analysis.special_functions.complex.circle

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

f333194f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4280f5f3

bump to nightly-2023-12-14-06

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

a154f5e6

Diff

@@ -56,11 +56,11 @@ theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
 
 namespace circle
 
-#print circle.argLocalEquiv /-
+#print circle.argPartialEquiv /-
 /-- `complex.arg ∘ coe` and `exp_map_circle` define a local equivalence between `circle and `ℝ` with
 `source = set.univ` and `target = set.Ioc (-π) π`. -/
 @[simps (config := { fullyApplied := false })]
-noncomputable def argLocalEquiv : LocalEquiv circle ℝ
+noncomputable def argPartialEquiv : PartialEquiv circle ℝ
     where
   toFun := arg ∘ coe
   invFun := expMapCircle
@@ -70,7 +70,7 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ
   map_target' := mapsTo_univ _ _
   left_inv' z _ := expMapCircle_arg z
   right_inv' x hx := arg_expMapCircle hx.1 hx.2
-#align circle.arg_local_equiv circle.argLocalEquiv
+#align circle.arg_local_equiv circle.argPartialEquiv
 -/
 
 #print circle.argEquiv /-
@@ -80,8 +80,8 @@ noncomputable def argEquiv : circle ≃ Ioc (-π) π
     where
   toFun z := ⟨arg z, neg_pi_lt_arg _, arg_le_pi _⟩
   invFun := expMapCircle ∘ coe
-  left_inv z := argLocalEquiv.left_inv trivial
-  right_inv x := Subtype.ext <| argLocalEquiv.right_inv x.2
+  left_inv z := argPartialEquiv.left_inv trivial
+  right_inv x := Subtype.ext <| argPartialEquiv.right_inv x.2
 #align circle.arg_equiv circle.argEquiv
 -/
 
@@ -95,13 +95,13 @@ theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ coe) :=
 
 #print invOn_arg_expMapCircle /-
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ coe) expMapCircle (Ioc (-π) π) univ :=
-  circle.argLocalEquiv.symm.InvOn
+  circle.argPartialEquiv.symm.InvOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
 -/
 
 #print surjOn_expMapCircle_neg_pi_pi /-
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
-  circle.argLocalEquiv.symm.SurjOn
+  circle.argPartialEquiv.symm.SurjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
 -/

4280f5f3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Analysis.Complex.Circle
-import Mathbin.Analysis.SpecialFunctions.Complex.Log
+import Analysis.Complex.Circle
+import Analysis.SpecialFunctions.Complex.Log
 
 #align_import analysis.special_functions.complex.circle from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"

4280f5f3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.complex.circle
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.Circle
 import Mathbin.Analysis.SpecialFunctions.Complex.Log
 
+#align_import analysis.special_functions.complex.circle from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Maps on the unit circle

4280f5f3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -29,28 +29,37 @@ open scoped Real
 
 namespace circle
 
+#print circle.injective_arg /-
 theorem injective_arg : Injective fun z : circle => arg z := fun z w h =>
   Subtype.ext <| ext_abs_arg ((abs_coe_circle z).trans (abs_coe_circle w).symm) h
 #align circle.injective_arg circle.injective_arg
+-/
 
+#print circle.arg_eq_arg /-
 @[simp]
 theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
   injective_arg.eq_iff
 #align circle.arg_eq_arg circle.arg_eq_arg
+-/
 
 end circle
 
+#print arg_expMapCircle /-
 theorem arg_expMapCircle {x : ℝ} (h₁ : -π < x) (h₂ : x ≤ π) : arg (expMapCircle x) = x := by
   rw [expMapCircle_apply, exp_mul_I, arg_cos_add_sin_mul_I ⟨h₁, h₂⟩]
 #align arg_exp_map_circle arg_expMapCircle
+-/
 
+#print expMapCircle_arg /-
 @[simp]
 theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
   circle.injective_arg <| arg_expMapCircle (neg_pi_lt_arg _) (arg_le_pi _)
 #align exp_map_circle_arg expMapCircle_arg
+-/
 
 namespace circle
 
+#print circle.argLocalEquiv /-
 /-- `complex.arg ∘ coe` and `exp_map_circle` define a local equivalence between `circle and `ℝ` with
 `source = set.univ` and `target = set.Ioc (-π) π`. -/
 @[simps (config := { fullyApplied := false })]
@@ -65,7 +74,9 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ
   left_inv' z _ := expMapCircle_arg z
   right_inv' x hx := arg_expMapCircle hx.1 hx.2
 #align circle.arg_local_equiv circle.argLocalEquiv
+-/
 
+#print circle.argEquiv /-
 /-- `complex.arg` and `exp_map_circle` define an equivalence between `circle and `(-π, π]`. -/
 @[simps (config := { fullyApplied := false })]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π
@@ -75,21 +86,29 @@ noncomputable def argEquiv : circle ≃ Ioc (-π) π
   left_inv z := argLocalEquiv.left_inv trivial
   right_inv x := Subtype.ext <| argLocalEquiv.right_inv x.2
 #align circle.arg_equiv circle.argEquiv
+-/
 
 end circle
 
+#print leftInverse_expMapCircle_arg /-
 theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ coe) :=
   expMapCircle_arg
 #align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_arg
+-/
 
+#print invOn_arg_expMapCircle /-
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ coe) expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.InvOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
+-/
 
+#print surjOn_expMapCircle_neg_pi_pi /-
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.SurjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
+-/
 
+#print expMapCircle_eq_expMapCircle /-
 theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     expMapCircle x = expMapCircle y ↔ ∃ m : ℤ, x = y + m * (2 * π) :=
   by
@@ -98,45 +117,63 @@ theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
   rw [← mul_assoc, ← add_mul, mul_left_inj' I_ne_zero, ← of_real_one, ← of_real_bit0, ← of_real_mul,
     ← of_real_int_cast, ← of_real_mul, ← of_real_add, of_real_inj]
 #align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircle
+-/
 
+#print periodic_expMapCircle /-
 theorem periodic_expMapCircle : Periodic expMapCircle (2 * π) := fun z =>
   expMapCircle_eq_expMapCircle.2 ⟨1, by rw [Int.cast_one, one_mul]⟩
 #align periodic_exp_map_circle periodic_expMapCircle
+-/
 
+#print expMapCircle_two_pi /-
 @[simp]
 theorem expMapCircle_two_pi : expMapCircle (2 * π) = 1 :=
   periodic_expMapCircle.Eq.trans expMapCircle_zero
 #align exp_map_circle_two_pi expMapCircle_two_pi
+-/
 
+#print expMapCircle_sub_two_pi /-
 theorem expMapCircle_sub_two_pi (x : ℝ) : expMapCircle (x - 2 * π) = expMapCircle x :=
   periodic_expMapCircle.sub_eq x
 #align exp_map_circle_sub_two_pi expMapCircle_sub_two_pi
+-/
 
+#print expMapCircle_add_two_pi /-
 theorem expMapCircle_add_two_pi (x : ℝ) : expMapCircle (x + 2 * π) = expMapCircle x :=
   periodic_expMapCircle x
 #align exp_map_circle_add_two_pi expMapCircle_add_two_pi
+-/
 
+#print Real.Angle.expMapCircle /-
 /-- `exp_map_circle`, applied to a `real.angle`. -/
 noncomputable def Real.Angle.expMapCircle (θ : Real.Angle) : circle :=
   periodic_expMapCircle.lift θ
 #align real.angle.exp_map_circle Real.Angle.expMapCircle
+-/
 
+#print Real.Angle.expMapCircle_coe /-
 @[simp]
 theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expMapCircle x :=
   rfl
 #align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coe
+-/
 
+#print Real.Angle.coe_expMapCircle /-
 theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * I :=
   by
   induction θ using Real.Angle.induction_on
   simp [Complex.exp_mul_I]
 #align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircle
+-/
 
+#print Real.Angle.expMapCircle_zero /-
 @[simp]
 theorem Real.Angle.expMapCircle_zero : Real.Angle.expMapCircle 0 = 1 := by
   rw [← Real.Angle.coe_zero, Real.Angle.expMapCircle_coe, expMapCircle_zero]
 #align real.angle.exp_map_circle_zero Real.Angle.expMapCircle_zero
+-/
 
