diff --git a/Mathbin/Analysis/NormedSpace/Star/Spectrum.lean b/Mathbin/Analysis/NormedSpace/Star/Spectrum.lean
index f6f58fb89e..20cdde234a 100644
--- a/Mathbin/Analysis/NormedSpace/Star/Spectrum.lean
+++ b/Mathbin/Analysis/NormedSpace/Star/Spectrum.lean
@@ -193,7 +193,7 @@ noncomputable instance (priority := 100) : StarHomClass F A ℂ
   coe_injective' := FunLike.coe_injective'
   map_star φ a := by
     suffices hsa : ∀ s : selfAdjoint A, (φ s)⋆ = φ s
-    · rw [← realPart_add_i_smul_imaginaryPart a]
+    · rw [← realPart_add_I_smul_imaginaryPart a]
       simp only [map_add, map_smul, star_add, star_smul, hsa, selfAdjoint.star_val_eq]
     · intro s
       have := AlgHom.apply_mem_spectrum φ (s : A)
diff --git a/Mathbin/Data/Complex/Basic.lean b/Mathbin/Data/Complex/Basic.lean
index 1868a0e32a..40be2a1423 100644
--- a/Mathbin/Data/Complex/Basic.lean
+++ b/Mathbin/Data/Complex/Basic.lean
@@ -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 =>
diff --git a/Mathbin/Data/Complex/Exponential.lean b/Mathbin/Data/Complex/Exponential.lean
index 2e8af064ae..52ee586097 100644
--- a/Mathbin/Data/Complex/Exponential.lean
+++ b/Mathbin/Data/Complex/Exponential.lean
@@ -432,7 +432,7 @@ namespace Complex
 lean 3 declaration is
   forall (z : Complex), IsCauSeq.{0, 0} Real Real.linearOrderedField Real Real.ring (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.addCommMonoid (Finset.range n) (fun (m : Nat) => coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.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 (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)))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z m) ((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))))) (Nat.factorial m)))))
 but is expected to have type
-  forall (z : Complex), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (m : Nat) => FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.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 (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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 m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))
+  forall (z : Complex), IsCauSeq.{0, 0} Real Real.instLinearOrderedFieldReal Real Real.instRingReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal)) (fun (n : Nat) => Finset.sum.{0, 0} Real Nat Real.instAddCommMonoidReal (Finset.range n) (fun (m : Nat) => 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 (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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 m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_abs_exp Complex.isCauSeq_abs_expₓ'. -/
 theorem isCauSeq_abs_exp (z : ℂ) : IsCauSeq Abs.abs fun n => ∑ m in range n, abs (z ^ m / m !) :=
   let ⟨n, hn⟩ := exists_nat_gt (abs z)
@@ -453,7 +453,7 @@ noncomputable section
 lean 3 declaration is
   forall (z : 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) (fun (n : Nat) => Finset.sum.{0, 0} Complex Nat (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Finset.range n) (fun (m : Nat) => 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)))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) z m) ((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))))) (Nat.factorial m))))
 but is expected to have type
-  forall (z : 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) (fun (n : Nat) => Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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 m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m))))
+  forall (z : 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) (fun (n : Nat) => Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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 m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m))))
 Case conversion may be inaccurate. Consider using '#align complex.is_cau_exp Complex.isCauSeq_expₓ'. -/
 theorem isCauSeq_exp (z : ℂ) : IsCauSeq abs fun n => ∑ m in range n, z ^ m / m ! :=
   isCauSeq_series_of_abv_isCauSeq (isCauSeq_abs_exp z)
@@ -463,7 +463,7 @@ theorem isCauSeq_exp (z : ℂ) : IsCauSeq abs fun n => ∑ m in range n, z ^ m /
 lean 3 declaration is
   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))
 but is expected to have type
-  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 -> (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.exp' Complex.exp'ₓ'. -/
 /-- The Cauchy sequence consisting of partial sums of the Taylor series of
 the complex exponential function -/
@@ -672,7 +672,7 @@ theorem exp_sum {α : Type _} (s : Finset α) (f : α → ℂ) :
 lean 3 declaration is
   forall (x : Complex) (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) 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) x)) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.exp x) n)
 but is expected to have type
-  forall (x : Complex) (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) x)) (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))))))) (Complex.exp x) n)
+  forall (x : Complex) (n : Nat), Eq.{1} Complex (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) x)) (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.exp x) n)
 Case conversion may be inaccurate. Consider using '#align complex.exp_nat_mul Complex.exp_nat_mulₓ'. -/
 theorem exp_nat_mul (x : ℂ) : ∀ n : ℕ, exp (n * x) = exp x ^ n
   | 0 => by rw [Nat.cast_zero, MulZeroClass.zero_mul, exp_zero, pow_zero]
@@ -1066,7 +1066,7 @@ theorem sinh_sub_cosh : sinh x - cosh x = -exp (-x) := by rw [← neg_sub, cosh_
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cosh 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} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sinh x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
 but is expected to have type
-  forall (x : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (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))))))) (Complex.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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))))))) (Complex.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+  forall (x : Complex), Eq.{1} Complex (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (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.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
 Case conversion may be inaccurate. Consider using '#align complex.cosh_sq_sub_sinh_sq Complex.cosh_sq_sub_sinh_sqₓ'. -/
 @[simp]
 theorem cosh_sq_sub_sinh_sq : cosh x ^ 2 - sinh x ^ 2 = 1 := by
@@ -1077,7 +1077,7 @@ theorem cosh_sq_sub_sinh_sq : cosh x ^ 2 - sinh x ^ 2 = 1 := by
 lean 3 declaration is
   forall (x : Complex), 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.cosh x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sinh x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
 but is expected to have type
-  forall (x : Complex), 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Complex.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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))))))) (Complex.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+  forall (x : Complex), 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.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.cosh_sq Complex.cosh_sqₓ'. -/
 theorem cosh_sq : cosh x ^ 2 = sinh x ^ 2 + 1 :=
   by
@@ -1089,7 +1089,7 @@ theorem cosh_sq : cosh x ^ 2 = sinh x ^ 2 + 1 :=
 lean 3 declaration is
   forall (x : Complex), 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.sinh x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cosh x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))
 but is expected to have type
-  forall (x : Complex), 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Complex.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (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))))))) (Complex.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
+  forall (x : Complex), 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.sinh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (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.cosh x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))
 Case conversion may be inaccurate. Consider using '#align complex.sinh_sq Complex.sinh_sqₓ'. -/
 theorem sinh_sq : sinh x ^ 2 = cosh x ^ 2 - 1 :=
   by
@@ -1501,7 +1501,7 @@ theorem cos_sub_sin_I : cos x - sin x * I = exp (-x * I) := by
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sin 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} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
 but is expected to have type
-  forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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))))))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+  forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
 Case conversion may be inaccurate. Consider using '#align complex.sin_sq_add_cos_sq Complex.sin_sq_add_cos_sqₓ'. -/
 @[simp]
 theorem sin_sq_add_cos_sq : sin x ^ 2 + cos x ^ 2 = 1 :=
@@ -1513,7 +1513,7 @@ theorem sin_sq_add_cos_sq : sin x ^ 2 + cos x ^ 2 = 1 :=
 lean 3 declaration is
   forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cos 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} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))
 but is expected to have type
-  forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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))))))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
+  forall (x : Complex), Eq.{1} Complex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (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.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))
 Case conversion may be inaccurate. Consider using '#align complex.cos_sq_add_sin_sq Complex.cos_sq_add_sin_sqₓ'. -/
 @[simp]
 theorem cos_sq_add_sin_sq : cos x ^ 2 + sin x ^ 2 = 1 := by rw [add_comm, sin_sq_add_cos_sq]
@@ -1541,7 +1541,7 @@ theorem sin_two_mul : sin (2 * x) = 2 * sin x * cos x := by
 lean 3 declaration is
   forall (x : Complex), 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.cos x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (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)))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (OfNat.ofNat.{0} Complex 2 (OfNat.mk.{0} Complex 2 (bit0.{0} Complex Complex.hasAdd (One.one.{0} Complex Complex.hasOne))))) (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)))) (Complex.cos (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)))) x)) (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 (x : Complex), 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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)))))) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (Complex.cos (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))))) x)) (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 (x : Complex), 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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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)))))) (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (Complex.cos (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))))) x)) (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.cos_sq Complex.cos_sqₓ'. -/
 theorem cos_sq : cos x ^ 2 = 1 / 2 + cos (2 * x) / 2 := by
   simp [cos_two_mul, div_add_div_same, mul_div_cancel_left, two_ne_zero, -one_div]
@@ -1551,7 +1551,7 @@ theorem cos_sq : cos x ^ 2 = 1 / 2 + cos (2 * x) / 2 := by
 lean 3 declaration is
   forall (x : Complex), 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.cos x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sin 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} 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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))))))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall (x : Complex), 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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.cos_sq' Complex.cos_sq'ₓ'. -/
 theorem cos_sq' : cos x ^ 2 = 1 - sin x ^ 2 := by rw [← sin_sq_add_cos_sq x, add_sub_cancel']
 #align complex.cos_sq' Complex.cos_sq'
@@ -1560,7 +1560,7 @@ theorem cos_sq' : cos x ^ 2 = 1 - sin x ^ 2 := by rw [← sin_sq_add_cos_sq x, a
 lean 3 declaration is
   forall (x : Complex), 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.sin x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cos 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} 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall (x : Complex), 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.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.sin_sq Complex.sin_sqₓ'. -/
 theorem sin_sq : sin x ^ 2 = 1 - cos x ^ 2 := by rw [← sin_sq_add_cos_sq x, add_sub_cancel]
 #align complex.sin_sq Complex.sin_sq
@@ -1569,7 +1569,7 @@ theorem sin_sq : sin x ^ 2 = 1 - cos x ^ 2 := by rw [← sin_sq_add_cos_sq x, ad
 lean 3 declaration is
   forall {x : Complex}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (Eq.{1} Complex (Inv.inv.{0} Complex Complex.hasInv (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.tan 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} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.cos 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}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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))))))) (Complex.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (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))))))) (Complex.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall {x : Complex}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Eq.{1} Complex (Inv.inv.{0} Complex Complex.instInvComplex (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (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.cos x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.inv_one_add_tan_sq Complex.inv_one_add_tan_sqₓ'. -/
 theorem inv_one_add_tan_sq {x : ℂ} (hx : cos x ≠ 0) : (1 + tan x ^ 2)⁻¹ = cos x ^ 2 :=
   by
@@ -1582,7 +1582,7 @@ theorem inv_one_add_tan_sq {x : ℂ} (hx : cos x ≠ 0) : (1 + tan x ^ 2)⁻¹ =
 lean 3 declaration is
   forall {x : Complex}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (OfNat.mk.{0} Complex 0 (Zero.zero.{0} Complex Complex.hasZero)))) -> (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)))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.tan x) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.tan 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} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) (Complex.sin 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}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Eq.{1} Complex (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) (Complex.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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))))))) (Complex.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (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))))))) (Complex.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+  forall {x : Complex}, (Ne.{1} Complex (Complex.cos x) (OfNat.ofNat.{0} Complex 0 (Zero.toOfNat0.{0} Complex Complex.instZeroComplex))) -> (Eq.{1} Complex (HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (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.tan x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))) (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.sin x) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
 Case conversion may be inaccurate. Consider using '#align complex.tan_sq_div_one_add_tan_sq Complex.tan_sq_div_one_add_tan_sqₓ'. -/
 theorem tan_sq_div_one_add_tan_sq {x : ℂ} (hx : cos x ≠ 0) :
     tan x ^ 2 / (1 + tan x ^ 2) = sin x ^ 2 := by
@@ -1692,7 +1692,7 @@ theorem exp_ofReal_mul_I_im (x : ℝ) : (exp (x * I)).im = Real.sin x := by
 lean 3 declaration is
