, ofReal_re]
-#align complex.int_cast_re Complex.int_cast_re
-
-@[simp, norm_cast]
-theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← ofReal_int_cast, ofReal_im]
-#align complex.int_cast_im Complex.int_cast_im
-
 @[simp, norm_cast]
 theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = (n : ℂ) :=
   map_ratCast ofReal n
 #align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
--- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
-@[simp]
-theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℂ) := by
- rw [← ofReal_rat_cast, ofReal_re]
-#align complex.rat_cast_re Complex.rat_cast_re
-
--- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
-@[simp]
-theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by
- rw [← ofReal_rat_cast, ofReal_im]
-#align complex.rat_cast_im Complex.rat_cast_im
 
 /-! ### Characteristic zero -/
 
@@ -882,6 +913,9 @@ instance charZero : CharZero ℂ :=
     rwa [← ofReal_nat_cast, ofReal_eq_zero, Nat.cast_eq_zero] at h
 #align complex.char_zero_complex Complex.charZero
 
+-- Test if the `ℚ` smul instance is correct.
+example : (Complex.instSMulComplex : SMul ℚ ℂ) = (Algebra.toSMul : SMul ℚ ℂ) := rfl
+
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
   have : (↑(↑2 : ℝ) : ℂ)  = (2 : ℂ) := by rfl

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -760,10 +760,11 @@ protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
 /-! ### Field instance and lemmas -/
 
 
-noncomputable instance : Field ℂ :=
+noncomputable instance instField : Field ℂ :=
 { inv := Inv.inv
   mul_inv_cancel := @Complex.mul_inv_cancel
   inv_zero := Complex.inv_zero }
+#align complex.field Complex.instField
 
 section
 set_option linter.deprecated false

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

@@ -367,25 +367,25 @@ instance : Nontrivial ℂ :=
 
 -- Porting note: proof needed modifications and rewritten fields
 instance addCommGroup : AddCommGroup ℂ :=
-{ zero := (0 : ℂ)
-  add := (· + ·)
-  neg := Neg.neg
-  sub := Sub.sub
-  nsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
-  zsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
-  zsmul_zero':= by intros; ext <;> simp
-  nsmul_zero := by intros; ext <;> simp
-  nsmul_succ := by
-    intros; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm]
-  zsmul_succ' := by
-    intros; ext <;> simp [SubNegMonoid.zsmul_succ', add_mul, add_comm]
-  zsmul_neg' := by
-    intros; ext <;> simp [zsmul_neg', add_mul]
-  add_assoc := by intros; ext <;> simp [add_assoc]
-  zero_add := by intros; ext <;> simp
-  add_zero := by intros; ext <;> simp
-  add_comm := by intros; ext <;> simp [add_comm]
-  add_left_neg := by intros; ext <;> simp }
+  { zero := (0 : ℂ)
+    add := (· + ·)
+    neg := Neg.neg
+    sub := Sub.sub
+    nsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
+    zsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
+    zsmul_zero' := by intros; ext <;> simp
+    nsmul_zero := by intros; ext <;> simp
+    nsmul_succ := by
+      intros; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm]
+    zsmul_succ' := by
+      intros; ext <;> simp [SubNegMonoid.zsmul_succ', add_mul, add_comm]
+    zsmul_neg' := by
+      intros; ext <;> simp [zsmul_neg', add_mul]
+    add_assoc := by intros; ext <;> simp [add_assoc]
+    zero_add := by intros; ext <;> simp
+    add_zero := by intros; ext <;> simp
+    add_comm := by intros; ext <;> simp [add_comm]
+    add_left_neg := by intros; ext <;> simp }
 
 
 instance Complex.addGroupWithOne : AddGroupWithOne ℂ :=
@@ -1197,11 +1197,11 @@ theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re :=
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
 -/
 protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
-{ zero_le_one := ⟨zero_le_one, rfl⟩
-  add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
-  mul_pos := fun z w hz hw => by
-    simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
-  mul_comm := by intros; ext <;> ring_nf }
+  { zero_le_one := ⟨zero_le_one, rfl⟩
+    add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
+    mul_pos := fun z w hz hw => by
+      simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
+    mul_comm := by intros; ext <;> ring_nf }
 #align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
 
 scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing

These are all doc fixes

@@ -23,7 +23,7 @@ open BigOperators
 
 open Set Function
 
-/-! ### Definition and basic arithmmetic -/
+/-! ### Definition and basic arithmetic -/
 
 
 /-- Complex numbers consist of two `Real`s: a real part `re` and an imaginary part `im`. -/

This forward-ports all the files from leanprover-community/mathlib#18854 which have already been ported, and it also ports the new file algebra.star.order, which is a split from algebra.star.basic and was necessary to do at the same time.

Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
+! leanprover-community/mathlib commit 31c24aa72e7b3e5ed97a8412470e904f82b81004
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1210,7 +1210,7 @@ scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
 protected def starOrderedRing : StarOrderedRing ℂ :=
-{ nonneg_iff := fun r => by
+  StarOrderedRing.ofNonnegIff' add_le_add_left fun r => by
     refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
     · have h₁ : 0 ≤ r.re := by
         rw [le_def] at hr
@@ -1219,13 +1219,12 @@ protected def starOrderedRing : StarOrderedRing ℂ :=
         rw [le_def] at hr
         exact hr.2.symm
       ext
-      · simp only [ofReal_im, star_def, ofReal_re, sub_zero, conj_re, mul_re, mul_zero, ←
-          Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
+      · simp only [ofReal_im, star_def, ofReal_re, sub_zero, conj_re, mul_re, mul_zero,
+          ← Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
       · simp only [h₂, add_zero, ofReal_im, star_def, zero_mul, conj_im, mul_im, mul_zero,
           neg_zero]
     · obtain ⟨s, rfl⟩ := h
       simp only [← normSq_eq_conj_mul_self, normSq_nonneg, zero_le_real, star_def]
-  add_le_add_left := by intros; simp [le_def] at *; assumption }
 #align complex.star_ordered_ring Complex.starOrderedRing
 
 scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing

@@ -1281,7 +1281,7 @@ theorem equiv_limAux (f : CauSeq ℂ Complex.abs) :
     rwa [add_halves] at this
 #align complex.equiv_lim_aux Complex.equiv_limAux
 