+#print Real.Angle.expMapCircle_neg /-
 @[simp]
 theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
     Real.Angle.expMapCircle (-θ) = (Real.Angle.expMapCircle θ)⁻¹ :=
@@ -144,7 +181,9 @@ theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
   induction θ using Real.Angle.induction_on
   simp_rw [← Real.Angle.coe_neg, Real.Angle.expMapCircle_coe, expMapCircle_neg]
 #align real.angle.exp_map_circle_neg Real.Angle.expMapCircle_neg
+-/
 
+#print Real.Angle.expMapCircle_add /-
 @[simp]
 theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
     Real.Angle.expMapCircle (θ₁ + θ₂) = Real.Angle.expMapCircle θ₁ * Real.Angle.expMapCircle θ₂ :=
@@ -153,7 +192,9 @@ theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
   induction θ₂ using Real.Angle.induction_on
   exact expMapCircle_add θ₁ θ₂
 #align real.angle.exp_map_circle_add Real.Angle.expMapCircle_add
+-/
 
+#print Real.Angle.arg_expMapCircle /-
 @[simp]
 theorem Real.Angle.arg_expMapCircle (θ : Real.Angle) :
     (arg (Real.Angle.expMapCircle θ) : Real.Angle) = θ :=
@@ -162,4 +203,5 @@ theorem Real.Angle.arg_expMapCircle (θ : Real.Angle) :
   rw [Real.Angle.expMapCircle_coe, expMapCircle_apply, exp_mul_I, ← of_real_cos, ← of_real_sin, ←
     Real.Angle.cos_coe, ← Real.Angle.sin_coe, arg_cos_add_sin_mul_I_coe_angle]
 #align real.angle.arg_exp_map_circle Real.Angle.arg_expMapCircle
+-/

4280f5f3

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -25,7 +25,7 @@ to the unit circle. These two maps define a local equivalence between `circle` a
 
 open Complex Function Set
 
-open Real
+open scoped Real
 
 namespace circle

4280f5f3

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -29,19 +29,10 @@ open Real
 
 namespace circle
 
-/- warning: circle.injective_arg -> circle.injective_arg is a dubious translation:
-lean 3 declaration is
-  Function.Injective.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real (fun (z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) => Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z))
-but is expected to have type
-  Function.Injective.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real (fun (z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))
-Case conversion may be inaccurate. Consider using '#align circle.injective_arg circle.injective_argₓ'. -/
 theorem injective_arg : Injective fun z : circle => arg z := fun z w h =>
   Subtype.ext <| ext_abs_arg ((abs_coe_circle z).trans (abs_coe_circle w).symm) h
 #align circle.injective_arg circle.injective_arg
 
-/- warning: circle.arg_eq_arg -> circle.arg_eq_arg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align circle.arg_eq_arg circle.arg_eq_argₓ'. -/
 @[simp]
 theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
   injective_arg.eq_iff
@@ -49,16 +40,10 @@ theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
 
 end circle
 
-/- warning: arg_exp_map_circle -> arg_expMapCircle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align arg_exp_map_circle arg_expMapCircleₓ'. -/
 theorem arg_expMapCircle {x : ℝ} (h₁ : -π < x) (h₂ : x ≤ π) : arg (expMapCircle x) = x := by
   rw [expMapCircle_apply, exp_mul_I, arg_cos_add_sin_mul_I ⟨h₁, h₂⟩]
 #align arg_exp_map_circle arg_expMapCircle
 
-/- warning: exp_map_circle_arg -> expMapCircle_arg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exp_map_circle_arg expMapCircle_argₓ'. -/
 @[simp]
 theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
   circle.injective_arg <| arg_expMapCircle (neg_pi_lt_arg _) (arg_le_pi _)
@@ -66,12 +51,6 @@ theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
 
 namespace circle
 
-/- warning: circle.arg_local_equiv -> circle.argLocalEquiv is a dubious translation:
-lean 3 declaration is
-  LocalEquiv.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real
-but is expected to have type
-  LocalEquiv.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real
-Case conversion may be inaccurate. Consider using '#align circle.arg_local_equiv circle.argLocalEquivₓ'. -/
 /-- `complex.arg ∘ coe` and `exp_map_circle` define a local equivalence between `circle and `ℝ` with
 `source = set.univ` and `target = set.Ioc (-π) π`. -/
 @[simps (config := { fullyApplied := false })]
@@ -87,12 +66,6 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ
   right_inv' x hx := arg_expMapCircle hx.1 hx.2
 #align circle.arg_local_equiv circle.argLocalEquiv
 
-/- warning: circle.arg_equiv -> circle.argEquiv is a dubious translation:
-lean 3 declaration is
-  Equiv.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi))
-but is expected to have type
-  Equiv.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Set.Elem.{0} Real (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi))
-Case conversion may be inaccurate. Consider using '#align circle.arg_equiv circle.argEquivₓ'. -/
 /-- `complex.arg` and `exp_map_circle` define an equivalence between `circle and `(-π, π]`. -/
 @[simps (config := { fullyApplied := false })]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π
@@ -105,30 +78,18 @@ noncomputable def argEquiv : circle ≃ Ioc (-π) π
 
 end circle
 
-/- warning: left_inverse_exp_map_circle_arg -> leftInverse_expMapCircle_arg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_argₓ'. -/
 theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ coe) :=
   expMapCircle_arg
 #align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_arg
 
-/- warning: inv_on_arg_exp_map_circle -> invOn_arg_expMapCircle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align inv_on_arg_exp_map_circle invOn_arg_expMapCircleₓ'. -/
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ coe) expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.InvOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
 
-/- warning: surj_on_exp_map_circle_neg_pi_pi -> surjOn_expMapCircle_neg_pi_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_piₓ'. -/
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.SurjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
 
-/- warning: exp_map_circle_eq_exp_map_circle -> expMapCircle_eq_expMapCircle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircleₓ'. -/
 theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     expMapCircle x = expMapCircle y ↔ ∃ m : ℤ, x = y + m * (2 * π) :=
   by
@@ -138,83 +99,44 @@ theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     ← of_real_int_cast, ← of_real_mul, ← of_real_add, of_real_inj]
 #align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircle
 
-/- warning: periodic_exp_map_circle -> periodic_expMapCircle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align periodic_exp_map_circle periodic_expMapCircleₓ'. -/
 theorem periodic_expMapCircle : Periodic expMapCircle (2 * π) := fun z =>
   expMapCircle_eq_expMapCircle.2 ⟨1, by rw [Int.cast_one, one_mul]⟩
 #align periodic_exp_map_circle periodic_expMapCircle
 
-/- warning: exp_map_circle_two_pi -> expMapCircle_two_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exp_map_circle_two_pi expMapCircle_two_piₓ'. -/
 @[simp]
 theorem expMapCircle_two_pi : expMapCircle (2 * π) = 1 :=
   periodic_expMapCircle.Eq.trans expMapCircle_zero
 #align exp_map_circle_two_pi expMapCircle_two_pi
 
-/- warning: exp_map_circle_sub_two_pi -> expMapCircle_sub_two_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exp_map_circle_sub_two_pi expMapCircle_sub_two_piₓ'. -/
 theorem expMapCircle_sub_two_pi (x : ℝ) : expMapCircle (x - 2 * π) = expMapCircle x :=
   periodic_expMapCircle.sub_eq x
 #align exp_map_circle_sub_two_pi expMapCircle_sub_two_pi
 
-/- warning: exp_map_circle_add_two_pi -> expMapCircle_add_two_pi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align exp_map_circle_add_two_pi expMapCircle_add_two_piₓ'. -/
 theorem expMapCircle_add_two_pi (x : ℝ) : expMapCircle (x + 2 * π) = expMapCircle x :=
   periodic_expMapCircle x
 #align exp_map_circle_add_two_pi expMapCircle_add_two_pi
 
-/- warning: real.angle.exp_map_circle -> Real.Angle.expMapCircle is a dubious translation:
-lean 3 declaration is
-  Real.Angle -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)
-but is expected to have type
-  Real.Angle -> (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle))
-Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle Real.Angle.expMapCircleₓ'. -/
 /-- `exp_map_circle`, applied to a `real.angle`. -/
 noncomputable def Real.Angle.expMapCircle (θ : Real.Angle) : circle :=
   periodic_expMapCircle.lift θ
 #align real.angle.exp_map_circle Real.Angle.expMapCircle
 