   forall (n : Nat) (z : Complex), 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))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (Complex.cos z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.sin z) Complex.I)) n) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (Complex.cos (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) 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) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) (Complex.sin (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) 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) z)) Complex.I))
 but is expected to have type
-  forall (n : Nat) (z : Complex), 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 (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin z) Complex.I)) n) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) z)) Complex.I))
+  forall (n : Nat) (z : Complex), 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)))) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin z) Complex.I)) n) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) z)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) n) z)) Complex.I))
 Case conversion may be inaccurate. Consider using '#align complex.cos_add_sin_mul_I_pow Complex.cos_add_sin_mul_I_powₓ'. -/
 /-- **De Moivre's formula** -/
 theorem cos_add_sin_mul_I_pow (n : ℕ) (z : ℂ) :
@@ -2633,7 +2633,7 @@ theorem sum_div_factorial_le {α : Type _} [LinearOrderedField α] (n j : ℕ) (
 lean 3 declaration is
   forall {x : 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 x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (forall {n : Nat}, (LT.lt.{0} Nat Nat.hasLt (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n) -> (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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Finset.range n) (fun (m : Nat) => 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)))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) x m) ((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))))) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (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) n) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((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))) (Nat.succ n)) (Inv.inv.{0} Real Real.hasInv (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((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))) (Nat.factorial 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 {x : Complex}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMulReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : 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) n) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast (Nat.succ n)) (Inv.inv.{0} Real Real.instInvReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)) (Nat.cast.{0} Real Real.natCast n)))))))
+  forall {x : Complex}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (forall {n : Nat}, (LT.lt.{0} Nat instLTNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMulReal) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : 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) n) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast (Nat.succ n)) (Inv.inv.{0} Real Real.instInvReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Nat.cast.{0} Real Real.natCast (Nat.factorial n)) (Nat.cast.{0} Real Real.natCast n)))))))
 Case conversion may be inaccurate. Consider using '#align complex.exp_bound Complex.exp_boundₓ'. -/
 theorem exp_bound {x : ℂ} (hx : abs x ≤ 1) {n : ℕ} (hn : 0 < n) :
     abs (exp x - ∑ m in range n, x ^ m / m !) ≤ abs x ^ n * (n.succ * (n ! * n)⁻¹) :=
@@ -2674,7 +2674,7 @@ theorem exp_bound {x : ℂ} (hx : abs x ≤ 1) {n : ℕ} (hn : 0 < n) :
 lean 3 declaration is
   forall {x : Complex} {n : Nat}, (LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{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 x) ((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))) (Nat.succ n))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) -> (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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Finset.range n) (fun (m : Nat) => 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)))) (HPow.hPow.{0, 0, 0} Complex Nat Complex (instHPow.{0, 0} Complex Nat (Monoid.Pow.{0} Complex (Ring.toMonoid.{0} Complex Complex.ring))) x m) ((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))))) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (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) 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))) (Nat.factorial n))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
 but is expected to have type
-  forall {x : Complex} {n : Nat}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLEReal (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.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) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.natCast (Nat.succ n))) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMulReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : 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) n) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) Real.natCast (Nat.factorial n))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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))))))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+  forall {x : Complex} {n : Nat}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLEReal (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (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) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.natCast (Nat.succ n))) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instMulReal) (HDiv.hDiv.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (instHDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) (LinearOrderedField.toDiv.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instLinearOrderedFieldReal)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : 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) n) (Nat.cast.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) Real.natCast (Nat.factorial n))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (Finset.sum.{0, 0} Complex Nat (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Finset.range n) (fun (m : Nat) => HDiv.hDiv.{0, 0, 0} Complex Complex Complex (instHDiv.{0} Complex (Field.toDiv.{0} Complex Complex.instFieldComplex)) (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)))) x m) (Nat.cast.{0} Complex (NonAssocRing.toNatCast.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)) (Nat.factorial m)))))) 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
 Case conversion may be inaccurate. Consider using '#align complex.exp_bound' Complex.exp_bound'ₓ'. -/
 theorem exp_bound' {x : ℂ} {n : ℕ} (hx : abs x / n.succ ≤ 1 / 2) :
     abs (exp x - ∑ m in range n, x ^ m / m !) ≤ abs x ^ n / n ! * 2 :=
@@ -2720,7 +2720,7 @@ theorem exp_bound' {x : ℂ} {n : ℕ} (hx : abs x / n.succ ≤ 1 / 2) :
 lean 3 declaration is
   forall {x : 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 x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.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)))
 but is expected to have type
-  forall {x : Complex}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 2 Real.natCast (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 x)))
+  forall {x : Complex}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) (HMul.hMul.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) (instHMul.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) Real.instMulReal) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 2 (instOfNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)))) 2 Real.natCast (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 x)))
 Case conversion may be inaccurate. Consider using '#align complex.abs_exp_sub_one_le Complex.abs_exp_sub_one_leₓ'. -/
 theorem abs_exp_sub_one_le {x : ℂ} (hx : abs x ≤ 1) : abs (exp x - 1) ≤ 2 * abs x :=
   calc
@@ -2734,7 +2734,7 @@ theorem abs_exp_sub_one_le {x : ℂ} (hx : abs x ≤ 1) : abs (exp x - 1) ≤ 2
 lean 3 declaration is
   forall {x : 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 x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) -> (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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.hasSub) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne)))) 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}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) x)) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) x)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 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}, (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 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 x) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Real.instOneReal))) -> (LE.le.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) x)) 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 (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) x)) (HPow.hPow.{0, 0, 0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) x) Nat ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (HSub.hSub.{0, 0, 0} Complex Complex Complex (instHSub.{0} Complex Complex.instSubComplex) (Complex.exp x) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex))) 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.abs_exp_sub_one_sub_id_le Complex.abs_exp_sub_one_sub_id_leₓ'. -/
 theorem abs_exp_sub_one_sub_id_le {x : ℂ} (hx : abs x ≤ 1) : abs (exp x - 1 - x) ≤ abs x ^ 2 :=
   calc
@@ -3256,7 +3256,7 @@ namespace Complex
 lean 3 declaration is
   forall (x : 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 (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.hasAdd) (Complex.cos ((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) (Complex.sin ((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)) Complex.I))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) 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 (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) Real.instOneReal))
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) 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 (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.cos (Complex.ofReal' x)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.sin (Complex.ofReal' x)) Complex.I))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_cos_add_sin_mul_I Complex.abs_cos_add_sin_mul_Iₓ'. -/
 @[simp]
 theorem abs_cos_add_sin_mul_I (x : ℝ) : abs (cos x + sin x * I) = 1 :=
@@ -3269,7 +3269,7 @@ theorem abs_cos_add_sin_mul_I (x : ℝ) : abs (cos x + sin x * I) = 1 :=
 lean 3 declaration is
   forall (x : 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 (Complex.exp ((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))) (Real.exp x)
 but is expected to have type
-  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (Complex.ofReal' x))) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.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.exp (Complex.ofReal' x))) (Real.exp x)
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (Complex.ofReal' x))) (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.exp (Complex.ofReal' x))) (Real.exp x)
 Case conversion may be inaccurate. Consider using '#align complex.abs_exp_of_real Complex.abs_exp_ofRealₓ'. -/
 @[simp]
 theorem abs_exp_ofReal (x : ℝ) : abs (exp x) = Real.exp x := by
@@ -3280,7 +3280,7 @@ theorem abs_exp_ofReal (x : ℝ) : abs (exp x) = Real.exp x := by
 lean 3 declaration is
   forall (x : 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 (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Complex (HasLiftT.mk.{1, 1} Real Complex (CoeTCₓ.coe.{1, 1} Real Complex (coeBase.{1, 1} Real Complex Complex.hasCoe))) x) Complex.I))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
 but is expected to have type
-  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) 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.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) Real.instOneReal))
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) 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.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) Complex.I))) Real.instOneReal))
 Case conversion may be inaccurate. Consider using '#align complex.abs_exp_of_real_mul_I Complex.abs_exp_ofReal_mul_Iₓ'. -/
 @[simp]
 theorem abs_exp_ofReal_mul_I (x : ℝ) : abs (exp (x * I)) = 1 := by
@@ -3291,7 +3291,7 @@ theorem abs_exp_ofReal_mul_I (x : ℝ) : abs (exp (x * I)) = 1 := by
 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 (Complex.exp z)) (Real.exp (Complex.re z))
 but is expected to have type
-  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp 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 (Complex.exp z)) (Real.exp (Complex.re z))
+  forall (z : Complex), Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp 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 (Complex.exp z)) (Real.exp (Complex.re z))
 Case conversion may be inaccurate. Consider using '#align complex.abs_exp Complex.abs_expₓ'. -/
 theorem abs_exp (z : ℂ) : abs (exp z) = Real.exp z.re := by
   rw [exp_eq_exp_re_mul_sin_add_cos, map_mul, abs_exp_of_real, abs_cos_add_sin_mul_I, mul_one]
@@ -3301,7 +3301,7 @@ theorem abs_exp (z : ℂ) : abs (exp z) = Real.exp z.re := by
 lean 3 declaration is
   forall {x : Complex} {y : Complex}, Iff (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.exp x)) (coeFn.{1, 1} (AbsoluteValue.{0, 0} Complex Real (Ring.toSemiring.{0} Complex Complex.ring) Real.orderedSemiring) (fun (f : AbsoluteValue.{0, 0} Complex Real (Ring.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.exp y))) (Eq.{1} Real (Complex.re x) (Complex.re y))
 but is expected to have type
-  forall {x : Complex} {y : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp x)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.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.exp x)) (FunLike.coe.{1, 1, 1} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex (fun (f : Complex) => (fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) f) (SubadditiveHomClass.toFunLike.{0, 0, 0} (AbsoluteValue.{0, 0} Complex Real (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))) Real.orderedSemiring) Complex Real (Distrib.toAdd.{0} Complex (NonUnitalNonAssocSemiring.toDistrib.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (DivisionSemiring.toSemiring.{0} Complex (Semifield.toDivisionSemiring.{0} Complex (Field.toSemifield.{0} Complex Complex.instFieldComplex))))))) (Distrib.toAdd.{0} Real (NonUnitalNonAssocSemiring.toDistrib.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (OrderedSemiring.toSemiring.{0} Real Real.orderedSemiring))))) (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (OrderedSemiring.toPartialOrder.{0} Real Real.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.exp y))) (Eq.{1} Real (Complex.re x) (Complex.re y))
+  forall {x : Complex} {y : Complex}, Iff (Eq.{1} ((fun (x._@.Mathlib.Algebra.Order.Hom.Basic._hyg.99 : Complex) => Real) (Complex.exp x)) (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.exp x)) (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.exp y))) (Eq.{1} Real (Complex.re x) (Complex.re y))
 Case conversion may be inaccurate. Consider using '#align complex.abs_exp_eq_iff_re_eq Complex.abs_exp_eq_iff_re_eqₓ'. -/
 theorem abs_exp_eq_iff_re_eq {x y : ℂ} : abs (exp x) = abs (exp y) ↔ x.re = y.re := by
   rw [abs_exp, abs_exp, Real.exp_eq_exp]
diff --git a/Mathbin/Data/Complex/Module.lean b/Mathbin/Data/Complex/Module.lean
index c595e06a58..c1fade1094 100644
--- a/Mathbin/Data/Complex/Module.lean
+++ b/Mathbin/Data/Complex/Module.lean
@@ -61,12 +61,30 @@ variable [SMul R ℝ]
 `restrict_scalars.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⟩
 