-instance : CauSeq.IsComplete ℂ Complex.abs :=
+instance instIsComplete : CauSeq.IsComplete ℂ Complex.abs :=
   ⟨fun f => ⟨limAux f, equiv_limAux f⟩⟩
 
 open CauSeq

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

@@ -557,7 +557,7 @@ theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
 #align complex.conj_eq_iff_im Complex.conj_eq_iff_im
 
--- `simpNF` complains about this being provable by `is_R_or_C.star_def` even
+-- `simpNF` complains about this being provable by `IsROrC.star_def` even
 -- though it's not imported by this file.
 -- Porting note: linter `simpNF` not found
 @[simp]

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -924,8 +924,8 @@ private theorem abs_mul (z w : ℂ) : (abs z * w) = (abs z) * abs w := by
   rw [normSq_mul, Real.sqrt_mul (normSq_nonneg _)]
 
 private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
-  (mul_self_le_mul_self_iff (abs_nonneg' (z + w)) (add_nonneg (abs_nonneg' z) (abs_nonneg' w))).2 <|
-    by
+  (mul_self_le_mul_self_iff (abs_nonneg' (z + w))
+      (add_nonneg (abs_nonneg' z) (abs_nonneg' w))).2 <| by
     rw [mul_self_abs, add_mul_self_eq, mul_self_abs, mul_self_abs, add_right_comm, normSq_add,
       add_le_add_iff_left, mul_assoc, mul_le_mul_left (zero_lt_two' ℝ), ←
       Real.sqrt_mul <| normSq_nonneg z, ← normSq_conj w, ← map_mul]

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kevin Buzzard, Mario Carneiro
 
 ! This file was ported from Lean 3 source module data.complex.basic
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -543,19 +543,19 @@ theorem conj_neg_I : conj (-I) = I :=
 set_option linter.uppercaseLean3 false in
 #align complex.conj_neg_I Complex.conj_neg_I
 
-theorem eq_conj_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
+theorem conj_eq_iff_real {z : ℂ} : conj z = z ↔ ∃ r : ℝ, z = r :=
   ⟨fun h => ⟨z.re, ext rfl <| eq_zero_of_neg_eq (congr_arg im h)⟩, fun ⟨h, e⟩ => by
     rw [e, conj_ofReal]⟩
-#align complex.eq_conj_iff_real Complex.eq_conj_iff_real
+#align complex.conj_eq_iff_real Complex.conj_eq_iff_real
 
-theorem eq_conj_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
-  eq_conj_iff_real.trans ⟨by rintro ⟨r, rfl⟩ ; simp [ofReal'], fun h => ⟨_, h.symm⟩⟩
-#align complex.eq_conj_iff_re Complex.eq_conj_iff_re
+theorem conj_eq_iff_re {z : ℂ} : conj z = z ↔ (z.re : ℂ) = z :=
+  conj_eq_iff_real.trans ⟨by rintro ⟨r, rfl⟩ ; simp [ofReal'], fun h => ⟨_, h.symm⟩⟩
+#align complex.conj_eq_iff_re Complex.conj_eq_iff_re
 
-theorem eq_conj_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
+theorem conj_eq_iff_im {z : ℂ} : conj z = z ↔ z.im = 0 :=
   ⟨fun h => add_self_eq_zero.mp (neg_eq_iff_add_eq_zero.mp (congr_arg im h)), fun h =>
     ext rfl (neg_eq_iff_add_eq_zero.mpr (add_self_eq_zero.mpr h))⟩
-#align complex.eq_conj_iff_im Complex.eq_conj_iff_im
+#align complex.conj_eq_iff_im Complex.conj_eq_iff_im
 
 -- `simpNF` complains about this being provable by `is_R_or_C.star_def` even
 -- though it's not imported by this file.

Co-authored-by: int-y1 <jason_yuen2007@hotmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -90,9 +90,7 @@ def ofReal' (r : ℝ) : ℂ :=
 instance : Coe ℝ ℂ :=
   ⟨ofReal'⟩
 
-/- Porting note: `simp` attribute removed as this has a variable as head symbol of
-the left-hand side (after whnfR)-/
-@[norm_cast]
+@[simp, norm_cast]
 theorem ofReal_re (r : ℝ) : Complex.re (r : ℂ) = r :=
   rfl
 #align complex.of_real_re Complex.ofReal_re
@@ -437,6 +435,12 @@ instance : Ring ℂ := by infer_instance
 instance : CommSemiring ℂ :=
   inferInstance
 
+-- porting note: added due to changes in typeclass search order
+/-- This shortcut instance ensures we do not find `Semiring` via the noncomputable
+`Complex.field` instance. -/
+instance : Semiring ℂ :=
+  inferInstance
+
 /-- The "real part" map, considered as an additive group homomorphism. -/
 def reAddGroupHom : ℂ →+ ℝ where
   toFun := re

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -959,7 +959,6 @@ theorem abs_of_nat (n : ℕ) : Complex.abs n = n :=
   calc
     Complex.abs n = Complex.abs (n : ℝ) := by rw [ofReal_nat_cast]
     _ = _ := Complex.abs_of_nonneg (Nat.cast_nonneg n)
-
 #align complex.abs_of_nat Complex.abs_of_nat
 
 theorem mul_self_abs (z : ℂ) : Complex.abs z * Complex.abs z = normSq z :=
@@ -1199,7 +1198,6 @@ protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
   mul_pos := fun z w hz hw => by
     simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
   mul_comm := by intros; ext <;> ring_nf }
-
 #align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
 
 scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
@@ -1292,7 +1290,6 @@ theorem lim_eq_lim_im_add_lim_re (f : CauSeq ℂ Complex.abs) :
       _ = CauSeq.const Complex.abs (↑(lim (cauSeqRe f)) + ↑(lim (cauSeqIm f)) * I) :=
         CauSeq.ext fun _ =>
           Complex.ext (by simp [limAux, cauSeqRe, ofReal']) (by simp [limAux, cauSeqIm, ofReal'])
-
 #align complex.lim_eq_lim_im_add_lim_re Complex.lim_eq_lim_im_add_lim_re
 
 theorem lim_re (f : CauSeq ℂ Complex.abs) : lim (cauSeqRe f) = (lim f).re := by

@@ -15,7 +15,7 @@ import Mathlib.Data.Real.Sqrt
 
 The complex numbers are modelled as ℝ^2 in the obvious way and it is shown that they form a field
 of characteristic zero. The result that the complex numbers are algebraically closed, see
-`field_theory.algebraic_closure`.
+`FieldTheory.AlgebraicClosure`.
 -/
 