-/- warning: real.angle.exp_map_circle_coe -> Real.Angle.expMapCircle_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coeₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expMapCircle x :=
   rfl
 #align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coe
 
-/- warning: real.angle.coe_exp_map_circle -> Real.Angle.coe_expMapCircle is a dubious translation:
-lean 3 declaration is
-  forall (θ : Real.Angle), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (Real.Angle.expMapCircle θ)) (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))) (Real.Angle.cos θ)) (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))) (Real.Angle.sin θ)) Complex.I))
-but is expected to have type
-  forall (θ : Real.Angle), Eq.{1} Complex (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (Real.Angle.expMapCircle θ)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (Real.Angle.cos θ)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (Real.Angle.sin θ)) Complex.I))
-Case conversion may be inaccurate. Consider using '#align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircleₓ'. -/
 theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * I :=
   by
   induction θ using Real.Angle.induction_on
   simp [Complex.exp_mul_I]
 #align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircle
 
-/- warning: real.angle.exp_map_circle_zero -> Real.Angle.expMapCircle_zero is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (OfNat.ofNat.{0} Real.Angle 0 (OfNat.mk.{0} Real.Angle 0 (Zero.zero.{0} Real.Angle (AddZeroClass.toHasZero.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup)))))))))) (OfNat.ofNat.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (One.one.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle))))
-but is expected to have type
-  Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (OfNat.ofNat.{0} Real.Angle 0 (Zero.toOfNat0.{0} Real.Angle (NegZeroClass.toZero.{0} Real.Angle (SubNegZeroMonoid.toNegZeroClass.{0} Real.Angle (SubtractionMonoid.toSubNegZeroMonoid.{0} Real.Angle (SubtractionCommMonoid.toSubtractionMonoid.{0} Real.Angle (AddCommGroup.toDivisionAddCommMonoid.{0} Real.Angle (NormedAddCommGroup.toAddCommGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle))))))))) (OfNat.ofNat.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) 1 (One.toOfNat1.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)))
-Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_zero Real.Angle.expMapCircle_zeroₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_zero : Real.Angle.expMapCircle 0 = 1 := by
   rw [← Real.Angle.coe_zero, Real.Angle.expMapCircle_coe, expMapCircle_zero]
 #align real.angle.exp_map_circle_zero Real.Angle.expMapCircle_zero
 
-/- warning: real.angle.exp_map_circle_neg -> Real.Angle.expMapCircle_neg is a dubious translation:
-lean 3 declaration is
-  forall (θ : Real.Angle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (Neg.neg.{0} Real.Angle (SubNegMonoid.toHasNeg.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup)))) θ)) (Inv.inv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (DivInvMonoid.toHasInv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Group.toDivInvMonoid.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (CommGroup.toGroup.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) circle.commGroup))) (Real.Angle.expMapCircle θ))
-but is expected to have type
-  forall (θ : Real.Angle), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (Neg.neg.{0} Real.Angle (NegZeroClass.toNeg.{0} Real.Angle (SubNegZeroMonoid.toNegZeroClass.{0} Real.Angle (SubtractionMonoid.toSubNegZeroMonoid.{0} Real.Angle (SubtractionCommMonoid.toSubtractionMonoid.{0} Real.Angle (AddCommGroup.toDivisionAddCommMonoid.{0} Real.Angle (NormedAddCommGroup.toAddCommGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle)))))) θ)) (Inv.inv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (InvOneClass.toInv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivInvOneMonoid.toInvOneClass.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionMonoid.toDivInvOneMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionCommMonoid.toDivisionMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (CommGroup.toDivisionCommMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) commGroup))))) (Real.Angle.expMapCircle θ))
-Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_neg Real.Angle.expMapCircle_negₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
     Real.Angle.expMapCircle (-θ) = (Real.Angle.expMapCircle θ)⁻¹ :=
@@ -223,12 +145,6 @@ theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
   simp_rw [← Real.Angle.coe_neg, Real.Angle.expMapCircle_coe, expMapCircle_neg]
 #align real.angle.exp_map_circle_neg Real.Angle.expMapCircle_neg
 
-/- warning: real.angle.exp_map_circle_add -> Real.Angle.expMapCircle_add is a dubious translation:
-lean 3 declaration is
-  forall (θ₁ : Real.Angle) (θ₂ : Real.Angle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (HAdd.hAdd.{0, 0, 0} Real.Angle Real.Angle Real.Angle (instHAdd.{0} Real.Angle (AddZeroClass.toHasAdd.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup))))))) θ₁ θ₂)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (instHMul.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle)) (Real.Angle.expMapCircle θ₁) (Real.Angle.expMapCircle θ₂))
-but is expected to have type
-  forall (θ₁ : Real.Angle) (θ₂ : Real.Angle), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (HAdd.hAdd.{0, 0, 0} Real.Angle Real.Angle Real.Angle (instHAdd.{0} Real.Angle (AddZeroClass.toAdd.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle))))))) θ₁ θ₂)) (HMul.hMul.{0, 0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (instHMul.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)) (Real.Angle.expMapCircle θ₁) (Real.Angle.expMapCircle θ₂))
-Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_add Real.Angle.expMapCircle_addₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
     Real.Angle.expMapCircle (θ₁ + θ₂) = Real.Angle.expMapCircle θ₁ * Real.Angle.expMapCircle θ₂ :=
@@ -238,12 +154,6 @@ theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
   exact expMapCircle_add θ₁ θ₂
 #align real.angle.exp_map_circle_add Real.Angle.expMapCircle_add
 
-/- warning: real.angle.arg_exp_map_circle -> Real.Angle.arg_expMapCircle is a dubious translation:
-lean 3 declaration is
-  forall (θ : Real.Angle), Eq.{1} Real.Angle ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Real.Angle (HasLiftT.mk.{1, 1} Real Real.Angle (CoeTCₓ.coe.{1, 1} Real Real.Angle Real.Angle.hasCoeT)) (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (Real.Angle.expMapCircle θ)))) θ
-but is expected to have type
-  forall (θ : Real.Angle), Eq.{1} Real.Angle (Real.Angle.coe (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (Real.Angle.expMapCircle θ)))) θ
-Case conversion may be inaccurate. Consider using '#align real.angle.arg_exp_map_circle Real.Angle.arg_expMapCircleₓ'. -/
 @[simp]
 theorem Real.Angle.arg_expMapCircle (θ : Real.Angle) :
     (arg (Real.Angle.expMapCircle θ) : Real.Angle) = θ :=

4280f5f3

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -40,10 +40,7 @@ theorem injective_arg : Injective fun z : circle => arg z := fun z w h =>
 #align circle.injective_arg circle.injective_arg
 
 /- warning: circle.arg_eq_arg -> circle.arg_eq_arg is a dubious translation:
-lean 3 declaration is
-  forall {z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle} {w : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle}, Iff (Eq.{1} Real (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z)) (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) w))) (Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) z w)
-but is expected to have type
-  forall {z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)} {w : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)}, Iff (Eq.{1} Real (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z)) (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) w))) (Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) z w)
+<too large>
 Case conversion may be inaccurate. Consider using '#align circle.arg_eq_arg circle.arg_eq_argₓ'. -/
 @[simp]
 theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
@@ -53,20 +50,14 @@ theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
 end circle
 
 /- warning: arg_exp_map_circle -> arg_expMapCircle is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LE.le.{0} Real Real.hasLe x Real.pi) -> (Eq.{1} Real (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x))) x)
-but is expected to have type
-  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LE.le.{0} Real Real.instLEReal x Real.pi) -> (Eq.{1} Real (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x))) x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align arg_exp_map_circle arg_expMapCircleₓ'. -/
 theorem arg_expMapCircle {x : ℝ} (h₁ : -π < x) (h₂ : x ≤ π) : arg (expMapCircle x) = x := by
   rw [expMapCircle_apply, exp_mul_I, arg_cos_add_sin_mul_I ⟨h₁, h₂⟩]
 #align arg_exp_map_circle arg_expMapCircle
 
 /- warning: exp_map_circle_arg -> expMapCircle_arg is a dubious translation:
-lean 3 declaration is
-  forall (z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z))) z
-but is expected to have type
-  forall (z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))) z
+<too large>
 Case conversion may be inaccurate. Consider using '#align exp_map_circle_arg expMapCircle_argₓ'. -/
 @[simp]
 theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
@@ -115,40 +106,28 @@ noncomputable def argEquiv : circle ≃ Ioc (-π) π
 end circle
 