+/- warning: complex.smul_re -> Complex.smul_re is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : SMul.{u1, 0} R Real] (r : R) (z : Complex), Eq.{1} Real (Complex.re (SMul.smul.{u1, 0} R Complex (Complex.hasSmul.{u1} R _inst_1) r z)) (SMul.smul.{u1, 0} R Real _inst_1 r (Complex.re z))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : SMul.{u1, 0} R Real] (r : R) (z : Complex), Eq.{1} Real (Complex.re (HSMul.hSMul.{u1, 0, 0} R Complex Complex (instHSMul.{u1, 0} R Complex (Complex.instSMulComplex.{u1} R _inst_1)) r z)) (HSMul.hSMul.{u1, 0, 0} R Real Real (instHSMul.{u1, 0} R Real _inst_1) r (Complex.re z))
+Case conversion may be inaccurate. Consider using '#align complex.smul_re Complex.smul_reₓ'. -/
 theorem smul_re (r : R) (z : ℂ) : (r • z).re = r • z.re := by simp [(· • ·)]
 #align complex.smul_re Complex.smul_re
 
+/- warning: complex.smul_im -> Complex.smul_im is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_1 : SMul.{u1, 0} R Real] (r : R) (z : Complex), Eq.{1} Real (Complex.im (SMul.smul.{u1, 0} R Complex (Complex.hasSmul.{u1} R _inst_1) r z)) (SMul.smul.{u1, 0} R Real _inst_1 r (Complex.im z))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : SMul.{u1, 0} R Real] (r : R) (z : Complex), Eq.{1} Real (Complex.im (HSMul.hSMul.{u1, 0, 0} R Complex Complex (instHSMul.{u1, 0} R Complex (Complex.instSMulComplex.{u1} R _inst_1)) r z)) (HSMul.hSMul.{u1, 0, 0} R Real Real (instHSMul.{u1, 0} R Real _inst_1) r (Complex.im z))
+Case conversion may be inaccurate. Consider using '#align complex.smul_im Complex.smul_imₓ'. -/
 theorem smul_im (r : R) (z : ℂ) : (r • z).im = r • z.im := by simp [(· • ·)]
 #align complex.smul_im Complex.smul_im
 
+/- warning: complex.real_smul -> Complex.real_smul is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {z : Complex}, Eq.{1} Complex (SMul.smul.{0, 0} Real Complex (Complex.hasSmul.{0} Real (Mul.toSMul.{0} Real Real.hasMul)) x 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))) x) z)
+but is expected to have type
+  forall {x : Real} {z : Complex}, Eq.{1} Complex (HSMul.hSMul.{0, 0, 0} Real Complex Complex (instHSMul.{0, 0} Real Complex (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal)))) x z) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' x) z)
+Case conversion may be inaccurate. Consider using '#align complex.real_smul Complex.real_smulₓ'. -/
 @[simp]
 theorem real_smul {x : ℝ} {z : ℂ} : x • z = x * z :=
   rfl
@@ -110,6 +128,12 @@ instance [CommSemiring R] [Algebra R ℝ] : Algebra R ℂ :=
 instance : StarModule ℝ ℂ :=
   ⟨fun r x => by simp only [star_def, star_trivial, real_smul, map_mul, conj_of_real]⟩
 
+/- warning: complex.coe_algebra_map -> Complex.coe_algebraMap is a dubious translation:
+lean 3 declaration is
+  Eq.{1} ((fun (_x : RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) => Real -> Complex) (algebraMap.{0, 0} Real Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)))) (coeFn.{1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) (fun (_x : RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) => Real -> Complex) (RingHom.hasCoeToFun.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) (algebraMap.{0, 0} Real Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)))) ((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
+  Eq.{1} (forall (a : Real), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Real) => Complex) a) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (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 (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonUnitalNonAssocSemiring.toMul.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)))) (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 (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex) (RingHom.instRingHomClassRingHom.{0, 0} Real Complex (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal)) (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) (algebraMap.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))) Complex.ofReal'
+Case conversion may be inaccurate. Consider using '#align complex.coe_algebra_map Complex.coe_algebraMapₓ'. -/
 @[simp]
 theorem coe_algebraMap : (algebraMap ℝ ℂ : ℝ → ℂ) = coe :=
   rfl
@@ -119,6 +143,12 @@ section
 
 variable {A : Type _} [Semiring A] [Algebra ℝ A]
 
+/- warning: alg_hom.map_coe_real_complex -> AlgHom.map_coe_real_complex is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : Semiring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.commSemiring _inst_1] (f : AlgHom.{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) _inst_1 (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2) (x : Real), Eq.{succ u1} A (coeFn.{succ u1, succ u1} (AlgHom.{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) _inst_1 (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2) (fun (_x : AlgHom.{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) _inst_1 (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2) => Complex -> A) ([anonymous].{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) _inst_1 (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2) f ((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)) (coeFn.{succ u1, succ u1} (RingHom.{0, u1} Real A (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} A _inst_1)) (fun (_x : RingHom.{0, u1} Real A (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} A _inst_1)) => Real -> A) (RingHom.hasCoeToFun.{0, u1} Real A (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (Semiring.toNonAssocSemiring.{u1} A _inst_1)) (algebraMap.{0, u1} Real A Real.commSemiring _inst_1 _inst_2) x)
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : Semiring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.instCommSemiringReal _inst_1] (f : AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) (x : Real), Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Complex) => A) (Complex.ofReal' x)) (FunLike.coe.{succ u1, 1, succ u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Complex) => A) _x) (SMulHomClass.toFunLike.{u1, 0, 0, u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (SMulZeroClass.toSMul.{0, 0} Real Complex (AddMonoid.toZero.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) (DistribSMul.toSMulZeroClass.{0, 0} Real Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) (DistribMulAction.toDistribSMul.{0, 0} Real Complex (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Algebra.toModule.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))))))) (SMulZeroClass.toSMul.{0, u1} Real A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1))))) (DistribSMul.toSMulZeroClass.{0, u1} Real A 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Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1)))) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex 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+Case conversion may be inaccurate. Consider using '#align alg_hom.map_coe_real_complex AlgHom.map_coe_real_complexₓ'. -/
 /-- We need this lemma since `complex.coe_algebra_map` diverts the simp-normal form away from
 `alg_hom.commutes`. -/
 @[simp]
@@ -126,6 +156,12 @@ theorem AlgHom.map_coe_real_complex (f : ℂ →ₐ[ℝ] A) (x : ℝ) : f x = al
   f.commutes x
 #align alg_hom.map_coe_real_complex AlgHom.map_coe_real_complex
 
+/- warning: complex.alg_hom_ext -> Complex.algHom_ext is a dubious translation:
+lean 3 declaration is
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Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1)))) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Algebra.toModule.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))) (Module.toDistribMulAction.{0, u1} Real A (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1))) (Algebra.toModule.{0, u1} Real A Real.instCommSemiringReal _inst_1 _inst_2)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, 0, u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1)) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Algebra.toModule.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))) (Module.toDistribMulAction.{0, u1} Real A (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_1))) (Algebra.toModule.{0, u1} Real A Real.instCommSemiringReal _inst_1 _inst_2)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{0, 0, u1, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2 (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) (AlgHom.algHomClass.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2))))) g Complex.I)) -> (Eq.{succ u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex _inst_1 (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) f g)
+Case conversion may be inaccurate. Consider using '#align complex.alg_hom_ext Complex.algHom_extₓ'. -/
 /-- Two `ℝ`-algebra homomorphisms from ℂ are equal if they agree on `complex.I`. -/
 @[ext]
 theorem algHom_ext ⦃f g : ℂ →ₐ[ℝ] A⦄ (h : f I = g I) : f = g :=
@@ -140,6 +176,12 @@ section
 
 open ComplexOrder
 
+/- warning: complex.ordered_smul -> Complex.orderedSMul is a dubious translation:
+lean 3 declaration is
+  OrderedSMul.{0, 0} Real Complex Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{0} Complex (StrictOrderedSemiring.toOrderedSemiring.{0} Complex (StrictOrderedRing.toStrictOrderedSemiring.{0} Complex (StrictOrderedCommRing.toStrictOrderedRing.{0} Complex Complex.strictOrderedCommRing)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex Real.monoidWithZero (AddZeroClass.toHasZero.{0} Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (OrderedAddCommMonoid.toAddCommMonoid.{0} Complex (OrderedSemiring.toOrderedAddCommMonoid.{0} Complex (StrictOrderedSemiring.toOrderedSemiring.{0} Complex (StrictOrderedRing.toStrictOrderedSemiring.{0} Complex (StrictOrderedCommRing.toStrictOrderedRing.{0} Complex Complex.strictOrderedCommRing)))))))) (Module.toMulActionWithZero.{0, 0} Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))))
+but is expected to have type
+  OrderedSMul.{0, 0} Real Complex Real.orderedSemiring (OrderedSemiring.toOrderedAddCommMonoid.{0} Complex (OrderedCommSemiring.toOrderedSemiring.{0} Complex (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Complex (StrictOrderedCommRing.toStrictOrderedCommSemiring.{0} Complex Complex.strictOrderedCommRing)))) (MulActionWithZero.toSMulWithZero.{0, 0} Real Complex Real.instMonoidWithZeroReal (AddMonoid.toZero.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (OrderedAddCommMonoid.toAddCommMonoid.{0} Complex (OrderedSemiring.toOrderedAddCommMonoid.{0} Complex (OrderedCommSemiring.toOrderedSemiring.{0} Complex (StrictOrderedCommSemiring.toOrderedCommSemiring.{0} Complex (StrictOrderedCommRing.toStrictOrderedCommSemiring.{0} Complex Complex.strictOrderedCommRing))))))) (Module.toMulActionWithZero.{0, 0} Real Complex Real.semiring (OrderedCancelAddCommMonoid.toAddCommMonoid.{0} Complex (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Complex (StrictOrderedCommSemiring.toStrictOrderedSemiring.{0} Complex (StrictOrderedCommRing.toStrictOrderedCommSemiring.{0} Complex Complex.strictOrderedCommRing)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))))
+Case conversion may be inaccurate. Consider using '#align complex.ordered_smul Complex.orderedSMulₓ'. -/
 protected theorem orderedSMul : OrderedSMul ℝ ℂ :=
   OrderedSMul.mk' fun a b r hab hr => ⟨by simp [hr, hab.1.le], by simp [hab.2]⟩
 #align complex.ordered_smul Complex.orderedSMul
@@ -150,6 +192,12 @@ end
 
 open Submodule FiniteDimensional
 
+/- warning: complex.basis_one_I -> Complex.basisOneI is a dubious translation:
+lean 3 declaration is
+  Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))
+but is expected to have type
+  Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real Complex Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))
+Case conversion may be inaccurate. Consider using '#align complex.basis_one_I Complex.basisOneIₓ'. -/
 /-- `ℂ` has a basis over `ℝ` given by `1` and `I`. -/
 noncomputable def basisOneI : Basis (Fin 2) ℝ ℂ :=
   Basis.ofEquivFun
@@ -164,11 +212,23 @@ noncomputable def basisOneI : Basis (Fin 2) ℝ ℂ :=
       map_smul' := fun c z => by simp [Matrix.smul_cons c z.re, Matrix.smul_cons c z.im] }
 #align complex.basis_one_I Complex.basisOneI
 