 
@@ -26,14 +26,13 @@ open Set Function
 /-! ### Definition and basic arithmmetic -/
 
 
-/-- Complex numbers consist of two `real`s: a real part `re` and an imaginary part `im`. -/
+/-- Complex numbers consist of two `Real`s: a real part `re` and an imaginary part `im`. -/
 structure Complex : Type where
   re : ℝ
   im : ℝ
 #align complex Complex
 
 
--- mathport name: exprℂ
 notation "ℂ" => Complex
 
 namespace Complex
@@ -103,13 +102,10 @@ theorem ofReal_im (r : ℝ) : (r : ℂ).im = 0 :=
   rfl
 #align complex.of_real_im Complex.ofReal_im
 
--- Was warned that this is a syntactic tautology.
-@[nolint synTaut]
 theorem ofReal_def (r : ℝ) : (r : ℂ) = ⟨r, 0⟩ :=
   rfl
 #align complex.of_real_def Complex.ofReal_def
 
-
 @[simp, norm_cast]
 theorem ofReal_inj {z w : ℝ} : (z : ℂ) = w ↔ z = w :=
   ⟨congrArg re, by apply congrArg⟩
@@ -120,8 +116,8 @@ theorem ofReal_injective : Function.Injective ((↑) : ℝ → ℂ) := fun _ _ =
 #align complex.of_real_injective Complex.ofReal_injective
 
 -- Porting note: made coercion explicit
-instance canLift : CanLift ℂ ℝ (↑) fun z =>
-    z.im = 0 where prf z hz := ⟨z.re, ext rfl hz.symm⟩
+instance canLift : CanLift ℂ ℝ (↑) fun z => z.im = 0 where
+  prf z hz := ⟨z.re, ext rfl hz.symm⟩
 #align complex.can_lift Complex.canLift
 
 /-- The product of a set on the real axis and a set on the imaginary axis of the complex plane,
@@ -130,7 +126,6 @@ def Set.reProdIm (s t : Set ℝ) : Set ℂ :=
   re ⁻¹' s ∩ im ⁻¹' t
 #align set.re_prod_im Complex.Set.reProdIm
 
--- mathport name: «expr ×ℂ »
 infixl:72 " ×ℂ " => Set.reProdIm
 
 theorem mem_reProdIm {z : ℂ} {s t : Set ℝ} : z ∈ s ×ℂ t ↔ z.re ∈ s ∧ z.im ∈ t :=
@@ -368,31 +363,31 @@ theorem equivRealProd_symm_apply (p : ℝ × ℝ) : equivRealProd.symm p = p.1 +
 
 /- We use a nonstandard formula for the `ℕ` and `ℤ` actions to make sure there is no
 diamond from the other actions they inherit through the `ℝ`-action on `ℂ` and action transitivity
-defined in `data.complex.module.lean`. -/
+defined in `Data.Complex.Module`. -/
 instance : Nontrivial ℂ :=
   pullback_nonzero re rfl rfl
 
 -- Porting note: proof needed modifications and rewritten fields
-instance addCommGroup : AddCommGroup ℂ := {
-  zero := (0 : ℂ)
+instance addCommGroup : AddCommGroup ℂ :=
+{ zero := (0 : ℂ)
   add := (· + ·)
   neg := Neg.neg
   sub := Sub.sub
   nsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
   zsmul := fun n z => ⟨n • z.re - 0 * z.im, n • z.im + 0 * z.re⟩
-  zsmul_zero':= by intros ; ext <;> simp
-  nsmul_zero := by intros ; ext <;> simp
+  zsmul_zero':= by intros; ext <;> simp
+  nsmul_zero := by intros; ext <;> simp
   nsmul_succ := by
-    intros ; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm]
+    intros; ext <;> simp [AddMonoid.nsmul_succ, add_mul, add_comm]
   zsmul_succ' := by
     intros; ext <;> simp [SubNegMonoid.zsmul_succ', add_mul, add_comm]
   zsmul_neg' := by
-    intros ; ext <;> simp [zsmul_neg', add_mul]
-  add_assoc := by intros ; ext <;> simp [add_assoc]
-  zero_add := by intros ; ext <;> simp
-  add_zero := by intros ; ext <;> simp
-  add_comm := by intros ; ext <;> simp [add_comm]
-  add_left_neg := by intros ; ext <;> simp }
+    intros; ext <;> simp [zsmul_neg', add_mul]
+  add_assoc := by intros; ext <;> simp [add_assoc]
+  zero_add := by intros; ext <;> simp
+  add_zero := by intros; ext <;> simp
+  add_comm := by intros; ext <;> simp [add_comm]
+  add_left_neg := by intros; ext <;> simp }
 