 /- warning: left_inverse_exp_map_circle_arg -> leftInverse_expMapCircle_arg is a dubious translation:
-lean 3 declaration is
-  Function.LeftInverse.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Function.comp.{1, 1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex Real Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle)))))))
-but is expected to have type
-  Function.LeftInverse.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Function.comp.{1, 1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Complex Real Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_argₓ'. -/
 theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ coe) :=
   expMapCircle_arg
 #align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_arg
 
 /- warning: inv_on_arg_exp_map_circle -> invOn_arg_expMapCircle is a dubious translation:
-lean 3 declaration is
-  Set.InvOn.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Function.comp.{1, 1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex Real Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi) (Set.univ.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle))
-but is expected to have type
-  Set.InvOn.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Function.comp.{1, 1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Complex Real Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi) (Set.univ.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align inv_on_arg_exp_map_circle invOn_arg_expMapCircleₓ'. -/
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ coe) expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.InvOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
 
 /- warning: surj_on_exp_map_circle_neg_pi_pi -> surjOn_expMapCircle_neg_pi_pi is a dubious translation:
-lean 3 declaration is
-  Set.SurjOn.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi) (Set.univ.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle))
-but is expected to have type
-  Set.SurjOn.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi) (Set.univ.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_piₓ'. -/
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.SurjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
 
 /- warning: exp_map_circle_eq_exp_map_circle -> expMapCircle_eq_expMapCircle is a dubious translation:
-lean 3 declaration is
-  forall {x : Real} {y : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle y)) (Exists.{1} Int (fun (m : Int) => Eq.{1} Real x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) y (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) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) m) (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)))) Real.pi)))))
-but is expected to have type
-  forall {x : Real} {y : Real}, Iff (Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) x) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle y)) (Exists.{1} Int (fun (m : Int) => Eq.{1} Real x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) y (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast m) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircleₓ'. -/
 theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     expMapCircle x = expMapCircle y ↔ ∃ m : ℤ, x = y + m * (2 * π) :=
@@ -160,20 +139,14 @@ theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
 #align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircle
 
 /- warning: periodic_exp_map_circle -> periodic_expMapCircle is a dubious translation:
-lean 3 declaration is
-  Function.Periodic.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real.hasAdd (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (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)))) Real.pi)
-but is expected to have type
-  Function.Periodic.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real.instAddReal (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)
+<too large>
 Case conversion may be inaccurate. Consider using '#align periodic_exp_map_circle periodic_expMapCircleₓ'. -/
 theorem periodic_expMapCircle : Periodic expMapCircle (2 * π) := fun z =>
   expMapCircle_eq_expMapCircle.2 ⟨1, by rw [Int.cast_one, one_mul]⟩
 #align periodic_exp_map_circle periodic_expMapCircle
 
 /- warning: exp_map_circle_two_pi -> expMapCircle_two_pi is a dubious translation:
-lean 3 declaration is
-  Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (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)))) Real.pi)) (OfNat.ofNat.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (One.one.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle))))
-but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align exp_map_circle_two_pi expMapCircle_two_piₓ'. -/
 @[simp]
 theorem expMapCircle_two_pi : expMapCircle (2 * π) = 1 :=
@@ -181,20 +154,14 @@ theorem expMapCircle_two_pi : expMapCircle (2 * π) = 1 :=
 #align exp_map_circle_two_pi expMapCircle_two_pi
 
 /- warning: exp_map_circle_sub_two_pi -> expMapCircle_sub_two_pi is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x (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)))) Real.pi))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
-but is expected to have type
-  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align exp_map_circle_sub_two_pi expMapCircle_sub_two_piₓ'. -/
 theorem expMapCircle_sub_two_pi (x : ℝ) : expMapCircle (x - 2 * π) = expMapCircle x :=
   periodic_expMapCircle.sub_eq x
 #align exp_map_circle_sub_two_pi expMapCircle_sub_two_pi
 
 /- warning: exp_map_circle_add_two_pi -> expMapCircle_add_two_pi is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x (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)))) Real.pi))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
-but is expected to have type
-  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align exp_map_circle_add_two_pi expMapCircle_add_two_piₓ'. -/
 theorem expMapCircle_add_two_pi (x : ℝ) : expMapCircle (x + 2 * π) = expMapCircle x :=
   periodic_expMapCircle x
@@ -212,10 +179,7 @@ noncomputable def Real.Angle.expMapCircle (θ : Real.Angle) : circle :=
 #align real.angle.exp_map_circle Real.Angle.expMapCircle
 
 /- warning: real.angle.exp_map_circle_coe -> Real.Angle.expMapCircle_coe is a dubious translation:
-lean 3 declaration is
-  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Real.Angle (HasLiftT.mk.{1, 1} Real Real.Angle (CoeTCₓ.coe.{1, 1} Real Real.Angle Real.Angle.hasCoeT)) x)) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
-but is expected to have type
-  forall (x : Real), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (Real.Angle.coe x)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+<too large>
 Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coeₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expMapCircle x :=

4280f5f3

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.special_functions.complex.circle
-! leanprover-community/mathlib commit f333194f5ecd1482191452c5ea60b37d4d6afa08
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.SpecialFunctions.Complex.Log
 /-!
 # Maps on the unit circle
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove some basic lemmas about `exp_map_circle` and the restriction of `complex.arg`
 to the unit circle. These two maps define a local equivalence between `circle` and `ℝ`, see
 `circle.arg_local_equiv` and `circle.arg_equiv`, that sends the whole circle to `(-π, π]`.

f333194f

bump to nightly-2023-05-21-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

876ce566

Diff

@@ -26,10 +26,22 @@ open Real
 
 namespace circle
 
+/- warning: circle.injective_arg -> circle.injective_arg is a dubious translation:
+lean 3 declaration is
+  Function.Injective.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real (fun (z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) => Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z))
+but is expected to have type
+  Function.Injective.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real (fun (z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) => Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))
+Case conversion may be inaccurate. Consider using '#align circle.injective_arg circle.injective_argₓ'. -/
 theorem injective_arg : Injective fun z : circle => arg z := fun z w h =>
   Subtype.ext <| ext_abs_arg ((abs_coe_circle z).trans (abs_coe_circle w).symm) h
 #align circle.injective_arg circle.injective_arg
 
+/- warning: circle.arg_eq_arg -> circle.arg_eq_arg is a dubious translation:
+lean 3 declaration is
+  forall {z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle} {w : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle}, Iff (Eq.{1} Real (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z)) (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) w))) (Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) z w)
+but is expected to have type
+  forall {z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)} {w : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)}, Iff (Eq.{1} Real (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z)) (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) w))) (Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) z w)
+Case conversion may be inaccurate. Consider using '#align circle.arg_eq_arg circle.arg_eq_argₓ'. -/
 @[simp]
 theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
   injective_arg.eq_iff
@@ -37,10 +49,22 @@ theorem arg_eq_arg {z w : circle} : arg z = arg w ↔ z = w :=
 
 end circle
 
+/- warning: arg_exp_map_circle -> arg_expMapCircle is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, (LT.lt.{0} Real Real.hasLt (Neg.neg.{0} Real Real.hasNeg Real.pi) x) -> (LE.le.{0} Real Real.hasLe x Real.pi) -> (Eq.{1} Real (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x))) x)
+but is expected to have type
+  forall {x : Real}, (LT.lt.{0} Real Real.instLTReal (Neg.neg.{0} Real Real.instNegReal Real.pi) x) -> (LE.le.{0} Real Real.instLEReal x Real.pi) -> (Eq.{1} Real (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x))) x)
+Case conversion may be inaccurate. Consider using '#align arg_exp_map_circle arg_expMapCircleₓ'. -/
 theorem arg_expMapCircle {x : ℝ} (h₁ : -π < x) (h₂ : x ≤ π) : arg (expMapCircle x) = x := by
   rw [expMapCircle_apply, exp_mul_I, arg_cos_add_sin_mul_I ⟨h₁, h₂⟩]
 #align arg_exp_map_circle arg_expMapCircle
 