+/- warning: complex.coe_basis_one_I_repr -> Complex.coe_basisOneI_repr is a dubious translation:
+lean 3 declaration is
+  forall (z : Complex), Eq.{1} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (coeFn.{1, 1} (Finsupp.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) (fun (_x : Finsupp.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))))) => (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (Finsupp.coeFun.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} 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+but is expected to have type
+  forall (z : Complex), Eq.{1} (forall (ᾰ : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (Finsupp.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => Real) _x) (Finsupp.funLike.{0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring))) (FunLike.coe.{1, 1, 1} (LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) 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+Case conversion may be inaccurate. Consider using '#align complex.coe_basis_one_I_repr Complex.coe_basisOneI_reprₓ'. -/
 @[simp]
 theorem coe_basisOneI_repr (z : ℂ) : ⇑(basisOneI.repr z) = ![z.re, z.im] :=
   rfl
 #align complex.coe_basis_one_I_repr Complex.coe_basisOneI_repr
 
+/- warning: complex.coe_basis_one_I -> Complex.coe_basisOneI is a dubious translation:
+lean 3 declaration is
+  Eq.{1} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Complex) (coeFn.{1, 1} (Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (fun (_x : Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) => (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Complex) (FunLike.hasCoeToFun.{1, 1, 1} (Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) => Complex) (Basis.funLike.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)))) Complex.basisOneI) (Matrix.vecCons.{0} Complex (Nat.succ (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (OfNat.ofNat.{0} Complex 1 (OfNat.mk.{0} Complex 1 (One.one.{0} Complex Complex.hasOne))) (Matrix.vecCons.{0} Complex (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) Complex.I (Matrix.vecEmpty.{0} Complex)))
+but is expected to have type
+  Eq.{1} (forall (a : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))), (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => Complex) a) (FunLike.coe.{1, 1, 1} (Basis.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real Complex Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (fun (_x : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) => Complex) _x) (Basis.funLike.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) Real Complex Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) Complex.basisOneI) (Matrix.vecCons.{0} Complex (Nat.succ (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex Complex.instOneComplex)) (Matrix.vecCons.{0} Complex (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) Complex.I (Matrix.vecEmpty.{0} Complex)))
+Case conversion may be inaccurate. Consider using '#align complex.coe_basis_one_I Complex.coe_basisOneIₓ'. -/
 @[simp]
 theorem coe_basisOneI : ⇑basisOneI = ![1, I] :=
   funext fun i =>
@@ -183,19 +243,43 @@ theorem coe_basisOneI : ⇑basisOneI = ![1, I] :=
 instance : FiniteDimensional ℝ ℂ :=
   of_fintype_basis basisOneI
 
+/- warning: complex.finrank_real_complex -> Complex.finrank_real_complex is a dubious translation:
+lean 3 declaration is
+  Eq.{1} Nat (FiniteDimensional.finrank.{0, 0} Real Complex Real.semiring Complex.addCommGroup (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (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
+  Eq.{1} Nat (FiniteDimensional.finrank.{0, 0} Real Complex Real.semiring Complex.addCommGroup (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))
+Case conversion may be inaccurate. Consider using '#align complex.finrank_real_complex Complex.finrank_real_complexₓ'. -/
 @[simp]
 theorem finrank_real_complex : FiniteDimensional.finrank ℝ ℂ = 2 := by
   rw [finrank_eq_card_basis basis_one_I, Fintype.card_fin]
 #align complex.finrank_real_complex Complex.finrank_real_complex
 
+/- warning: complex.rank_real_complex -> Complex.rank_real_complex is a dubious translation:
+lean 3 declaration is
+  Eq.{2} Cardinal.{0} (Module.rank.{0, 0} Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (OfNat.ofNat.{1} Cardinal.{0} 2 (OfNat.mk.{1} Cardinal.{0} 2 (bit0.{1} Cardinal.{0} Cardinal.hasAdd.{0} (One.one.{1} Cardinal.{0} Cardinal.hasOne.{0}))))
+but is expected to have type
+  Eq.{2} Cardinal.{0} (Module.rank.{0, 0} Real Complex Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (OfNat.ofNat.{1} Cardinal.{0} 2 (instOfNat.{1} Cardinal.{0} 2 Cardinal.instNatCastCardinal.{0} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align complex.rank_real_complex Complex.rank_real_complexₓ'. -/
 @[simp]
 theorem rank_real_complex : Module.rank ℝ ℂ = 2 := by simp [← finrank_eq_rank, finrank_real_complex]
 #align complex.rank_real_complex Complex.rank_real_complex
 
+/- warning: complex.rank_real_complex' -> Complex.rank_real_complex' is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.lift.{u1, 0} (Module.rank.{0, 0} Real Complex Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))))
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.lift.{u1, 0} (Module.rank.{0, 0} Real Complex Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+Case conversion may be inaccurate. Consider using '#align complex.rank_real_complex' Complex.rank_real_complex'ₓ'. -/
 theorem rank_real_complex'.{u} : Cardinal.lift.{u} (Module.rank ℝ ℂ) = 2 := by
   simp [← finrank_eq_rank, finrank_real_complex, bit0]
 #align complex.rank_real_complex' Complex.rank_real_complex'
 
+/- warning: complex.finrank_real_complex_fact -> Complex.finrank_real_complex_fact is a dubious translation:
+lean 3 declaration is
+  Fact (Eq.{1} Nat (FiniteDimensional.finrank.{0, 0} Real Complex Real.semiring Complex.addCommGroup (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (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
+  Fact (Eq.{1} Nat (FiniteDimensional.finrank.{0, 0} Real Complex Real.semiring Complex.addCommGroup (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))
+Case conversion may be inaccurate. Consider using '#align complex.finrank_real_complex_fact Complex.finrank_real_complex_factₓ'. -/
 /-- `fact` version of the dimension of `ℂ` over `ℝ`, locally useful in the definition of the
 circle. -/
 theorem finrank_real_complex_fact : Fact (finrank ℝ ℂ = 2) :=
@@ -204,36 +288,64 @@ theorem finrank_real_complex_fact : Fact (finrank ℝ ℂ = 2) :=
 
 end Complex
 
+#print Module.complexToReal /-
 /- Register as an instance (with low priority) the fact that a complex vector space is also a real
 vector space. -/
 instance (priority := 900) Module.complexToReal (E : Type _) [AddCommGroup E] [Module ℂ E] :
     Module ℝ E :=
   RestrictScalars.module ℝ ℂ E
 #align module.complex_to_real Module.complexToReal
+-/
 
+/- warning: module.real_complex_tower -> Module.real_complex_tower is a dubious translation:
+lean 3 declaration is
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+  forall (E : Type.{u1}) [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)], IsScalarTower.{0, 0, u1} Real Complex E (Complex.instSMulComplex.{0} Real (Algebra.toSMul.{0, 0} Real Real Real.instCommSemiringReal Real.semiring (Algebra.id.{0} Real Real.instCommSemiringReal))) (SMulZeroClass.toSMul.{0, u1} Complex E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2)))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (Module.complexToReal.{u1} E _inst_1 _inst_2)))))
+Case conversion may be inaccurate. Consider using '#align module.real_complex_tower Module.real_complex_towerₓ'. -/
 instance Module.real_complex_tower (E : Type _) [AddCommGroup E] [Module ℂ E] :
     IsScalarTower ℝ ℂ E :=
   RestrictScalars.isScalarTower ℝ ℂ E
 #align module.real_complex_tower Module.real_complex_tower
 
+/- warning: complex.coe_smul -> Complex.coe_smul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complex.coe_smul Complex.coe_smulₓ'. -/
 @[simp, norm_cast]
 theorem Complex.coe_smul {E : Type _} [AddCommGroup E] [Module ℂ E] (x : ℝ) (y : E) :
     (x : ℂ) • y = x • y :=
   rfl
 #align complex.coe_smul Complex.coe_smul
 
+#print SMulCommClass.complexToReal /-
 /-- The scalar action of `ℝ` on a `ℂ`-module `E` induced by `module.complex_to_real` commutes with
 another scalar action of `M` on `E` whenever the action of `ℂ` commutes with the action of `M`. -/
 instance (priority := 900) SMulCommClass.complexToReal {M E : Type _} [AddCommGroup E] [Module ℂ E]
     [SMul M E] [SMulCommClass ℂ M E] : SMulCommClass ℝ M E
     where smul_comm r _ _ := (smul_comm (r : ℂ) _ _ : _)
 #align smul_comm_class.complex_to_real SMulCommClass.complexToReal
+-/
 
+/- warning: finite_dimensional.complex_to_real -> FiniteDimensional.complexToReal is a dubious translation:
+lean 3 declaration is
+  forall (E : Type.{u1}) [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : FiniteDimensional.{0, u1} Complex E (Field.toDivisionRing.{0} Complex Complex.field) _inst_1 _inst_2], FiniteDimensional.{0, u1} Real E Real.divisionRing _inst_1 (Module.complexToReal.{u1} E _inst_1 _inst_2)
+but is expected to have type
+  forall (E : Type.{u1}) [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_3 : FiniteDimensional.{0, u1} Complex E (Field.toDivisionRing.{0} Complex Complex.instFieldComplex) _inst_1 _inst_2], FiniteDimensional.{0, u1} Real E Real.instDivisionRingReal _inst_1 (Module.complexToReal.{u1} E _inst_1 _inst_2)
+Case conversion may be inaccurate. Consider using '#align finite_dimensional.complex_to_real FiniteDimensional.complexToRealₓ'. -/
 instance (priority := 100) FiniteDimensional.complexToReal (E : Type _) [AddCommGroup E]
     [Module ℂ E] [FiniteDimensional ℂ E] : FiniteDimensional ℝ E :=
   FiniteDimensional.trans ℝ ℂ E
 #align finite_dimensional.complex_to_real FiniteDimensional.complexToReal
 
+/- warning: rank_real_of_complex -> rank_real_of_complex is a dubious translation:
+lean 3 declaration is
+  forall (E : Type.{u1}) [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (Module.complexToReal.{u1} E _inst_1 _inst_2)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) (Module.rank.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2))
+but is expected to have type
+  forall (E : Type.{u1}) [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Module.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)], Eq.{succ (succ u1)} Cardinal.{u1} (Module.rank.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (Module.complexToReal.{u1} E _inst_1 _inst_2)) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Module.rank.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_2))
+Case conversion may be inaccurate. Consider using '#align rank_real_of_complex rank_real_of_complexₓ'. -/
 theorem rank_real_of_complex (E : Type _) [AddCommGroup E] [Module ℂ E] :
     Module.rank ℝ E = 2 * Module.rank ℂ E :=
   Cardinal.lift_inj.1 <|
@@ -242,11 +354,19 @@ theorem rank_real_of_complex (E : Type _) [AddCommGroup E] [Module ℂ E] :
     simp [bit0]
 #align rank_real_of_complex rank_real_of_complex
 