 
 instance Complex.addGroupWithOne : AddGroupWithOne ℂ :=
@@ -421,24 +416,24 @@ instance commRing : CommRing ℂ :=
     one := 1
     mul := (· * ·)
     npow := @npowRec _ ⟨(1 : ℂ)⟩ ⟨(· * ·)⟩
-    add_comm := by intros ; ext <;> simp [add_comm]
+    add_comm := by intros; ext <;> simp [add_comm]
     left_distrib := by
-      intros ; ext <;> simp [mul_re, mul_im] <;> ring
+      intros; ext <;> simp [mul_re, mul_im] <;> ring
     right_distrib := by
-      intros ; ext <;> simp [mul_re, mul_im] <;> ring
-    zero_mul := by intros ; ext <;> simp [zero_mul]
-    mul_zero := by intros ; ext <;> simp [mul_zero]
-    mul_assoc := by intros ; ext <;> simp [mul_assoc] <;> ring
-    one_mul := by intros ; ext <;> simp [one_mul]
-    mul_one := by intros ; ext <;> simp [mul_one]
-    mul_comm := by intros ; ext <;> simp [mul_comm] ; ring }
-
-/-- This shortcut instance ensures we do not find `ring` via the noncomputable `complex.field`
+      intros; ext <;> simp [mul_re, mul_im] <;> ring
+    zero_mul := by intros; ext <;> simp [zero_mul]
+    mul_zero := by intros; ext <;> simp [mul_zero]
+    mul_assoc := by intros; ext <;> simp [mul_assoc] <;> ring
+    one_mul := by intros; ext <;> simp [one_mul]
+    mul_one := by intros; ext <;> simp [mul_one]
+    mul_comm := by intros; ext <;> simp [mul_comm] ; ring }
+
+/-- This shortcut instance ensures we do not find `Ring` via the noncomputable `Complex.field`
 instance. -/
 instance : Ring ℂ := by infer_instance
 
-/-- This shortcut instance ensures we do not find `comm_semiring` via the noncomputable
-`complex.field` instance. -/
+/-- This shortcut instance ensures we do not find `CommSemiring` via the noncomputable
+`Complex.field` instance. -/
 instance : CommSemiring ℂ :=
   inferInstance
 
@@ -495,9 +490,9 @@ end
 /-! ### Complex conjugation -/
 
 
-/-- This defines the complex conjugate as the `star` operation of the `star_ring ℂ`. It
-is recommended to use the ring endomorphism version `star_ring_end`, available under the
-notation `conj` in the locale `complex_conjugate`. -/
+/-- This defines the complex conjugate as the `star` operation of the `StarRing ℂ`. It
+is recommended to use the ring endomorphism version `starRingEnd`, available under the
+notation `conj` in the locale `ComplexConjugate`. -/
 instance : StarRing ℂ where
   star z := ⟨z.re, -z.im⟩
   star_involutive x := by simp only [eta, neg_neg]
@@ -586,8 +581,6 @@ theorem normSq_apply (z : ℂ) : normSq z = z.re * z.re + z.im * z.im :=
 #align complex.norm_sq_apply Complex.normSq_apply
 
 @[simp]
-/- Porting note: `simp` attribute removed as the result could be proved
-by `simp only [Complex.normSq_mk, @mul_zero, @add_zero]` -/
 theorem normSq_ofReal (r : ℝ) : normSq r = r * r := by
   simp [normSq, ofReal']
 #align complex.norm_sq_of_real Complex.normSq_ofReal
@@ -679,9 +672,9 @@ theorem add_conj (z : ℂ) : z + conj z = (2 * z.re : ℝ) :=
   ext_iff.2 <| by simp [two_mul, ofReal']
 #align complex.add_conj Complex.add_conj
 
-/-- The coercion `ℝ → ℂ` as a `ring_hom`. -/
+/-- The coercion `ℝ → ℂ` as a `RingHom`. -/
 def ofReal : ℝ →+* ℂ where
-  toFun := fun (x: ℝ) ↦ (↑x : ℂ)
+  toFun x := (x : ℂ)
   map_one' := ofReal_one
   map_zero' := ofReal_zero
   map_mul' := ofReal_mul
@@ -763,11 +756,10 @@ protected theorem mul_inv_cancel {z : ℂ} (h : z ≠ 0) : z * z⁻¹ = 1 := by
 /-! ### Field instance and lemmas -/
 
 
-noncomputable instance : Field ℂ := {
-    inv := Inv.inv
-    mul_inv_cancel := @Complex.mul_inv_cancel
-    inv_zero := Complex.inv_zero
-    }
+noncomputable instance : Field ℂ :=
+{ inv := Inv.inv
+  mul_inv_cancel := @Complex.mul_inv_cancel
+  inv_zero := Complex.inv_zero }
 
 section
 set_option linter.deprecated false
@@ -813,9 +805,7 @@ set_option linter.uppercaseLean3 false in
 
 @[simp]
 theorem inv_I : I⁻¹ = -I := by
-  rw [inv_eq_one_div]
-  rw [div_I]
-  rw [one_mul]
+  rw [inv_eq_one_div, div_I, one_mul]
 set_option linter.uppercaseLean3 false in
 #align complex.inv_I Complex.inv_I
 
@@ -863,29 +853,29 @@ theorem int_cast_im (n : ℤ) : (n : ℂ).im = 0 := by rw [← ofReal_int_cast,
 #align complex.int_cast_im Complex.int_cast_im
 
 @[simp, norm_cast]
-theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = @RatCast.ratCast ℂ _ n :=
+theorem ofReal_rat_cast (n : ℚ) : ((n : ℝ) : ℂ) = (n : ℂ) :=
   map_ratCast ofReal n
 #align complex.of_real_rat_cast Complex.ofReal_rat_cast
 
 -- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
 @[simp]
-theorem rat_cast_re (q : ℚ) : (RatCast.ratCast q : ℂ).re = @RatCast.ratCast ℂ _ q := by
+theorem rat_cast_re (q : ℚ) : (q : ℂ).re = (q : ℂ) := by
  rw [← ofReal_rat_cast, ofReal_re]
 #align complex.rat_cast_re Complex.rat_cast_re
 
 -- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`
 @[simp]
-theorem rat_cast_im (q : ℚ) : (RatCast.ratCast q : ℂ).im = @RatCast.ratCast ℂ _ 0 := by
- rw [← ofReal_rat_cast, ofReal_im]; norm_cast
+theorem rat_cast_im (q : ℚ) : (q : ℂ).im = 0 := by
+ rw [← ofReal_rat_cast, ofReal_im]
 #align complex.rat_cast_im Complex.rat_cast_im
 
 /-! ### Characteristic zero -/
 
 
-instance charZero_complex : CharZero ℂ :=
+instance charZero : CharZero ℂ :=
   charZero_of_inj_zero fun n h => by
     rwa [← ofReal_nat_cast, ofReal_eq_zero, Nat.cast_eq_zero] at h
-#align complex.char_zero_complex Complex.charZero_complex
+#align complex.char_zero_complex Complex.charZero
 