+/- warning: exp_map_circle_arg -> expMapCircle_arg is a dubious translation:
+lean 3 declaration is
+  forall (z : coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) z))) z
+but is expected to have type
+  forall (z : Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) z))) z
+Case conversion may be inaccurate. Consider using '#align exp_map_circle_arg expMapCircle_argₓ'. -/
 @[simp]
 theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
   circle.injective_arg <| arg_expMapCircle (neg_pi_lt_arg _) (arg_le_pi _)
@@ -48,6 +72,12 @@ theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
 
 namespace circle
 
+/- warning: circle.arg_local_equiv -> circle.argLocalEquiv is a dubious translation:
+lean 3 declaration is
+  LocalEquiv.{0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real
+but is expected to have type
+  LocalEquiv.{0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real
+Case conversion may be inaccurate. Consider using '#align circle.arg_local_equiv circle.argLocalEquivₓ'. -/
 /-- `complex.arg ∘ coe` and `exp_map_circle` define a local equivalence between `circle and `ℝ` with
 `source = set.univ` and `target = set.Ioc (-π) π`. -/
 @[simps (config := { fullyApplied := false })]
@@ -63,6 +93,12 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ
   right_inv' x hx := arg_expMapCircle hx.1 hx.2
 #align circle.arg_local_equiv circle.argLocalEquiv
 
+/- warning: circle.arg_equiv -> circle.argEquiv is a dubious translation:
+lean 3 declaration is
+  Equiv.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi))
+but is expected to have type
+  Equiv.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Set.Elem.{0} Real (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi))
+Case conversion may be inaccurate. Consider using '#align circle.arg_equiv circle.argEquivₓ'. -/
 /-- `complex.arg` and `exp_map_circle` define an equivalence between `circle and `(-π, π]`. -/
 @[simps (config := { fullyApplied := false })]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π
@@ -75,18 +111,42 @@ noncomputable def argEquiv : circle ≃ Ioc (-π) π
 
 end circle
 
+/- warning: left_inverse_exp_map_circle_arg -> leftInverse_expMapCircle_arg is a dubious translation:
+lean 3 declaration is
+  Function.LeftInverse.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Function.comp.{1, 1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex Real Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle)))))))
+but is expected to have type
+  Function.LeftInverse.{1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Function.comp.{1, 1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Complex Real Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle))))
+Case conversion may be inaccurate. Consider using '#align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_argₓ'. -/
 theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ coe) :=
   expMapCircle_arg
 #align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_arg
 
+/- warning: inv_on_arg_exp_map_circle -> invOn_arg_expMapCircle is a dubious translation:
+lean 3 declaration is
+  Set.InvOn.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Function.comp.{1, 1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex Real Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi) (Set.univ.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle))
+but is expected to have type
+  Set.InvOn.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Function.comp.{1, 1, 1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Complex Real Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi) (Set.univ.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)))
+Case conversion may be inaccurate. Consider using '#align inv_on_arg_exp_map_circle invOn_arg_expMapCircleₓ'. -/
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ coe) expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.InvOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
 
+/- warning: surj_on_exp_map_circle_neg_pi_pi -> surjOn_expMapCircle_neg_pi_pi is a dubious translation:
+lean 3 declaration is
+  Set.SurjOn.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (Set.Ioc.{0} Real Real.preorder (Neg.neg.{0} Real Real.hasNeg Real.pi) Real.pi) (Set.univ.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle))
+but is expected to have type
+  Set.SurjOn.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (Set.Ioc.{0} Real Real.instPreorderReal (Neg.neg.{0} Real Real.instNegReal Real.pi) Real.pi) (Set.univ.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)))
+Case conversion may be inaccurate. Consider using '#align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_piₓ'. -/
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
   circle.argLocalEquiv.symm.SurjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
 
+/- warning: exp_map_circle_eq_exp_map_circle -> expMapCircle_eq_expMapCircle is a dubious translation:
+lean 3 declaration is
+  forall {x : Real} {y : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle y)) (Exists.{1} Int (fun (m : Int) => Eq.{1} Real x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) y (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) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) m) (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)))) Real.pi)))))
+but is expected to have type
+  forall {x : Real} {y : Real}, Iff (Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) x) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle y)) (Exists.{1} Int (fun (m : Int) => Eq.{1} Real x (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) y (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast m) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)))))
+Case conversion may be inaccurate. Consider using '#align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircleₓ'. -/
 theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     expMapCircle x = expMapCircle y ↔ ∃ m : ℤ, x = y + m * (2 * π) :=
   by
@@ -96,44 +156,98 @@ theorem expMapCircle_eq_expMapCircle {x y : ℝ} :
     ← of_real_int_cast, ← of_real_mul, ← of_real_add, of_real_inj]
 #align exp_map_circle_eq_exp_map_circle expMapCircle_eq_expMapCircle
 
+/- warning: periodic_exp_map_circle -> periodic_expMapCircle is a dubious translation:
+lean 3 declaration is
+  Function.Periodic.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Real.hasAdd (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle) (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)))) Real.pi)
+but is expected to have type
+  Function.Periodic.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) Real.instAddReal (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)
+Case conversion may be inaccurate. Consider using '#align periodic_exp_map_circle periodic_expMapCircleₓ'. -/
 theorem periodic_expMapCircle : Periodic expMapCircle (2 * π) := fun z =>
   expMapCircle_eq_expMapCircle.2 ⟨1, by rw [Int.cast_one, one_mul]⟩
 #align periodic_exp_map_circle periodic_expMapCircle
 
+/- warning: exp_map_circle_two_pi -> expMapCircle_two_pi is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (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)))) Real.pi)) (OfNat.ofNat.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (One.one.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle))))
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi)) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)))
+Case conversion may be inaccurate. Consider using '#align exp_map_circle_two_pi expMapCircle_two_piₓ'. -/
 @[simp]
 theorem expMapCircle_two_pi : expMapCircle (2 * π) = 1 :=
   periodic_expMapCircle.Eq.trans expMapCircle_zero
 #align exp_map_circle_two_pi expMapCircle_two_pi
 
+/- warning: exp_map_circle_sub_two_pi -> expMapCircle_sub_two_pi is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x (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)))) Real.pi))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
+but is expected to have type
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+Case conversion may be inaccurate. Consider using '#align exp_map_circle_sub_two_pi expMapCircle_sub_two_piₓ'. -/
 theorem expMapCircle_sub_two_pi (x : ℝ) : expMapCircle (x - 2 * π) = expMapCircle x :=
   periodic_expMapCircle.sub_eq x
 #align exp_map_circle_sub_two_pi expMapCircle_sub_two_pi
 
+/- warning: exp_map_circle_add_two_pi -> expMapCircle_add_two_pi is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x (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)))) Real.pi))) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
+but is expected to have type
+  forall (x : Real), Eq.{1} ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Real.pi))) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+Case conversion may be inaccurate. Consider using '#align exp_map_circle_add_two_pi expMapCircle_add_two_piₓ'. -/
 theorem expMapCircle_add_two_pi (x : ℝ) : expMapCircle (x + 2 * π) = expMapCircle x :=
   periodic_expMapCircle x
 #align exp_map_circle_add_two_pi expMapCircle_add_two_pi
 
+/- warning: real.angle.exp_map_circle -> Real.Angle.expMapCircle is a dubious translation:
+lean 3 declaration is
+  Real.Angle -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)
+but is expected to have type
+  Real.Angle -> (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle))
+Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle Real.Angle.expMapCircleₓ'. -/
 /-- `exp_map_circle`, applied to a `real.angle`. -/
 noncomputable def Real.Angle.expMapCircle (θ : Real.Angle) : circle :=
   periodic_expMapCircle.lift θ
 #align real.angle.exp_map_circle Real.Angle.expMapCircle
 
+/- warning: real.angle.exp_map_circle_coe -> Real.Angle.expMapCircle_coe is a dubious translation:
+lean 3 declaration is
+  forall (x : Real), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Real.Angle (HasLiftT.mk.{1, 1} Real Real.Angle (CoeTCₓ.coe.{1, 1} Real Real.Angle Real.Angle.hasCoeT)) x)) (coeFn.{1, 1} (ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) (fun (_x : ContinuousMap.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) => Real -> (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle)) (ContinuousMap.hasCoeToFun.{0, 0} Real (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (Subtype.topologicalSpace.{0} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))))))) expMapCircle x)
+but is expected to have type
+  forall (x : Real), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (Real.Angle.coe x)) (FunLike.coe.{1, 1, 1} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (fun (_x : Real) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : Real) => Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) _x) (ContinuousMapClass.toFunLike.{0, 0, 0} (ContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))))))) Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))) (ContinuousMap.instContinuousMapClassContinuousMap.{0, 0} Real (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (instTopologicalSpaceSubtype.{0} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle) (UniformSpace.toTopologicalSpace.{0} Complex (PseudoMetricSpace.toUniformSpace.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex))))))))) expMapCircle x)
+Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coeₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expMapCircle x :=
   rfl
 #align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coe
 