+#print finrank_real_of_complex /-
 theorem finrank_real_of_complex (E : Type _) [AddCommGroup E] [Module ℂ E] :
     FiniteDimensional.finrank ℝ E = 2 * FiniteDimensional.finrank ℂ E := by
   rw [← FiniteDimensional.finrank_mul_finrank ℝ ℂ E, Complex.finrank_real_complex]
 #align finrank_real_of_complex finrank_real_of_complex
+-/
 
+/- warning: star_module.complex_to_real -> StarModule.complexToReal is a dubious translation:
+lean 3 declaration is
+  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Star.{u1} E] [_inst_3 : Module.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_4 : StarModule.{0, u1} Complex E (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))) _inst_2 (SMulZeroClass.toHasSmul.{0, u1} Complex E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex E (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex E (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_3))))], StarModule.{0, u1} Real E (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) _inst_2 (SMulZeroClass.toHasSmul.{0, u1} Real E (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} E (AddMonoid.toAddZeroClass.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (Module.complexToReal.{u1} E _inst_1 _inst_3)))))
+but is expected to have type
+  forall {E : Type.{u1}} [_inst_1 : AddCommGroup.{u1} E] [_inst_2 : Star.{u1} E] [_inst_3 : Module.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1)] [_inst_4 : StarModule.{0, u1} Complex E (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))) _inst_2 (SMulZeroClass.toSMul.{0, u1} Complex E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex E Complex.instZeroComplex (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex E (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex E Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) _inst_3))))], StarModule.{0, u1} Real E (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) _inst_2 (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E _inst_1) (Module.complexToReal.{u1} E _inst_1 _inst_3)))))
+Case conversion may be inaccurate. Consider using '#align star_module.complex_to_real StarModule.complexToRealₓ'. -/
 instance (priority := 900) StarModule.complexToReal {E : Type _} [AddCommGroup E] [Star E]
     [Module ℂ E] [StarModule ℂ E] : StarModule ℝ E :=
   ⟨fun r a => by rw [← smul_one_smul ℂ r a, star_smul, star_smul, star_one, smul_one_smul]⟩
@@ -256,6 +376,12 @@ namespace Complex
 
 open ComplexConjugate
 
+/- warning: complex.re_lm -> Complex.reLm is a dubious translation:
+lean 3 declaration is
+  LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)
+but is expected to have type
+  LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)
+Case conversion may be inaccurate. Consider using '#align complex.re_lm Complex.reLmₓ'. -/
 /-- Linear map version of the real part function, from `ℂ` to `ℝ`. -/
 def reLm : ℂ →ₗ[ℝ] ℝ where
   toFun x := x.re
@@ -263,11 +389,23 @@ def reLm : ℂ →ₗ[ℝ] ℝ where
   map_smul' := by simp
 #align complex.re_lm Complex.reLm
 
+/- warning: complex.re_lm_coe -> Complex.reLm_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Complex -> Real) (coeFn.{1, 1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) (fun (_x : LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) => Complex -> Real) (LinearMap.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex.reLm) Complex.re
+but is expected to have type
+  Eq.{1} (forall (ᾰ : Complex), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Complex) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Complex) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, 0, 0} Real Real Complex Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex.reLm) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.re_lm_coe Complex.reLm_coeₓ'. -/
 @[simp]
 theorem reLm_coe : ⇑reLm = re :=
   rfl
 #align complex.re_lm_coe Complex.reLm_coe
 
+/- warning: complex.im_lm -> Complex.imLm is a dubious translation:
+lean 3 declaration is
+  LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)
+but is expected to have type
+  LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)
+Case conversion may be inaccurate. Consider using '#align complex.im_lm Complex.imLmₓ'. -/
 /-- Linear map version of the imaginary part function, from `ℂ` to `ℝ`. -/
 def imLm : ℂ →ₗ[ℝ] ℝ where
   toFun x := x.im
@@ -275,21 +413,41 @@ def imLm : ℂ →ₗ[ℝ] ℝ where
   map_smul' := by simp
 #align complex.im_lm Complex.imLm
 
+/- warning: complex.im_lm_coe -> Complex.imLm_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (Complex -> Real) (coeFn.{1, 1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) (fun (_x : LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) Complex Real (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) => Complex -> Real) (LinearMap.hasCoeToFun.{0, 0, 0, 0} Real Real Complex Real Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) Real.addCommMonoid (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) Complex.imLm) Complex.im
+but is expected to have type
+  Eq.{1} (forall (ᾰ : Complex), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Complex) => Real) ᾰ) (FunLike.coe.{1, 1, 1} (LinearMap.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) Complex Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring)) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : Complex) => Real) _x) (LinearMap.instFunLikeLinearMap.{0, 0, 0, 0} Real Real Complex Real Real.semiring Real.semiring (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Real.instAddCommMonoidReal (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Semiring.toModule.{0} Real Real.semiring) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) Complex.imLm) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.im_lm_coe Complex.imLm_coeₓ'. -/
 @[simp]
 theorem imLm_coe : ⇑imLm = im :=
   rfl
 #align complex.im_lm_coe Complex.imLm_coe
 
+/- warning: complex.of_real_am -> Complex.ofRealAm is a dubious translation:
+lean 3 declaration is
+  AlgHom.{0, 0, 0} Real Real Complex Real.commSemiring Real.semiring (Ring.toSemiring.{0} Complex Complex.ring) (Algebra.id.{0} Real Real.commSemiring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))
+but is expected to have type
+  AlgHom.{0, 0, 0} Real Real Complex Real.instCommSemiringReal Real.semiring Complex.instSemiringComplex (Algebra.id.{0} Real Real.instCommSemiringReal) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))
+Case conversion may be inaccurate. Consider using '#align complex.of_real_am Complex.ofRealAmₓ'. -/
 /-- `ℝ`-algebra morphism version of the canonical embedding of `ℝ` in `ℂ`. -/
 def ofRealAm : ℝ →ₐ[ℝ] ℂ :=
   Algebra.ofId ℝ ℂ
 #align complex.of_real_am Complex.ofRealAm
 
+#print Complex.ofRealAm_coe /-
 @[simp]
 theorem ofRealAm_coe : ⇑ofRealAm = coe :=
   rfl
 #align complex.of_real_am_coe Complex.ofRealAm_coe
+-/
 
+/- warning: complex.conj_ae -> Complex.conjAe is a dubious translation:
+lean 3 declaration is
+  AlgEquiv.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))
+but is expected to have type
+  AlgEquiv.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))
+Case conversion may be inaccurate. Consider using '#align complex.conj_ae Complex.conjAeₓ'. -/
 /-- `ℝ`-algebra isomorphism version of the complex conjugation function from `ℂ` to `ℂ` -/
 def conjAe : ℂ ≃ₐ[ℝ] ℂ :=
   { conj with
@@ -299,11 +457,23 @@ def conjAe : ℂ ≃ₐ[ℝ] ℂ :=
     commutes' := conj_ofReal }
 #align complex.conj_ae Complex.conjAe
 
+/- warning: complex.conj_ae_coe -> Complex.conjAe_coe is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complex.conj_ae_coe Complex.conjAe_coeₓ'. -/
 @[simp]
 theorem conjAe_coe : ⇑conjAe = conj :=
   rfl
 #align complex.conj_ae_coe Complex.conjAe_coe
 
+/- warning: complex.to_matrix_conj_ae -> Complex.toMatrix_conjAe is a dubious translation:
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(LinearMap.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real Real.commSemiring) (CommSemiring.toSemiring.{0} Real Real.commSemiring) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) Complex Complex (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring))) -> (Matrix.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real)) (LinearEquiv.hasCoeToFun.{0, 0, 0, 0} Real Real (LinearMap.{0, 0, 0, 0} Real Real (CommSemiring.toSemiring.{0} Real Real.commSemiring) (CommSemiring.toSemiring.{0} Real Real.commSemiring) 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(AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)))) (Matrix.addCommMonoid.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (LinearMap.module.{0, 0, 0, 0, 0} Real Real Real Complex Complex (CommSemiring.toSemiring.{0} Real Real.commSemiring) (CommSemiring.toSemiring.{0} Real Real.commSemiring) (AddCommGroup.toAddCommMonoid.{0} 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(CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)))) (Semiring.toModule.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))) (LinearMap.toMatrix._proof_1.{0} Real Real.commSemiring) (LinearMap.toMatrix._proof_2.{0} Real Real.commSemiring)) (LinearMap.toMatrix.{0, 0, 0, 0, 0} Real Real.commSemiring (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin.fintype (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} 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(Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.conjAe)) (coeFn.{1, 1} (Equiv.{1, 1} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (Matrix.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real)) (fun (_x : Equiv.{1, 1} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (Matrix.{0, 0, 0} (Fin 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(bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real)) (Matrix.of.{0, 0, 0} (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) Real) (Matrix.vecCons.{0} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (Matrix.vecCons.{0} Real (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (Matrix.vecCons.{0} Real (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Matrix.vecEmpty.{0} Real))) (Matrix.vecCons.{0} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Matrix.vecCons.{0} Real (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Matrix.vecCons.{0} Real (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) (Neg.neg.{0} Real Real.hasNeg (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Matrix.vecEmpty.{0} Real))) (Matrix.vecEmpty.{0} ((Fin (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) -> Real)))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align complex.to_matrix_conj_ae Complex.toMatrix_conjAeₓ'. -/
 /-- The matrix representation of `conj_ae`. -/
 @[simp]
 theorem toMatrix_conjAe :
@@ -314,6 +484,12 @@ theorem toMatrix_conjAe :
   fin_cases i <;> fin_cases j <;> simp
 #align complex.to_matrix_conj_ae Complex.toMatrix_conjAe
 
+/- warning: complex.real_alg_hom_eq_id_or_conj -> Complex.real_algHom_eq_id_or_conj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align complex.real_alg_hom_eq_id_or_conj Complex.real_algHom_eq_id_or_conjₓ'. -/
 /-- The identity and the complex conjugation are the only two `ℝ`-algebra homomorphisms of `ℂ`. -/
 theorem real_algHom_eq_id_or_conj (f : ℂ →ₐ[ℝ] ℂ) : f = AlgHom.id ℝ ℂ ∨ f = conjAe :=
   by
@@ -323,12 +499,24 @@ theorem real_algHom_eq_id_or_conj (f : ℂ →ₐ[ℝ] ℂ) : f = AlgHom.id ℝ
   exacts[h, conj_I.symm ▸ h]
 #align complex.real_alg_hom_eq_id_or_conj Complex.real_algHom_eq_id_or_conj
 
+/- warning: complex.equiv_real_prod_add_hom -> Complex.equivRealProdAddHom is a dubious translation:
+lean 3 declaration is
+  AddEquiv.{0, 0} Complex (Prod.{0, 0} Real Real) Complex.hasAdd (Prod.hasAdd.{0, 0} Real Real Real.hasAdd Real.hasAdd)
+but is expected to have type
+  AddEquiv.{0, 0} Complex (Prod.{0, 0} Real Real) Complex.instAddComplex (Prod.instAddSum.{0, 0} Real Real Real.instAddReal Real.instAddReal)
+Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_add_hom Complex.equivRealProdAddHomₓ'. -/
 /-- The natural `add_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdAddHom : ℂ ≃+ ℝ × ℝ :=
   { equivRealProd with map_add' := by simp }
 #align complex.equiv_real_prod_add_hom Complex.equivRealProdAddHom
 