 /-- A complex number `z` plus its conjugate `conj z` is `2` times its real part. -/
 theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
@@ -899,8 +889,6 @@ theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   have : (↑2 : ℝ ) * I = 2 * I := by rfl
   simp only [sub_conj, ofReal_mul, ofReal_one, ofReal_bit0, mul_right_comm, this,
     mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
-
-
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
 
 /-! ### Absolute value -/
@@ -908,19 +896,15 @@ theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
 
 namespace AbsTheory
 
--- mathport name: abs
--- We develop enough theory to bundle `abs` into an `absolute_value` before making things public;
+-- We develop enough theory to bundle `abs` into an `AbsoluteValue` before making things public;
 -- this is so there's not two versions of it hanging around.
-set_option quotPrecheck false
-local notation "abs" z => (normSq z).sqrt
+local notation "abs" z => Real.sqrt (normSq z)
 
 private theorem mul_self_abs (z : ℂ) : ((abs z) * abs z) = normSq z :=
   Real.mul_self_sqrt (normSq_nonneg _)
--- #align complex.abs_theory.mul_self_abs Complex.AbsTheory.mul_self_abs
 
 private theorem abs_nonneg' (z : ℂ) : 0 ≤ abs z :=
   Real.sqrt_nonneg _
--- #align complex.abs_theory.abs_nonneg' Complex.AbsTheory.abs_nonneg'
 
 theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 #align complex.abs_theory.abs_conj Complex.AbsTheory.abs_conj
@@ -928,15 +912,12 @@ theorem abs_conj (z : ℂ) : (abs conj z) = abs z := by simp
 private theorem abs_re_le_abs (z : ℂ) : |z.re| ≤ abs z := by
   rw [mul_self_le_mul_self_iff (abs_nonneg z.re) (abs_nonneg' _), abs_mul_abs_self, mul_self_abs]
   apply re_sq_le_normSq
--- #align complex.abs_theory.abs_re_le_abs Complex.AbsTheory.abs_re_le_abs
 
 private theorem re_le_abs (z : ℂ) : z.re ≤ abs z :=
   (abs_le.1 (abs_re_le_abs _)).2
--- #align complex.abs_theory.re_le_abs complex.abs_theory.re_le_abs
 
 private theorem abs_mul (z w : ℂ) : (abs z * w) = (abs z) * abs w := by
   rw [normSq_mul, Real.sqrt_mul (normSq_nonneg _)]
--- #align complex.abs_theory.abs_mul complex.abs_theory.abs_mul
 
 private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
   (mul_self_le_mul_self_iff (abs_nonneg' (z + w)) (add_nonneg (abs_nonneg' z) (abs_nonneg' w))).2 <|
@@ -945,7 +926,6 @@ private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
       add_le_add_iff_left, mul_assoc, mul_le_mul_left (zero_lt_two' ℝ), ←
       Real.sqrt_mul <| normSq_nonneg z, ← normSq_conj w, ← map_mul]
     exact re_le_abs (z * conj w)
--- #align complex.abs_theory.abs_add complex.abs_theory.abs_add
 
 /-- The complex absolute value function, defined as the square root of the norm squared. -/
 noncomputable def _root_.Complex.abs : AbsoluteValue ℂ ℝ where
@@ -1014,9 +994,9 @@ theorem abs_two : Complex.abs 2 = 2 :=
 
 @[simp]
 theorem range_abs : range Complex.abs = Ici 0 :=
-  Subset.antisymm (
-    by apply range_subset_iff.2 ; simp only [Ici, mem_setOf_eq, map_nonneg, forall_const]
-    ) fun x hx => ⟨x, Complex.abs_of_nonneg hx⟩
+  Subset.antisymm
+    (by simp only [range_subset_iff, Ici, mem_setOf_eq, map_nonneg, forall_const])
+    (fun x hx => ⟨x, Complex.abs_of_nonneg hx⟩)
 #align complex.range_abs Complex.range_abs
 
 @[simp]
@@ -1086,6 +1066,7 @@ theorem abs_le_abs_re_add_abs_im (z : ℂ) : Complex.abs z ≤ |z.re| + |z.im| :
 #align complex.abs_le_abs_re_add_abs_im Complex.abs_le_abs_re_add_abs_im
 
 -- Porting note: added so `two_pos` in the next proof works
+-- TODO: move somewhere else
 instance : NeZero (1 : ℝ) :=
  ⟨by apply one_ne_zero⟩
 
@@ -1098,15 +1079,13 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : Complex.abs z ≤ Real.sqrt 2 * max
         Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle) _)
       _ = Real.sqrt 2 * max (|x|) (|y|) := by
         rw [max_eq_right hle, ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
-  · let hle' := le_of_not_le hle
+  · have hle' := le_of_not_le hle
     rw [add_comm]
     calc
       Real.sqrt (y ^ 2 + x ^ 2) ≤ Real.sqrt (x ^ 2 + x ^ 2) :=
         Real.sqrt_le_sqrt (add_le_add_right (sq_le_sq.2 hle') _)
       _ = Real.sqrt 2 * max (|x|) (|y|) := by
         rw [max_eq_left hle', ← two_mul, Real.sqrt_mul two_pos.le, Real.sqrt_sq_eq_abs]
-
-
 #align complex.abs_le_sqrt_two_mul_max Complex.abs_le_sqrt_two_mul_max
 
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / Complex.abs z| ≤ 1 :=
@@ -1139,8 +1118,7 @@ theorem normSq_eq_abs (x : ℂ) : normSq x = (Complex.abs x) ^ 2 := by
 /-- We put a partial order on ℂ so that `z ≤ w` exactly if `w - z` is real and nonnegative.
 Complex numbers with different imaginary parts are incomparable.
 -/
-protected def partialOrder : PartialOrder ℂ
-    where
+protected def partialOrder : PartialOrder ℂ where
   le z w := z.re ≤ w.re ∧ z.im = w.im
   lt z w := z.re < w.re ∧ z.im = w.im
   lt_iff_le_not_le z w := by
@@ -1152,111 +1130,108 @@ protected def partialOrder : PartialOrder ℂ
   le_antisymm z w h₁ h₂ := ext (h₁.1.antisymm h₂.1) h₁.2
 #align complex.partial_order Complex.partialOrder
 