+/- warning: real.angle.coe_exp_map_circle -> Real.Angle.coe_expMapCircle is a dubious translation:
+lean 3 declaration is
+  forall (θ : Real.Angle), Eq.{1} Complex ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (Real.Angle.expMapCircle θ)) (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))) (Real.Angle.cos θ)) (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))) (Real.Angle.sin θ)) Complex.I))
+but is expected to have type
+  forall (θ : Real.Angle), Eq.{1} Complex (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (Real.Angle.expMapCircle θ)) (HAdd.hAdd.{0, 0, 0} Complex Complex Complex (instHAdd.{0} Complex Complex.instAddComplex) (Complex.ofReal' (Real.Angle.cos θ)) (HMul.hMul.{0, 0, 0} Complex Complex Complex (instHMul.{0} Complex Complex.instMulComplex) (Complex.ofReal' (Real.Angle.sin θ)) Complex.I))
+Case conversion may be inaccurate. Consider using '#align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircleₓ'. -/
 theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * I :=
   by
   induction θ using Real.Angle.induction_on
   simp [Complex.exp_mul_I]
 #align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircle
 
+/- warning: real.angle.exp_map_circle_zero -> Real.Angle.expMapCircle_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (OfNat.ofNat.{0} Real.Angle 0 (OfNat.mk.{0} Real.Angle 0 (Zero.zero.{0} Real.Angle (AddZeroClass.toHasZero.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup)))))))))) (OfNat.ofNat.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) 1 (One.one.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle))))
+but is expected to have type
+  Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (OfNat.ofNat.{0} Real.Angle 0 (Zero.toOfNat0.{0} Real.Angle (NegZeroClass.toZero.{0} Real.Angle (SubNegZeroMonoid.toNegZeroClass.{0} Real.Angle (SubtractionMonoid.toSubNegZeroMonoid.{0} Real.Angle (SubtractionCommMonoid.toSubtractionMonoid.{0} Real.Angle (AddCommGroup.toDivisionAddCommMonoid.{0} Real.Angle (NormedAddCommGroup.toAddCommGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle))))))))) (OfNat.ofNat.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) 1 (One.toOfNat1.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.one.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)))
+Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_zero Real.Angle.expMapCircle_zeroₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_zero : Real.Angle.expMapCircle 0 = 1 := by
   rw [← Real.Angle.coe_zero, Real.Angle.expMapCircle_coe, expMapCircle_zero]
 #align real.angle.exp_map_circle_zero Real.Angle.expMapCircle_zero
 
+/- warning: real.angle.exp_map_circle_neg -> Real.Angle.expMapCircle_neg is a dubious translation:
+lean 3 declaration is
+  forall (θ : Real.Angle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (Neg.neg.{0} Real.Angle (SubNegMonoid.toHasNeg.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup)))) θ)) (Inv.inv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (DivInvMonoid.toHasInv.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Group.toDivInvMonoid.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (CommGroup.toGroup.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) circle.commGroup))) (Real.Angle.expMapCircle θ))
+but is expected to have type
+  forall (θ : Real.Angle), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (Neg.neg.{0} Real.Angle (NegZeroClass.toNeg.{0} Real.Angle (SubNegZeroMonoid.toNegZeroClass.{0} Real.Angle (SubtractionMonoid.toSubNegZeroMonoid.{0} Real.Angle (SubtractionCommMonoid.toSubtractionMonoid.{0} Real.Angle (AddCommGroup.toDivisionAddCommMonoid.{0} Real.Angle (NormedAddCommGroup.toAddCommGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle)))))) θ)) (Inv.inv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (InvOneClass.toInv.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivInvOneMonoid.toInvOneClass.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionMonoid.toDivInvOneMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (DivisionCommMonoid.toDivisionMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (CommGroup.toDivisionCommMonoid.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) commGroup))))) (Real.Angle.expMapCircle θ))
+Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_neg Real.Angle.expMapCircle_negₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
     Real.Angle.expMapCircle (-θ) = (Real.Angle.expMapCircle θ)⁻¹ :=
@@ -142,6 +256,12 @@ theorem Real.Angle.expMapCircle_neg (θ : Real.Angle) :
   simp_rw [← Real.Angle.coe_neg, Real.Angle.expMapCircle_coe, expMapCircle_neg]
 #align real.angle.exp_map_circle_neg Real.Angle.expMapCircle_neg
 
+/- warning: real.angle.exp_map_circle_add -> Real.Angle.expMapCircle_add is a dubious translation:
+lean 3 declaration is
+  forall (θ₁ : Real.Angle) (θ₂ : Real.Angle), Eq.{1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Real.Angle.expMapCircle (HAdd.hAdd.{0, 0, 0} Real.Angle Real.Angle Real.Angle (instHAdd.{0} Real.Angle (AddZeroClass.toHasAdd.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.normedAddCommGroup))))))) θ₁ θ₂)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (instHMul.{0} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))) circle)) (Real.Angle.expMapCircle θ₁) (Real.Angle.expMapCircle θ₂))
+but is expected to have type
+  forall (θ₁ : Real.Angle) (θ₂ : Real.Angle), Eq.{1} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Real.Angle.expMapCircle (HAdd.hAdd.{0, 0, 0} Real.Angle Real.Angle Real.Angle (instHAdd.{0} Real.Angle (AddZeroClass.toAdd.{0} Real.Angle (AddMonoid.toAddZeroClass.{0} Real.Angle (SubNegMonoid.toAddMonoid.{0} Real.Angle (AddGroup.toSubNegMonoid.{0} Real.Angle (NormedAddGroup.toAddGroup.{0} Real.Angle (NormedAddCommGroup.toNormedAddGroup.{0} Real.Angle Real.Angle.instNormedAddCommGroupAngle))))))) θ₁ θ₂)) (HMul.hMul.{0, 0, 0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (instHMul.{0} (Subtype.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) (SetLike.instMembership.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))))) x circle)) (Submonoid.mul.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) circle)) (Real.Angle.expMapCircle θ₁) (Real.Angle.expMapCircle θ₂))
+Case conversion may be inaccurate. Consider using '#align real.angle.exp_map_circle_add Real.Angle.expMapCircle_addₓ'. -/
 @[simp]
 theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
     Real.Angle.expMapCircle (θ₁ + θ₂) = Real.Angle.expMapCircle θ₁ * Real.Angle.expMapCircle θ₂ :=
@@ -151,6 +271,12 @@ theorem Real.Angle.expMapCircle_add (θ₁ θ₂ : Real.Angle) :
   exact expMapCircle_add θ₁ θ₂
 #align real.angle.exp_map_circle_add Real.Angle.expMapCircle_add
 
+/- warning: real.angle.arg_exp_map_circle -> Real.Angle.arg_expMapCircle is a dubious translation:
+lean 3 declaration is
+  forall (θ : Real.Angle), Eq.{1} Real.Angle ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real Real.Angle (HasLiftT.mk.{1, 1} Real Real.Angle (CoeTCₓ.coe.{1, 1} Real Real.Angle Real.Angle.hasCoeT)) (Complex.arg ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeBase.{1, 1} (coeSort.{1, 2} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Type (SetLike.hasCoeToSort.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) circle) Complex (coeSubtype.{1} Complex (fun (x : Complex) => Membership.Mem.{0, 0} Complex (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) (SetLike.hasMem.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring))))) Complex (Submonoid.setLike.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (NonAssocRing.toNonAssocSemiring.{0} Complex (Ring.toNonAssocRing.{0} Complex Complex.ring)))))) x circle))))) (Real.Angle.expMapCircle θ)))) θ
+but is expected to have type
+  forall (θ : Real.Angle), Eq.{1} Real.Angle (Real.Angle.coe (Complex.arg (Subtype.val.{1} Complex (fun (x : Complex) => Membership.mem.{0, 0} Complex (Set.{0} Complex) (Set.instMembershipSet.{0} Complex) x (SetLike.coe.{0, 0} (Submonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) Complex (Submonoid.instSetLikeSubmonoid.{0} Complex (MulZeroOneClass.toMulOneClass.{0} Complex (NonAssocSemiring.toMulZeroOneClass.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)))) circle)) (Real.Angle.expMapCircle θ)))) θ
+Case conversion may be inaccurate. Consider using '#align real.angle.arg_exp_map_circle Real.Angle.arg_expMapCircleₓ'. -/
 @[simp]
 theorem Real.Angle.arg_expMapCircle (θ : Real.Angle) :
     (arg (Real.Angle.expMapCircle θ) : Real.Angle) = θ :=

f333194f

bump to nightly-2023-03-15-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

da6bb02a

Diff

@@ -126,7 +126,7 @@ theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expM
 theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * I :=
   by
   induction θ using Real.Angle.induction_on
-  simp [Complex.exp_mul_i]
+  simp [Complex.exp_mul_I]
 #align real.angle.coe_exp_map_circle Real.Angle.coe_expMapCircle
 