+/- warning: complex.equiv_real_prod_lm -> Complex.equivRealProdLm is a dubious translation:
+lean 3 declaration is
+  LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (Prod.{0, 0} Real Real) (AddCommGroup.toAddCommMonoid.{0} Complex Complex.addCommGroup) (Prod.addCommMonoid.{0, 0} Real Real Real.addCommMonoid Real.addCommMonoid) (Complex.module.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Prod.module.{0, 0, 0} Real Real Real Real.semiring Real.addCommMonoid Real.addCommMonoid (Semiring.toModule.{0} Real Real.semiring) (Semiring.toModule.{0} Real Real.semiring))
+but is expected to have type
+  LinearEquiv.{0, 0, 0, 0} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (RingHomInvPair.ids.{0} Real Real.semiring) (RingHomInvPair.ids.{0} Real Real.semiring) Complex (Prod.{0, 0} Real Real) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Prod.instAddCommMonoidSum.{0, 0} Real Real Real.instAddCommMonoidReal Real.instAddCommMonoidReal) (Complex.instModuleComplexToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRingInstRingComplex.{0} Real Real.semiring (Semiring.toModule.{0} Real Real.semiring)) (Prod.module.{0, 0, 0} Real Real Real Real.semiring Real.instAddCommMonoidReal Real.instAddCommMonoidReal (Semiring.toModule.{0} Real Real.semiring) (Semiring.toModule.{0} Real Real.semiring))
+Case conversion may be inaccurate. Consider using '#align complex.equiv_real_prod_lm Complex.equivRealProdLmₓ'. -/
 /-- The natural `linear_equiv` from `ℂ` to `ℝ × ℝ`. -/
 @[simps (config := { simpRhs := true }) apply symm_apply_re symm_apply_im]
 def equivRealProdLm : ℂ ≃ₗ[ℝ] ℝ × ℝ :=
@@ -339,6 +527,12 @@ section lift
 
 variable {A : Type _} [Ring A] [Algebra ℝ A]
 
+/- warning: complex.lift_aux -> Complex.liftAux is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : Ring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.commSemiring (Ring.toSemiring.{u1} A _inst_1)] (I' : A), (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (Distrib.toHasMul.{u1} A (Ring.toDistrib.{u1} A _inst_1))) I' I') (Neg.neg.{u1} A (SubNegMonoid.toHasNeg.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddGroupWithOne.toAddGroup.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A _inst_1))))) (OfNat.ofNat.{u1} A 1 (OfNat.mk.{u1} A 1 (One.one.{u1} A (AddMonoidWithOne.toOne.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A _inst_1))))))))) -> (AlgHom.{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{u1} A _inst_1) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2)
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : Ring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.instCommSemiringReal (Ring.toSemiring.{u1} A _inst_1)] (I' : A), (Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1)))) I' I') (Neg.neg.{u1} A (Ring.toNeg.{u1} A _inst_1) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (NonAssocRing.toOne.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1)))))) -> (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{u1} A _inst_1) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2)
+Case conversion may be inaccurate. Consider using '#align complex.lift_aux Complex.liftAuxₓ'. -/
 /-- There is an alg_hom from `ℂ` to any `ℝ`-algebra with an element that squares to `-1`.
 
 See `complex.lift` for this as an equiv. -/
@@ -362,14 +556,32 @@ def liftAux (I' : A) (hf : I' * I' = -1) : ℂ →ₐ[ℝ] A :=
           mul_assoc, ← add_mul, ← RingHom.map_mul, ← RingHom.map_mul, ← RingHom.map_add]
 #align complex.lift_aux Complex.liftAux
 
+/- warning: complex.lift_aux_apply -> Complex.liftAux_apply is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align complex.lift_aux_apply Complex.liftAux_applyₓ'. -/
 @[simp]
 theorem liftAux_apply (I' : A) (hI') (z : ℂ) : liftAux I' hI' z = algebraMap ℝ A z.re + z.im • I' :=
   rfl
 #align complex.lift_aux_apply Complex.liftAux_apply
 
-theorem liftAux_apply_i (I' : A) (hI') : liftAux I' hI' I = I' := by simp
-#align complex.lift_aux_apply_I Complex.liftAux_apply_i
-
+/- warning: complex.lift_aux_apply_I -> Complex.liftAux_apply_I is a dubious translation:
+lean 3 declaration is
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_x) (SMulHomClass.toFunLike.{u1, 0, 0, u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{u1} A _inst_1) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (SMulZeroClass.toSMul.{0, 0} Real Complex (AddMonoid.toZero.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) (DistribSMul.toSMulZeroClass.{0, 0} Real Complex (AddMonoid.toAddZeroClass.{0} Complex (AddCommMonoid.toAddMonoid.{0} Complex (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) (DistribMulAction.toDistribSMul.{0, 0} Real Complex 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(AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))))) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) (Algebra.toModule.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))) (Module.toDistribMulAction.{0, u1} Real A (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1)))) (Algebra.toModule.{0, u1} Real A Real.instCommSemiringReal (Ring.toSemiring.{u1} A _inst_1) _inst_2)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{u1, 0, 0, u1} (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{u1} A _inst_1) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2) Real Complex A (MonoidWithZero.toMonoid.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A (Ring.toSemiring.{u1} A _inst_1))) (Module.toDistribMulAction.{0, 0} Real Complex (CommSemiring.toSemiring.{0} Real Real.instCommSemiringReal) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} 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+Case conversion may be inaccurate. Consider using '#align complex.lift_aux_apply_I Complex.liftAux_apply_Iₓ'. -/
+theorem liftAux_apply_I (I' : A) (hI') : liftAux I' hI' I = I' := by simp
+#align complex.lift_aux_apply_I Complex.liftAux_apply_I
+
+/- warning: complex.lift -> Complex.lift is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : Ring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.commSemiring (Ring.toSemiring.{u1} A _inst_1)], Equiv.{succ u1, succ u1} (Subtype.{succ u1} A (fun (I' : A) => Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (Distrib.toHasMul.{u1} A (Ring.toDistrib.{u1} A _inst_1))) I' I') (Neg.neg.{u1} A (SubNegMonoid.toHasNeg.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddGroupWithOne.toAddGroup.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A _inst_1))))) (OfNat.ofNat.{u1} A 1 (OfNat.mk.{u1} A 1 (One.one.{u1} A (AddMonoidWithOne.toOne.{u1} A (AddGroupWithOne.toAddMonoidWithOne.{u1} A (AddCommGroupWithOne.toAddGroupWithOne.{u1} A (Ring.toAddCommGroupWithOne.{u1} A _inst_1)))))))))) (AlgHom.{0, 0, u1} Real Complex A Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{u1} A _inst_1) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) _inst_2)
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : Ring.{u1} A] [_inst_2 : Algebra.{0, u1} Real A Real.instCommSemiringReal (Ring.toSemiring.{u1} A _inst_1)], Equiv.{succ u1, succ u1} (Subtype.{succ u1} A (fun (I' : A) => Eq.{succ u1} A (HMul.hMul.{u1, u1, u1} A A A (instHMul.{u1} A (NonUnitalNonAssocRing.toMul.{u1} A (NonAssocRing.toNonUnitalNonAssocRing.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1)))) I' I') (Neg.neg.{u1} A (Ring.toNeg.{u1} A _inst_1) (OfNat.ofNat.{u1} A 1 (One.toOfNat1.{u1} A (NonAssocRing.toOne.{u1} A (Ring.toNonAssocRing.{u1} A _inst_1))))))) (AlgHom.{0, 0, u1} Real Complex A Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{u1} A _inst_1) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) _inst_2)
+Case conversion may be inaccurate. Consider using '#align complex.lift Complex.liftₓ'. -/
 /-- A universal property of the complex numbers, providing a unique `ℂ →ₐ[ℝ] A` for every element
 of `A` which squares to `-1`.
 
@@ -381,21 +593,33 @@ def lift : { I' : A // I' * I' = -1 } ≃ (ℂ →ₐ[ℝ] A)
     where
   toFun I' := liftAux I' I'.Prop
   invFun F := ⟨F I, by rw [← F.map_mul, I_mul_I, AlgHom.map_neg, AlgHom.map_one]⟩
-  left_inv I' := Subtype.ext <| liftAux_apply_i I' I'.Prop
-  right_inv F := algHom_ext <| liftAux_apply_i _ _
+  left_inv I' := Subtype.ext <| liftAux_apply_I I' I'.Prop
+  right_inv F := algHom_ext <| liftAux_apply_I _ _
 #align complex.lift Complex.lift
 
+/- warning: complex.lift_aux_I -> Complex.liftAux_I is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (AlgHom.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) (Complex.liftAux.{0} Complex Complex.ring (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) Complex.I Complex.I_mul_I) (AlgHom.id.{0, 0} Real Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)))
+but is expected to have type
+  Eq.{1} (AlgHom.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))) (Complex.liftAux.{0} Complex Complex.instRingComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) Complex.I Complex.I_mul_I) (AlgHom.id.{0, 0} Real Complex Real.instCommSemiringReal Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))
+Case conversion may be inaccurate. Consider using '#align complex.lift_aux_I Complex.liftAux_Iₓ'. -/
 -- When applied to `complex.I` itself, `lift` is the identity.
 @[simp]
-theorem liftAux_i : liftAux I I_mul_I = AlgHom.id ℝ ℂ :=
-  algHom_ext <| liftAux_apply_i _ _
-#align complex.lift_aux_I Complex.liftAux_i
-
+theorem liftAux_I : liftAux I I_mul_I = AlgHom.id ℝ ℂ :=
+  algHom_ext <| liftAux_apply_I _ _
+#align complex.lift_aux_I Complex.liftAux_I
+
+/- warning: complex.lift_aux_neg_I -> Complex.liftAux_neg_I is a dubious translation:
+lean 3 declaration is
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Real.commSemiring))) (AlgHom.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) (HasLiftT.mk.{1, 1} (AlgEquiv.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) (AlgHom.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) (CoeTCₓ.coe.{1, 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Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) (AlgEquivClass.toAlgHomClass.{0, 0, 0, 0} (AlgEquiv.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))) Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (AlgEquiv.algEquivClass.{0, 0, 0} Real Complex Complex Real.commSemiring (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring)) (Complex.algebra.{0} Real Real.commSemiring (Algebra.id.{0} Real Real.commSemiring))))))) Complex.conjAe)
+but is expected to have type
+  Eq.{1} (AlgHom.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))) (Complex.liftAux.{0} Complex Complex.instRingComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I) (Eq.trans.{1} Complex (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex (NonUnitalNonAssocRing.toMul.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) (Neg.neg.{0} Complex (InvolutiveNeg.toNeg.{0} Complex (HasDistribNeg.toInvolutiveNeg.{0} Complex (NonUnitalNonAssocRing.toMul.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonUnitalNonAssocRing.toHasDistribNeg.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) Complex.I) (Neg.neg.{0} Complex (InvolutiveNeg.toNeg.{0} Complex (HasDistribNeg.toInvolutiveNeg.{0} Complex (NonUnitalNonAssocRing.toMul.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonUnitalNonAssocRing.toHasDistribNeg.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) Complex.I)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex (NonUnitalNonAssocRing.toMul.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex)))) Complex.I Complex.I) (Neg.neg.{0} Complex (Ring.toNeg.{0} Complex Complex.instRingComplex) (OfNat.ofNat.{0} Complex 1 (One.toOfNat1.{0} Complex (NonAssocRing.toOne.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))))) (neg_mul_neg.{0} Complex (NonUnitalNonAssocRing.toMul.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) (NonUnitalNonAssocRing.toHasDistribNeg.{0} Complex (NonAssocRing.toNonUnitalNonAssocRing.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.instRingComplex))) Complex.I Complex.I) Complex.I_mul_I)) (AlgHomClass.toAlgHom.{0, 0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (AlgEquiv.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))) (AlgEquivClass.toAlgHomClass.{0, 0, 0, 0} (AlgEquiv.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal))) Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex (Ring.toSemiring.{0} Complex Complex.instRingComplex) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (AlgEquiv.instAlgEquivClassAlgEquiv.{0, 0, 0} Real Complex Complex Real.instCommSemiringReal Complex.instSemiringComplex Complex.instSemiringComplex (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)) (Complex.instAlgebraComplexInstSemiringComplex.{0} Real Real.instCommSemiringReal (Algebra.id.{0} Real Real.instCommSemiringReal)))) Complex.conjAe)
+Case conversion may be inaccurate. Consider using '#align complex.lift_aux_neg_I Complex.liftAux_neg_Iₓ'. -/
 -- When applied to `-complex.I`, `lift` is conjugation, `conj`.
 @[simp]
-theorem liftAux_neg_i : liftAux (-I) ((neg_mul_neg _ _).trans I_mul_I) = conjAe :=
-  algHom_ext <| (liftAux_apply_i _ _).trans conj_I.symm
-#align complex.lift_aux_neg_I Complex.liftAux_neg_i
+theorem liftAux_neg_I : liftAux (-I) ((neg_mul_neg _ _).trans I_mul_I) = conjAe :=
+  algHom_ext <| (liftAux_apply_I _ _).trans conj_I.symm
+#align complex.lift_aux_neg_I Complex.liftAux_neg_I
 