-namespace ComplexOrder
+namespace _root_.ComplexOrder
 
 -- Porting note: made section into namespace to allow scoping
-scoped[Complex.ComplexOrder] attribute [instance] Complex.partialOrder
+scoped[ComplexOrder] attribute [instance] Complex.partialOrder
+
+end _root_.ComplexOrder
+
+section ComplexOrder
 
-example : PartialOrder ℂ := inferInstance
+open ComplexOrder
 
 theorem le_def {z w : ℂ} : z ≤ w ↔ z.re ≤ w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.le_def Complex.ComplexOrder.le_def
+#align complex.le_def Complex.le_def
 
 theorem lt_def {z w : ℂ} : z < w ↔ z.re < w.re ∧ z.im = w.im :=
   Iff.rfl
-#align complex.lt_def Complex.ComplexOrder.lt_def
+#align complex.lt_def Complex.lt_def
 
 
 @[simp, norm_cast]
 theorem real_le_real {x y : ℝ} : (x : ℂ) ≤ (y : ℂ) ↔ x ≤ y := by simp [le_def, ofReal']
-#align complex.real_le_real Complex.ComplexOrder.real_le_real
+#align complex.real_le_real Complex.real_le_real
 
 @[simp, norm_cast]
 theorem real_lt_real {x y : ℝ} : (x : ℂ) < (y : ℂ) ↔ x < y := by simp [lt_def, ofReal']
-#align complex.real_lt_real Complex.ComplexOrder.real_lt_real
+#align complex.real_lt_real Complex.real_lt_real
 
 
 @[simp, norm_cast]
 theorem zero_le_real {x : ℝ} : (0 : ℂ) ≤ (x : ℂ) ↔ 0 ≤ x :=
   real_le_real
-#align complex.zero_le_real Complex.ComplexOrder.zero_le_real
+#align complex.zero_le_real Complex.zero_le_real
 
 @[simp, norm_cast]
 theorem zero_lt_real {x : ℝ} : (0 : ℂ) < (x : ℂ) ↔ 0 < x :=
   real_lt_real
-#align complex.zero_lt_real Complex.ComplexOrder.zero_lt_real
+#align complex.zero_lt_real Complex.zero_lt_real
 
 theorem not_le_iff {z w : ℂ} : ¬z ≤ w ↔ w.re < z.re ∨ z.im ≠ w.im := by
   rw [le_def, not_and_or, not_le]
-#align complex.not_le_iff Complex.ComplexOrder.not_le_iff
+#align complex.not_le_iff Complex.not_le_iff
 
 theorem not_lt_iff {z w : ℂ} : ¬z < w ↔ w.re ≤ z.re ∨ z.im ≠ w.im := by
   rw [lt_def, not_and_or, not_lt]
-#align complex.not_lt_iff Complex.ComplexOrder.not_lt_iff
+#align complex.not_lt_iff Complex.not_lt_iff
 
 theorem not_le_zero_iff {z : ℂ} : ¬z ≤ 0 ↔ 0 < z.re ∨ z.im ≠ 0 :=
   not_le_iff
-#align complex.not_le_zero_iff Complex.ComplexOrder.not_le_zero_iff
+#align complex.not_le_zero_iff Complex.not_le_zero_iff
 
 theorem not_lt_zero_iff {z : ℂ} : ¬z < 0 ↔ 0 ≤ z.re ∨ z.im ≠ 0 :=
   not_lt_iff
-#align complex.not_lt_zero_iff Complex.ComplexOrder.not_lt_zero_iff
+#align complex.not_lt_zero_iff Complex.not_lt_zero_iff
 
 theorem eq_re_ofReal_le {r : ℝ} {z : ℂ} (hz : (r : ℂ) ≤ z) : z = z.re := by
   ext
   rfl
-  simp only [← (Complex.ComplexOrder.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
-#align complex.eq_re_of_real_le Complex.ComplexOrder.eq_re_ofReal_le
+  simp only [← (Complex.le_def.1 hz).2, Complex.zero_im, Complex.ofReal_im]
+#align complex.eq_re_of_real_le Complex.eq_re_ofReal_le
 
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a strictly ordered ring.
 -/
 protected def strictOrderedCommRing : StrictOrderedCommRing ℂ :=
-  {
-    zero_le_one := ⟨zero_le_one, rfl⟩
-    add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
-    mul_pos := fun z w hz hw => by
-      simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
-    mul_comm := by intros ;ext <;> ring_nf
-  }
+{ zero_le_one := ⟨zero_le_one, rfl⟩
+  add_le_add_left := fun w z h y => ⟨add_le_add_left h.1 _, congr_arg₂ (· + ·) rfl h.2⟩
+  mul_pos := fun z w hz hw => by
+    simp [lt_def, mul_re, mul_im, ← hz.2, ← hw.2, mul_pos hz.1 hw.1]
+  mul_comm := by intros; ext <;> ring_nf }
 
-#align complex.strict_ordered_comm_ring Complex.ComplexOrder.strictOrderedCommRing
+#align complex.strict_ordered_comm_ring Complex.strictOrderedCommRing
 
-scoped[Complex.ComplexOrder] attribute [instance] Complex.ComplexOrder.strictOrderedCommRing
+scoped[ComplexOrder] attribute [instance] Complex.strictOrderedCommRing
 