 @[simp]

f333194f

bump to nightly-2023-03-10-14

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

24f14899

Diff

@@ -123,7 +123,7 @@ theorem Real.Angle.expMapCircle_coe (x : ℝ) : Real.Angle.expMapCircle x = expM
   rfl
 #align real.angle.exp_map_circle_coe Real.Angle.expMapCircle_coe
 
-theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * i :=
+theorem Real.Angle.coe_expMapCircle (θ : Real.Angle) : (θ.expMapCircle : ℂ) = θ.cos + θ.sin * I :=
   by
   induction θ using Real.Angle.induction_on
   simp [Complex.exp_mul_i]

f333194f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f333194f

feat(Analysis/SpecialFunctions/Complex/Circle): expMapCircle as a PartialHomeomorph and prove IsLocalHomeomorph (#11334)

This PR proves IsLocalHomeomorph expMapCircle (eventually this should be upgraded to IsCoveringMap, but that's a good deal harder and is probably best done via general theory such as in #7596).

38a7a533

Diff

@@ -170,12 +170,14 @@ noncomputable def toCircle : AddCircle T → circle :=
   (@scaled_exp_map_periodic T).lift
 #align add_circle.to_circle AddCircle.toCircle
 
+theorem toCircle_apply_mk (x : ℝ) : @toCircle T x = expMapCircle (2 * π / T * x) :=
+  rfl
+
 theorem toCircle_add (x : AddCircle T) (y : AddCircle T) :
     @toCircle T (x + y) = toCircle x * toCircle y := by
   induction x using QuotientAddGroup.induction_on'
   induction y using QuotientAddGroup.induction_on'
-  rw [← QuotientAddGroup.mk_add]
-  simp_rw [toCircle, Function.Periodic.lift_coe, mul_add, expMapCircle_add]
+  simp_rw [← coe_add, toCircle_apply_mk, mul_add, expMapCircle_add]
 #align add_circle.to_circle_add AddCircle.toCircle_add
 
 theorem continuous_toCircle : Continuous (@toCircle T) :=
@@ -186,7 +188,7 @@ theorem injective_toCircle (hT : T ≠ 0) : Function.Injective (@toCircle T) :=
   intro a b h
   induction a using QuotientAddGroup.induction_on'
   induction b using QuotientAddGroup.induction_on'
-  simp_rw [toCircle, Function.Periodic.lift_coe] at h
+  simp_rw [toCircle_apply_mk] at h
   obtain ⟨m, hm⟩ := expMapCircle_eq_expMapCircle.mp h.symm
   rw [QuotientAddGroup.eq]; simp_rw [AddSubgroup.mem_zmultiples_iff, zsmul_eq_mul]
   use m
@@ -195,4 +197,38 @@ theorem injective_toCircle (hT : T ≠ 0) : Function.Injective (@toCircle T) :=
   linarith
 #align add_circle.injective_to_circle AddCircle.injective_toCircle
 
+/-- The homeomorphism between `AddCircle (2 * π)` and `circle`. -/
+@[simps] noncomputable def homeomorphCircle' : AddCircle (2 * π) ≃ₜ circle where
+  toFun := Angle.expMapCircle
+  invFun := fun x ↦ arg x
+  left_inv := Angle.arg_expMapCircle
+  right_inv := expMapCircle_arg
+  continuous_toFun := continuous_coinduced_dom.mpr expMapCircle.continuous
+  continuous_invFun := by
+    rw [continuous_iff_continuousAt]
+    intro x
+    apply (continuousAt_arg_coe_angle (ne_zero_of_mem_circle x)).comp
+      continuousAt_subtype_val
+
+theorem homeomorphCircle'_apply_mk (x : ℝ) : homeomorphCircle' x = expMapCircle x :=
+  rfl
+
+/-- The homeomorphism between `AddCircle` and `circle`. -/
+noncomputable def homeomorphCircle (hT : T ≠ 0) : AddCircle T ≃ₜ circle :=
+  (homeomorphAddCircle T (2 * π) hT (by positivity)).trans homeomorphCircle'
+
+theorem homeomorphCircle_apply (hT : T ≠ 0) (x : AddCircle T) :
+    homeomorphCircle hT x = toCircle x := by
+  induction' x using QuotientAddGroup.induction_on' with x
+  rw [homeomorphCircle, Homeomorph.trans_apply,
+    homeomorphAddCircle_apply_mk, homeomorphCircle'_apply_mk, toCircle_apply_mk]
+  ring_nf
+
 end AddCircle
+
+open AddCircle
+
+-- todo: upgrade this to `IsCoveringMap expMapCircle`.
+lemma isLocalHomeomorph_expMapCircle : IsLocalHomeomorph expMapCircle := by
+  have : Fact (0 < 2 * π) := ⟨by positivity⟩
+  exact homeomorphCircle'.isLocalHomeomorph.comp (isLocalHomeomorph_coe (2 * π))

f333194f

refactor: Move AddCircle.toCircle to earlier file (#12000)

This PR moves AddCircle.toCircle to the earlier file Analysis/SpecialFunctions/Complex/Circle since AddCircle.toCircle only depends on periodic_expMapCircle and not the heavy imports of Analysis/Fourier/AddCircle.

d8c86746

Diff

@@ -150,3 +150,49 @@ theorem Real.Angle.arg_expMapCircle (θ : Real.Angle) :
   rw [Real.Angle.expMapCircle_coe, expMapCircle_apply, exp_mul_I, ← ofReal_cos, ← ofReal_sin, ←
     Real.Angle.cos_coe, ← Real.Angle.sin_coe, arg_cos_add_sin_mul_I_coe_angle]
 #align real.angle.arg_exp_map_circle Real.Angle.arg_expMapCircle
+
+namespace AddCircle
+
+variable {T : ℝ}
+
+/-! ### Map from `AddCircle` to `Circle` -/
+
+theorem scaled_exp_map_periodic : Function.Periodic (fun x => expMapCircle (2 * π / T * x)) T := by
+  -- The case T = 0 is not interesting, but it is true, so we prove it to save hypotheses
+  rcases eq_or_ne T 0 with (rfl | hT)
+  · intro x; simp
+  · intro x; simp_rw [mul_add]; rw [div_mul_cancel₀ _ hT, periodic_expMapCircle]
+#align add_circle.scaled_exp_map_periodic AddCircle.scaled_exp_map_periodic
+
+/-- The canonical map `fun x => exp (2 π i x / T)` from `ℝ / ℤ • T` to the unit circle in `ℂ`.
+If `T = 0` we understand this as the constant function 1. -/
+noncomputable def toCircle : AddCircle T → circle :=
+  (@scaled_exp_map_periodic T).lift
+#align add_circle.to_circle AddCircle.toCircle
+
+theorem toCircle_add (x : AddCircle T) (y : AddCircle T) :
+    @toCircle T (x + y) = toCircle x * toCircle y := by
+  induction x using QuotientAddGroup.induction_on'
+  induction y using QuotientAddGroup.induction_on'
+  rw [← QuotientAddGroup.mk_add]
+  simp_rw [toCircle, Function.Periodic.lift_coe, mul_add, expMapCircle_add]
+#align add_circle.to_circle_add AddCircle.toCircle_add
+
+theorem continuous_toCircle : Continuous (@toCircle T) :=
+  continuous_coinduced_dom.mpr (expMapCircle.continuous.comp <| continuous_const.mul continuous_id')
+#align add_circle.continuous_to_circle AddCircle.continuous_toCircle
+
+theorem injective_toCircle (hT : T ≠ 0) : Function.Injective (@toCircle T) := by
+  intro a b h
+  induction a using QuotientAddGroup.induction_on'
+  induction b using QuotientAddGroup.induction_on'
+  simp_rw [toCircle, Function.Periodic.lift_coe] at h
+  obtain ⟨m, hm⟩ := expMapCircle_eq_expMapCircle.mp h.symm
+  rw [QuotientAddGroup.eq]; simp_rw [AddSubgroup.mem_zmultiples_iff, zsmul_eq_mul]
+  use m
+  field_simp at hm
+  rw [← mul_right_inj' Real.two_pi_pos.ne']
+  linarith
+#align add_circle.injective_to_circle AddCircle.injective_toCircle
+
+end AddCircle

f333194f

chore: rename LocalEquiv to PartialEquiv (#8984)