 end lift
 
@@ -407,10 +631,16 @@ open Complex
 
 variable {A : Type _} [AddCommGroup A] [Module ℂ A] [StarAddMonoid A] [StarModule ℂ A]
 
+/- warning: skew_adjoint.neg_I_smul -> skewAdjoint.negISMul is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (skewAdjoint.{u1} A _inst_1 _inst_3)) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (skewAdjoint.{u1} A _inst_1 _inst_3)) (AddSubgroup.toAddCommGroup.{u1} A _inst_1 (skewAdjoint.{u1} A _inst_1 _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddSubgroup.toAddCommGroup.{u1} A _inst_1 (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (skewAdjoint.module.{0, u1} Real A (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (skewAdjoint.negISMul._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4)) (selfAdjoint.module.{0, u1} Real A (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (skewAdjoint.negISMul._proof_2.{u1} A _inst_1 _inst_2 _inst_3 _inst_4))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (skewAdjoint.{u1} A _inst_1 _inst_3))) (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (skewAdjoint.{u1} A _inst_1 _inst_3))) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (skewAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSkewAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))
+Case conversion may be inaccurate. Consider using '#align skew_adjoint.neg_I_smul skewAdjoint.negISMulₓ'. -/
 /-- Create a `self_adjoint` element from a `skew_adjoint` element by multiplying by the scalar
 `-complex.I`. -/
 @[simps]
-def skewAdjoint.negISmul : skewAdjoint A →ₗ[ℝ] selfAdjoint A
+def skewAdjoint.negISMul : skewAdjoint A →ₗ[ℝ] selfAdjoint A
     where
   toFun a :=
     ⟨-I • a, by
@@ -424,13 +654,25 @@ def skewAdjoint.negISmul : skewAdjoint A →ₗ[ℝ] selfAdjoint A
     simp only [neg_smul, skewAdjoint.val_smul, AddSubgroup.coe_mk, RingHom.id_apply,
       selfAdjoint.val_smul, smul_neg, neg_inj]
     rw [smul_comm]
-#align skew_adjoint.neg_I_smul skewAdjoint.negISmul
-
-theorem skewAdjoint.i_smul_neg_i (a : skewAdjoint A) : I • (skewAdjoint.negISmul a : A) = a := by
-  simp only [smul_smul, skewAdjoint.negISmul_apply_coe, neg_smul, smul_neg, I_mul_I, one_smul,
+#align skew_adjoint.neg_I_smul skewAdjoint.negISMul
+
+/- warning: skew_adjoint.I_smul_neg_I -> skewAdjoint.I_smul_neg_I is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A 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+but is expected to have type
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(AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (skewAdjoint.{u1} A _inst_1 _inst_3))) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (skewAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSkewAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (skewAdjoint.negISMul.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a))) (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (skewAdjoint.{u1} A _inst_1 _inst_3))) a)
+Case conversion may be inaccurate. Consider using '#align skew_adjoint.I_smul_neg_I skewAdjoint.I_smul_neg_Iₓ'. -/
+theorem skewAdjoint.I_smul_neg_I (a : skewAdjoint A) : I • (skewAdjoint.negISMul a : A) = a := by
+  simp only [smul_smul, skewAdjoint.negISMul_apply_coe, neg_smul, smul_neg, I_mul_I, one_smul,
     neg_neg]
-#align skew_adjoint.I_smul_neg_I skewAdjoint.i_smul_neg_i
-
+#align skew_adjoint.I_smul_neg_I skewAdjoint.I_smul_neg_I
+
+/- warning: real_part -> realPart is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) A (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddSubgroup.toAddCommGroup.{u1} A _inst_1 (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.module.{0, u1} Real A (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (realPart._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))
+Case conversion may be inaccurate. Consider using '#align real_part realPartₓ'. -/
 /-- The real part `ℜ a` of an element `a` of a star module over `ℂ`, as a linear map. This is just
 `self_adjoint_part ℝ`, but we provide it as a separate definition in order to link it with lemmas
 concerning the `imaginary_part`, which doesn't exist in star modules over other rings. -/
@@ -438,13 +680,19 @@ noncomputable def realPart : A →ₗ[ℝ] selfAdjoint A :=
   selfAdjointPart ℝ
 #align real_part realPart
 
+/- warning: imaginary_part -> imaginaryPart is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) A (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddSubgroup.toAddCommGroup.{u1} A _inst_1 (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.module.{0, u1} Real A (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (imaginaryPart._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))], LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))
+Case conversion may be inaccurate. Consider using '#align imaginary_part imaginaryPartₓ'. -/
 /-- The imaginary part `ℑ a` of an element `a` of a star module over `ℂ`, as a linear map into the
 self adjoint elements. In a general star module, we have a decomposition into the `self_adjoint`
 and `skew_adjoint` parts, but in a star module over `ℂ` we have
 `real_part_add_I_smul_imaginary_part`, which allows us to decompose into a linear combination of
 `self_adjoint`s. -/
 noncomputable def imaginaryPart : A →ₗ[ℝ] selfAdjoint A :=
-  skewAdjoint.negISmul.comp (skewAdjointPart ℝ)
+  skewAdjoint.negISMul.comp (skewAdjointPart ℝ)
 #align imaginary_part imaginaryPart
 
 -- mathport name: exprℜ
@@ -453,6 +701,12 @@ scoped[ComplexStarModule] notation "ℜ" => realPart
 -- mathport name: exprℑ
 scoped[ComplexStarModule] notation "ℑ" => imaginaryPart
 
+/- warning: real_part_apply_coe -> realPart_apply_coe is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (Module.toMulActionWithZero.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))] (a : A), Eq.{succ u1} A ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) A (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) 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(realPart._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4))) (fun (_x : LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring)) A (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddCommGroup.toAddCommMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) 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(AddSubgroup.setLike.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3)) (AddSubgroup.toAddCommGroup.{u1} A _inst_1 (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.module.{0, u1} Real A (InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (realPart._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (realPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)) (SMul.smul.{0, u1} Real A (SMulZeroClass.toHasSmul.{0, u1} Real A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Real A (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Real A (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (Module.toMulActionWithZero.{0, u1} Real A Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (Module.complexToReal.{u1} A _inst_1 _inst_2))))) (Inv.inv.{0} Real Real.hasInv (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddZeroClass.toHasAdd.{u1} A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))))) a (Star.star.{u1} A (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) a)))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))] (a : A), Eq.{succ u1} A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Real Real A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (realPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)) (HSMul.hSMul.{0, u1, u1} Real A A (instHSMul.{0, u1} Real A (SMulZeroClass.toSMul.{0, u1} Real A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real A Real.instZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real A Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real A Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (Module.complexToReal.{u1} A _inst_1 _inst_2)))))) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HAdd.hAdd.{u1, u1, u1} A A A (instHAdd.{u1} A (AddZeroClass.toAdd.{u1} A (AddMonoid.toAddZeroClass.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))))) a (Star.star.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) a)))
+Case conversion may be inaccurate. Consider using '#align real_part_apply_coe realPart_apply_coeₓ'. -/
 @[simp]
 theorem realPart_apply_coe (a : A) : (ℜ a : A) = (2 : ℝ)⁻¹ • (a + star a) :=
   by
@@ -460,42 +714,78 @@ theorem realPart_apply_coe (a : A) : (ℜ a : A) = (2 : ℝ)⁻¹ • (a + star
   simp only [selfAdjointPart_apply_coe, invOf_eq_inv]
 #align real_part_apply_coe realPart_apply_coe
 
+/- warning: imaginary_part_apply_coe -> imaginaryPart_apply_coe is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))] (a : A), Eq.{succ u1} A (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Real Real A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (imaginaryPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)) (HSMul.hSMul.{0, u1, u1} Complex A A (instHSMul.{0, u1} Complex A (SMulZeroClass.toSMul.{0, u1} Complex A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Complex A Complex.instZeroComplex (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex Complex.instSemiringComplex) (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))) (Neg.neg.{0} Complex Complex.instNegComplex Complex.I) (HSMul.hSMul.{0, u1, u1} Real A A (instHSMul.{0, u1} Real A (SMulZeroClass.toSMul.{0, u1} Real A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real A Real.instZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real A Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real A Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (Module.complexToReal.{u1} A _inst_1 _inst_2)))))) (Inv.inv.{0} Real Real.instInvReal (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (HSub.hSub.{u1, u1, u1} A A A (instHSub.{u1} A (SubNegMonoid.toSub.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))) a (Star.star.{u1} A (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) a))))
+Case conversion may be inaccurate. Consider using '#align imaginary_part_apply_coe imaginaryPart_apply_coeₓ'. -/
 @[simp]
 theorem imaginaryPart_apply_coe (a : A) : (ℑ a : A) = -I • (2 : ℝ)⁻¹ • (a - star a) :=
   by
   unfold imaginaryPart
-  simp only [LinearMap.coe_comp, skewAdjoint.negISmul_apply_coe, skewAdjointPart_apply_coe,
+  simp only [LinearMap.coe_comp, skewAdjoint.negISMul_apply_coe, skewAdjointPart_apply_coe,
     invOf_eq_inv]
 #align imaginary_part_apply_coe imaginaryPart_apply_coe
 