 /-- With `z ≤ w` iff `w - z` is real and nonnegative, `ℂ` is a star ordered ring.
 (That is, a star ring in which the nonnegative elements are those of the form `star z * z`.)
 -/
 protected def starOrderedRing : StarOrderedRing ℂ :=
-  { nonneg_iff := fun r =>
-      by
-      refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
-      · have h₁ : 0 ≤ r.re := by
-          rw [le_def] at hr
-          exact hr.1
-        have h₂ : r.im = 0 := by
-          rw [le_def] at hr
-          exact hr.2.symm
-        ext
-        ·
-          simp only [ofReal_im, star_def, ofReal_re, sub_zero, conj_re, mul_re, mul_zero, ←
-            Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
-        ·
-          simp only [h₂, add_zero, ofReal_im, star_def, zero_mul, conj_im, mul_im, mul_zero,
-            neg_zero]
-      · obtain ⟨s, rfl⟩ := h
-        simp only [← normSq_eq_conj_mul_self, normSq_nonneg, zero_le_real, star_def]
-    add_le_add_left := by intros ; simp [le_def] at *; assumption
-  }
-#align complex.star_ordered_ring Complex.ComplexOrder.starOrderedRing
-
-scoped[ComplexOrder] attribute [instance] Complex.ComplexOrder.starOrderedRing
+{ nonneg_iff := fun r => by
+    refine' ⟨fun hr => ⟨Real.sqrt r.re, _⟩, fun h => _⟩
+    · have h₁ : 0 ≤ r.re := by
+        rw [le_def] at hr
+        exact hr.1
+      have h₂ : r.im = 0 := by
+        rw [le_def] at hr
+        exact hr.2.symm
+      ext
+      · simp only [ofReal_im, star_def, ofReal_re, sub_zero, conj_re, mul_re, mul_zero, ←
+          Real.sqrt_mul h₁ r.re, Real.sqrt_mul_self h₁]
+      · simp only [h₂, add_zero, ofReal_im, star_def, zero_mul, conj_im, mul_im, mul_zero,
+          neg_zero]
+    · obtain ⟨s, rfl⟩ := h
+      simp only [← normSq_eq_conj_mul_self, normSq_nonneg, zero_le_real, star_def]
+  add_le_add_left := by intros; simp [le_def] at *; assumption }
+#align complex.star_ordered_ring Complex.starOrderedRing
+
+scoped[ComplexOrder] attribute [instance] Complex.starOrderedRing
 
 end ComplexOrder
 
 /-! ### Cauchy sequences -/
 
--- mathport name: exprabs'
 local notation "abs'" => Abs.abs
 
 theorem isCauSeq_re (f : CauSeq ℂ Complex.abs) : IsCauSeq abs' fun n => (f n).re := fun ε ε0 =>

Co-authored-by: Lukas Miaskiwskyi <lukas.mias@gmail.com> Co-authored-by: qawbecrdtey <qawbecrdtey@naver.com> Co-authored-by: David Renshaw <dwrenshaw@gmail.com>

@@ -483,6 +483,14 @@ set_option linter.uppercaseLean3 false in
 theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ) : ℂ) = OfNat.ofNat n :=
   rfl
 
+@[simp]
+theorem re_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : ℂ).re = OfNat.ofNat n :=
+  rfl
+
+@[simp]
+theorem im_ofNat (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n : ℂ).im = 0 :=
+  rfl
+
 end
 /-! ### Complex conjugation -/
 

@@ -305,32 +305,32 @@ set_option linter.uppercaseLean3 false in
 #align complex.I Complex.I
 
 @[simp]
-theorem i_re : I.re = 0 :=
+theorem I_re : I.re = 0 :=
   rfl
 set_option linter.uppercaseLean3 false in
-#align complex.I_re Complex.i_re
+#align complex.I_re Complex.I_re
 
 @[simp]
-theorem i_im : I.im = 1 :=
+theorem I_im : I.im = 1 :=
   rfl
 set_option linter.uppercaseLean3 false in
-#align complex.I_im Complex.i_im
+#align complex.I_im Complex.I_im
 
 @[simp]
-theorem i_mul_I : I * I = -1 :=
+theorem I_mul_I : I * I = -1 :=
   ext_iff.2 <| by simp
 set_option linter.uppercaseLean3 false in
-#align complex.I_mul_I Complex.i_mul_I
+#align complex.I_mul_I Complex.I_mul_I
 
-theorem i_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
+theorem I_mul (z : ℂ) : I * z = ⟨-z.im, z.re⟩ :=
   ext_iff.2 <| by simp
 set_option linter.uppercaseLean3 false in
-#align complex.I_mul Complex.i_mul
+#align complex.I_mul Complex.I_mul
 
-theorem i_ne_zero : (I : ℂ) ≠ 0 :=
+theorem I_ne_zero : (I : ℂ) ≠ 0 :=
   mt (congr_arg im) zero_ne_one.symm
 set_option linter.uppercaseLean3 false in
-#align complex.I_ne_zero Complex.i_ne_zero
+#align complex.I_ne_zero Complex.I_ne_zero
 
 theorem mk_eq_add_mul_I (a b : ℝ) : Complex.mk a b = a + b * I :=
   ext_iff.2 <| by simp [ofReal']
@@ -350,13 +350,13 @@ theorem mul_I_im (z : ℂ) : (z * I).im = z.re := by simp
 set_option linter.uppercaseLean3 false in
 #align complex.mul_I_im Complex.mul_I_im
 
-theorem i_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
+theorem I_mul_re (z : ℂ) : (I * z).re = -z.im := by simp
 set_option linter.uppercaseLean3 false in
-#align complex.I_mul_re Complex.i_mul_re
+#align complex.I_mul_re Complex.I_mul_re
 
-theorem i_mul_im (z : ℂ) : (I * z).im = z.re := by simp
+theorem I_mul_im (z : ℂ) : (I * z).im = z.re := by simp
 set_option linter.uppercaseLean3 false in
-#align complex.I_mul_im Complex.i_mul_im
+#align complex.I_mul_im Complex.I_mul_im
 
 @[simp]
 theorem equivRealProd_symm_apply (p : ℝ × ℝ) : equivRealProd.symm p = p.1 + p.2 * I := by
@@ -469,14 +469,19 @@ theorem coe_imAddGroupHom : (imAddGroupHom : ℂ → ℝ) = im :=
 section
 set_option linter.deprecated false
 @[simp]
-theorem i_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', Complex.i_mul_I]
+theorem I_pow_bit0 (n : ℕ) : I ^ bit0 n = (-1) ^ n := by rw [pow_bit0', Complex.I_mul_I]
 set_option linter.uppercaseLean3 false in
-#align complex.I_pow_bit0 Complex.i_pow_bit0
+#align complex.I_pow_bit0 Complex.I_pow_bit0
 
 @[simp]
-theorem i_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', Complex.i_mul_I]
+theorem I_pow_bit1 (n : ℕ) : I ^ bit1 n = (-1) ^ n * I := by rw [pow_bit1', Complex.I_mul_I]
 set_option linter.uppercaseLean3 false in
-#align complex.I_pow_bit1 Complex.i_pow_bit1
+#align complex.I_pow_bit1 Complex.I_pow_bit1
+
+--Porting note: new theorem
+@[simp, norm_cast]
+theorem ofReal_ofNat (n : ℕ) [n.AtLeastTwo] : ((OfNat.ofNat n : ℝ) : ℂ) = OfNat.ofNat n :=
+  rfl
 
 end
 /-! ### Complex conjugation -/
@@ -681,9 +686,9 @@ theorem ofReal_eq_coe (r : ℝ) : ofReal r = r :=
 #align complex.of_real_eq_coe Complex.ofReal_eq_coe
 
 @[simp]
-theorem i_sq : I ^ 2 = -1 := by rw [sq, i_mul_I]
+theorem I_sq : I ^ 2 = -1 := by rw [sq, I_mul_I]
 set_option linter.uppercaseLean3 false in
-#align complex.I_sq Complex.i_sq
+#align complex.I_sq Complex.I_sq
 
 @[simp]
 theorem sub_re (z w : ℂ) : (z - w).re = z.re - w.re :=
@@ -759,14 +764,14 @@ noncomputable instance : Field ℂ := {
 section
 set_option linter.deprecated false
 @[simp]
-theorem i_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', i_mul_I]
+theorem I_zpow_bit0 (n : ℤ) : I ^ bit0 n = (-1) ^ n := by rw [zpow_bit0', I_mul_I]
 set_option linter.uppercaseLean3 false in
-#align complex.I_zpow_bit0 Complex.i_zpow_bit0
+#align complex.I_zpow_bit0 Complex.I_zpow_bit0
 
 @[simp]
-theorem i_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', i_mul_I]
+theorem I_zpow_bit1 (n : ℤ) : I ^ bit1 n = (-1) ^ n * I := by rw [zpow_bit1', I_mul_I]
 set_option linter.uppercaseLean3 false in
-#align complex.I_zpow_bit1 Complex.i_zpow_bit1
+#align complex.I_zpow_bit1 Complex.I_zpow_bit1
 
 end
 
@@ -794,7 +799,7 @@ theorem ofReal_zpow (r : ℝ) (n : ℤ) : ((r ^ n : ℝ) : ℂ) = (r : ℂ) ^ n
 
 @[simp]
 theorem div_I (z : ℂ) : z / I = -(z * I) :=
-  (div_eq_iff_mul_eq i_ne_zero).2 <| by simp [mul_assoc]
+  (div_eq_iff_mul_eq I_ne_zero).2 <| by simp [mul_assoc]
 set_option linter.uppercaseLean3 false in
 #align complex.div_I Complex.div_I
 
@@ -885,7 +890,7 @@ theorem re_eq_add_conj (z : ℂ) : (z.re : ℂ) = (z + conj z) / 2 := by
 theorem im_eq_sub_conj (z : ℂ) : (z.im : ℂ) = (z - conj z) / (2 * I) := by
   have : (↑2 : ℝ ) * I = 2 * I := by rfl
   simp only [sub_conj, ofReal_mul, ofReal_one, ofReal_bit0, mul_right_comm, this,
-    mul_div_cancel_left _ (mul_ne_zero two_ne_zero i_ne_zero : 2 * I ≠ 0)]
+    mul_div_cancel_left _ (mul_ne_zero two_ne_zero I_ne_zero : 2 * I ≠ 0)]
 
 
 #align complex.im_eq_sub_conj Complex.im_eq_sub_conj
@@ -935,21 +940,16 @@ private theorem abs_add (z w : ℂ) : (abs z + w) ≤ (abs z) + abs w :=
 -- #align complex.abs_theory.abs_add complex.abs_theory.abs_add
 
 /-- The complex absolute value function, defined as the square root of the norm squared. -/
-noncomputable def Complex.abs : AbsoluteValue ℂ ℝ
-    where
+noncomputable def _root_.Complex.abs : AbsoluteValue ℂ ℝ where
   toFun x := abs x
   map_mul' := abs_mul
   nonneg' := abs_nonneg'
   eq_zero' _ := (Real.sqrt_eq_zero <| normSq_nonneg _).trans normSq_eq_zero
   add_le' := abs_add
-#align complex.abs Complex.AbsTheory.Complex.abs
+#align complex.abs Complex.abs
 
 end AbsTheory
 
--- Porting note: Added this to make the following work.
--- Hope this is as intended. Also the name has been expanded.
-open Complex.AbsTheory
-
 theorem abs_def : (Complex.abs : ℂ → ℝ) = fun z => (normSq z).sqrt :=
   rfl
 #align complex.abs_def Complex.abs_def
@@ -1104,13 +1104,13 @@ theorem abs_le_sqrt_two_mul_max (z : ℂ) : Complex.abs z ≤ Real.sqrt 2 * max
 theorem abs_re_div_abs_le_one (z : ℂ) : |z.re / Complex.abs z| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs,
-    div_le_iff (AbsoluteValue.pos Complex.AbsTheory.Complex.abs hz), one_mul, abs_re_le_abs]
+    div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_re_le_abs]
 #align complex.abs_re_div_abs_le_one Complex.abs_re_div_abs_le_one
 
 theorem abs_im_div_abs_le_one (z : ℂ) : |z.im / Complex.abs z| ≤ 1 :=
   if hz : z = 0 then by simp [hz, zero_le_one]
   else by simp_rw [_root_.abs_div, abs_abs,
-    div_le_iff (AbsoluteValue.pos Complex.AbsTheory.Complex.abs hz), one_mul, abs_im_le_abs]
+    div_le_iff (AbsoluteValue.pos Complex.abs hz), one_mul, abs_im_le_abs]
 #align complex.abs_im_div_abs_le_one Complex.abs_im_div_abs_le_one
 
 -- Porting note: removed `norm_cast` attribute because the RHS can't start with `↑`