+/- warning: real_part_add_I_smul_imaginary_part -> realPart_add_I_smul_imaginaryPart is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) 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+but is expected to have type
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(AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Real Real A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) 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(NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))) Complex.I (Subtype.val.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (Set.{u1} A) (Set.instMembershipSet.{u1} A) x (SetLike.coe.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, 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(NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A 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(selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (imaginaryPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)))) a
+Case conversion may be inaccurate. Consider using '#align real_part_add_I_smul_imaginary_part realPart_add_I_smul_imaginaryPartₓ'. -/
 /-- The standard decomposition of `ℜ a + complex.I • ℑ a = a` of an element of a star module over
 `ℂ` into a linear combination of self adjoint elements. -/
-theorem realPart_add_i_smul_imaginaryPart (a : A) : (ℜ a + I • ℑ a : A) = a := by
+theorem realPart_add_I_smul_imaginaryPart (a : A) : (ℜ a + I • ℑ a : A) = a := by
   simpa only [smul_smul, realPart_apply_coe, imaginaryPart_apply_coe, neg_smul, I_mul_I, one_smul,
     neg_sub, add_add_sub_cancel, smul_sub, smul_add, neg_sub_neg, invOf_eq_inv] using
     invOf_two_smul_add_invOf_two_smul ℝ a
-#align real_part_add_I_smul_imaginary_part realPart_add_i_smul_imaginaryPart
-
+#align real_part_add_I_smul_imaginary_part realPart_add_I_smul_imaginaryPart
+
+/- warning: real_part_I_smul -> realPart_I_smul is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align real_part_I_smul realPart_I_smulₓ'. -/
 @[simp]
-theorem realPart_i_smul (a : A) : ℜ (I • a) = -ℑ a :=
+theorem realPart_I_smul (a : A) : ℜ (I • a) = -ℑ a :=
   by
   ext
   simp [smul_comm I, smul_sub, sub_eq_add_neg, add_comm]
-#align real_part_I_smul realPart_i_smul
-
+#align real_part_I_smul realPart_I_smul
+
+/- warning: imaginary_part_I_smul -> imaginaryPart_I_smul is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) 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+but is expected to have type
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(selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A 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(NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) _inst_2))))) Complex.I a)) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) 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_inst_1 _inst_2 _inst_3 _inst_4) a)
+Case conversion may be inaccurate. Consider using '#align imaginary_part_I_smul imaginaryPart_I_smulₓ'. -/
 @[simp]
-theorem imaginaryPart_i_smul (a : A) : ℑ (I • a) = ℜ a :=
+theorem imaginaryPart_I_smul (a : A) : ℑ (I • a) = ℜ a :=
   by
   ext
   simp [smul_comm I, smul_smul I]
-#align imaginary_part_I_smul imaginaryPart_i_smul
-
+#align imaginary_part_I_smul imaginaryPart_I_smul
+
+/- warning: real_part_smul -> realPart_smul is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) 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+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A 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(Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real 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_inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A 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+Case conversion may be inaccurate. Consider using '#align real_part_smul realPart_smulₓ'. -/
 theorem realPart_smul (z : ℂ) (a : A) : ℜ (z • a) = z.re • ℜ a - z.im • ℑ a :=
   by
   nth_rw 1 [← re_add_im z]
   simp [-re_add_im, add_smul, ← smul_smul, sub_eq_add_neg]
 #align real_part_smul realPart_smul
 
+/- warning: imaginary_part_smul -> imaginaryPart_smul is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A (Ring.toSemiring.{0} Complex Complex.ring) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toHasStar.{u1} A (StarAddMonoid.toHasInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) (SMulZeroClass.toHasSmul.{0, u1} Complex A (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (SMulWithZero.toSmulZeroClass.{0, u1} Complex A (MulZeroClass.toHasZero.{0} Complex (MulZeroOneClass.toMulZeroClass.{0} Complex (MonoidWithZero.toMulZeroOneClass.{0} Complex (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))))) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)))) (MulActionWithZero.toSMulWithZero.{0, u1} Complex A (Semiring.toMonoidWithZero.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring)) (AddZeroClass.toHasZero.{u1} A (AddMonoid.toAddZeroClass.{u1} A 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(InvolutiveStar.toHasStar.{0} Real (StarAddMonoid.toHasInvolutiveStar.{0} Real (AddCommMonoid.toAddMonoid.{0} Real (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} Real (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing)))))) (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.starRing))) Real.trivialStar _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (realPart._proof_1.{u1} A _inst_1 _inst_2 _inst_3 _inst_4)) (RingHom.id.{0} Real (Semiring.toNonAssocSemiring.{0} Real Real.semiring))) (realPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : AddCommGroup.{u1} A] [_inst_2 : Module.{0, u1} Complex A Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} A _inst_1)] [_inst_3 : StarAddMonoid.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)))] [_inst_4 : StarModule.{0, u1} Complex A (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))) (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A 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(StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3 (SMulZeroClass.toSMul.{0, u1} Real A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real A Real.instZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real A Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real A Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (Module.complexToReal.{u1} A _inst_1 _inst_2))))) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) (Complex.re z) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Real Real A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (imaginaryPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)) (HSMul.hSMul.{0, u1, u1} Real ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) a) ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) a) (instHSMul.{0, u1} Real ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) a) (selfAdjoint.instSMulSubtypeMemAddSubgroupInstMembershipInstSetLikeAddSubgroupSelfAdjoint.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3 (SMulZeroClass.toSMul.{0, u1} Real A (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real A Real.instZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real A Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} A (SubNegZeroMonoid.toNegZeroClass.{u1} A (SubtractionMonoid.toSubNegZeroMonoid.{u1} A (SubtractionCommMonoid.toSubtractionMonoid.{u1} A (AddCommGroup.toDivisionAddCommMonoid.{u1} A _inst_1))))) (Module.toMulActionWithZero.{0, u1} Real A Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (Module.complexToReal.{u1} A _inst_1 _inst_2))))) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) (Complex.im z) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Real Real Real.semiring Real.semiring (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal))) A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : A) => Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Real Real A (Subtype.{succ u1} A (fun (x : A) => Membership.mem.{u1, u1} A (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1)) A (AddSubgroup.instSetLikeAddSubgroup.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) x (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) Real.semiring Real.semiring (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubmonoid.toAddCommMonoid.{u1} A (AddCommGroup.toAddCommMonoid.{u1} A _inst_1) (AddSubgroup.toAddSubmonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) (selfAdjoint.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1) _inst_3))) (Module.complexToReal.{u1} A _inst_1 _inst_2) (selfAdjoint.instModuleSubtypeMemAddSubgroupToAddGroupInstMembershipInstSetLikeAddSubgroupSelfAdjointToAddCommMonoidToAddCommMonoidToAddSubmonoid.{0, u1} Real A (InvolutiveStar.toStar.{0} Real (StarAddMonoid.toInvolutiveStar.{0} Real Real.instAddMonoidReal (StarRing.toStarAddMonoid.{0} Real (NonUnitalRing.toNonUnitalSemiring.{0} Real (NonUnitalCommRing.toNonUnitalRing.{0} Real (CommRing.toNonUnitalCommRing.{0} Real Real.commRing))) Real.instStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing))) Real.instTrivialStarRealToStarToInvolutiveStarInstAddMonoidRealToStarAddMonoidToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRingInstStarRingRealToNonUnitalSemiringToNonUnitalRingToNonUnitalCommRingCommRing _inst_1 _inst_3 Real.semiring (Module.complexToReal.{u1} A _inst_1 _inst_2) (StarModule.complexToReal.{u1} A _inst_1 (InvolutiveStar.toStar.{u1} A (StarAddMonoid.toInvolutiveStar.{u1} A (SubNegMonoid.toAddMonoid.{u1} A (AddGroup.toSubNegMonoid.{u1} A (AddCommGroup.toAddGroup.{u1} A _inst_1))) _inst_3)) _inst_2 _inst_4)) (RingHom.id.{0} Real (NonAssocRing.toNonAssocSemiring.{0} Real (Ring.toNonAssocRing.{0} Real Real.instRingReal)))) (realPart.{u1} A _inst_1 _inst_2 _inst_3 _inst_4) a)))
+Case conversion may be inaccurate. Consider using '#align imaginary_part_smul imaginaryPart_smulₓ'. -/
 theorem imaginaryPart_smul (z : ℂ) (a : A) : ℑ (z • a) = z.re • ℑ a + z.im • ℜ a :=
   by
   nth_rw 1 [← re_add_im z]
diff --git a/Mathbin/LinearAlgebra/CliffordAlgebra/Equivs.lean b/Mathbin/LinearAlgebra/CliffordAlgebra/Equivs.lean
index d80ad44b61..0317753990 100644
--- a/Mathbin/LinearAlgebra/CliffordAlgebra/Equivs.lean
+++ b/Mathbin/LinearAlgebra/CliffordAlgebra/Equivs.lean
@@ -183,7 +183,7 @@ def ofComplex : ℂ →ₐ[ℝ] CliffordAlgebra q :=
 
 @[simp]
 theorem ofComplex_i : ofComplex Complex.I = ι q 1 :=
-  Complex.liftAux_apply_i _ _
+  Complex.liftAux_apply_I _ _
 #align clifford_algebra_complex.of_complex_I CliffordAlgebraComplex.ofComplex_i
 
 @[simp]
diff --git a/lake-manifest.json b/lake-manifest.json
index bd82108213..2f6707fa6e 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -4,15 +4,15 @@
  [{"git":
    {"url": "https://github.com/leanprover-community/lean3port.git",
     "subDir?": null,
-    "rev": "27674d71f2e3c650c886f678ec5e558abcd9a080",
+    "rev": "e45c4605d7b93cc5ed7d9c1e3312c5afe0d5020a",
     "name": "lean3port",
-    "inputRev?": "27674d71f2e3c650c886f678ec5e558abcd9a080"}},
+    "inputRev?": "e45c4605d7b93cc5ed7d9c1e3312c5afe0d5020a"}},
   {"git":
    {"url": "https://github.com/leanprover-community/mathlib4.git",
     "subDir?": null,
-    "rev": "d5f2c21d880775b1d309336bce5c58977751fb48",
+    "rev": "685bd4da4194abb102b827da14eac25c34d18c5f",
     "name": "mathlib",
-    "inputRev?": "d5f2c21d880775b1d309336bce5c58977751fb48"}},
+    "inputRev?": "685bd4da4194abb102b827da14eac25c34d18c5f"}},
   {"git":
    {"url": "https://github.com/gebner/quote4",
     "subDir?": null,
diff --git a/lakefile.lean b/lakefile.lean
index 9a9b5eb342..4fd77e558d 100644
--- a/lakefile.lean
+++ b/lakefile.lean
@@ -4,7 +4,7 @@ open Lake DSL System
 -- Usually the `tag` will be of the form `nightly-2021-11-22`.
 -- If you would like to use an artifact from a PR build,
 -- it will be of the form `pr-branchname-sha`.
-def tag : String := "nightly-2023-05-02-08"
+def tag : String := "nightly-2023-05-02-10"
 def releaseRepo : String := "leanprover-community/mathport"
 def oleanTarName : String := "mathlib3-binport.tar.gz"
 
@@ -38,7 +38,7 @@ target fetchOleans (_pkg : Package) : Unit := do
     untarReleaseArtifact releaseRepo tag oleanTarName libDir
   return .nil
 
-require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"27674d71f2e3c650c886f678ec5e558abcd9a080"
+require lean3port from git "https://github.com/leanprover-community/lean3port.git"@"e45c4605d7b93cc5ed7d9c1e3312c5afe0d5020a"
 
 @[default_target]
 lean_lib Mathbin where