The current name is misleading: there's no open set involved; it's just an equivalence between subsets of domain and target. zulip discussion

PEquiv is similarly named: this is fine, as they're different designs for the same concept.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

f7006a73

Diff

@@ -12,8 +12,8 @@ import Mathlib.Analysis.SpecialFunctions.Complex.Log
 # Maps on the unit circle
 
 In this file we prove some basic lemmas about `expMapCircle` and the restriction of `Complex.arg`
-to the unit circle. These two maps define a local equivalence between `circle` and `ℝ`, see
-`circle.argLocalEquiv` and `circle.argEquiv`, that sends the whole circle to `(-π, π]`.
+to the unit circle. These two maps define a partial equivalence between `circle` and `ℝ`, see
+`circle.argPartialEquiv` and `circle.argEquiv`, that sends the whole circle to `(-π, π]`.
 -/
 
 
@@ -45,10 +45,10 @@ theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
 
 namespace circle
 
-/-- `Complex.arg ∘ (↑)` and `expMapCircle` define a local equivalence between `circle` and `ℝ`
+/-- `Complex.arg ∘ (↑)` and `expMapCircle` define a partial equivalence between `circle` and `ℝ`
 with `source = Set.univ` and `target = Set.Ioc (-π) π`. -/
 @[simps (config := .asFn)]
-noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
+noncomputable def argPartialEquiv : PartialEquiv circle ℝ where
   toFun := arg ∘ (↑)
   invFun := expMapCircle
   source := univ
@@ -57,15 +57,15 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
   map_target' := mapsTo_univ _ _
   left_inv' z _ := expMapCircle_arg z
   right_inv' _ hx := arg_expMapCircle hx.1 hx.2
-#align circle.arg_local_equiv circle.argLocalEquiv
+#align circle.arg_local_equiv circle.argPartialEquiv
 
 /-- `Complex.arg` and `expMapCircle` define an equivalence between `circle` and `(-π, π]`. -/
 @[simps (config := .asFn)]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π where
   toFun z := ⟨arg z, neg_pi_lt_arg _, arg_le_pi _⟩
   invFun := expMapCircle ∘ (↑)
-  left_inv _ := argLocalEquiv.left_inv trivial
-  right_inv x := Subtype.ext <| argLocalEquiv.right_inv x.2
+  left_inv _ := argPartialEquiv.left_inv trivial
+  right_inv x := Subtype.ext <| argPartialEquiv.right_inv x.2
 #align circle.arg_equiv circle.argEquiv
 
 end circle
@@ -75,11 +75,11 @@ theorem leftInverse_expMapCircle_arg : LeftInverse expMapCircle (arg ∘ (↑))
 #align left_inverse_exp_map_circle_arg leftInverse_expMapCircle_arg
 
 theorem invOn_arg_expMapCircle : InvOn (arg ∘ (↑)) expMapCircle (Ioc (-π) π) univ :=
-  circle.argLocalEquiv.symm.invOn
+  circle.argPartialEquiv.symm.invOn
 #align inv_on_arg_exp_map_circle invOn_arg_expMapCircle
 
 theorem surjOn_expMapCircle_neg_pi_pi : SurjOn expMapCircle (Ioc (-π) π) univ :=
-  circle.argLocalEquiv.symm.surjOn
+  circle.argPartialEquiv.symm.surjOn
 #align surj_on_exp_map_circle_neg_pi_pi surjOn_expMapCircle_neg_pi_pi
 
 theorem expMapCircle_eq_expMapCircle {x y : ℝ} :

f333194f

style: shorten simps configurations (#8296)

Use .asFn and .lemmasOnly as simps configuration options.

For reference, these are defined here:

https://github.com/leanprover-community/mathlib4/blob/4055c8b471380825f07416b12cb0cf266da44d84/Mathlib/Tactic/Simps/Basic.lean#L843-L851

e0637173

Diff

@@ -47,7 +47,7 @@ namespace circle
 
 /-- `Complex.arg ∘ (↑)` and `expMapCircle` define a local equivalence between `circle` and `ℝ`
 with `source = Set.univ` and `target = Set.Ioc (-π) π`. -/
-@[simps (config := { fullyApplied := false })]
+@[simps (config := .asFn)]
 noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
   toFun := arg ∘ (↑)
   invFun := expMapCircle
@@ -60,7 +60,7 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
 #align circle.arg_local_equiv circle.argLocalEquiv
 
 /-- `Complex.arg` and `expMapCircle` define an equivalence between `circle` and `(-π, π]`. -/
-@[simps (config := { fullyApplied := false })]
+@[simps (config := .asFn)]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π where
   toFun z := ⟨arg z, neg_pi_lt_arg _, arg_le_pi _⟩
   invFun := expMapCircle ∘ (↑)

f333194f

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.special_functions.complex.circle
-! leanprover-community/mathlib commit f333194f5ecd1482191452c5ea60b37d4d6afa08
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.Circle
 import Mathlib.Analysis.SpecialFunctions.Complex.Log
 
+#align_import analysis.special_functions.complex.circle from "leanprover-community/mathlib"@"f333194f5ecd1482191452c5ea60b37d4d6afa08"
+
 /-!
 # Maps on the unit circle

f333194f

chore: fix upper/lowercase in comments (#4360)

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

27d257fc

Diff

@@ -14,7 +14,7 @@ import Mathlib.Analysis.SpecialFunctions.Complex.Log
 /-!
 # Maps on the unit circle
 
-In this file we prove some basic lemmas about `exp_map_circle` and the restriction of `Complex.arg`
+In this file we prove some basic lemmas about `expMapCircle` and the restriction of `Complex.arg`
 to the unit circle. These two maps define a local equivalence between `circle` and `ℝ`, see
 `circle.argLocalEquiv` and `circle.argEquiv`, that sends the whole circle to `(-π, π]`.
 -/
@@ -48,8 +48,8 @@ theorem expMapCircle_arg (z : circle) : expMapCircle (arg z) = z :=
 
 namespace circle
 
-/-- `complex.arg ∘ (↑)` and `exp_map_circle` define a local equivalence between `circle` and `ℝ`
-with `source = set.univ` and `target = set.Ioc (-π) π`. -/
+/-- `Complex.arg ∘ (↑)` and `expMapCircle` define a local equivalence between `circle` and `ℝ`
+with `source = Set.univ` and `target = Set.Ioc (-π) π`. -/
 @[simps (config := { fullyApplied := false })]
 noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
   toFun := arg ∘ (↑)
@@ -62,7 +62,7 @@ noncomputable def argLocalEquiv : LocalEquiv circle ℝ where
   right_inv' _ hx := arg_expMapCircle hx.1 hx.2
 #align circle.arg_local_equiv circle.argLocalEquiv
 
-/-- `complex.arg` and `exp_map_circle` define an equivalence between `circle` and `(-π, π]`. -/
+/-- `Complex.arg` and `expMapCircle` define an equivalence between `circle` and `(-π, π]`. -/
 @[simps (config := { fullyApplied := false })]
 noncomputable def argEquiv : circle ≃ Ioc (-π) π where
   toFun z := ⟨arg z, neg_pi_lt_arg _, arg_le_pi _⟩

f333194f

feat: port Analysis.SpecialFunctions.Complex.Circle (#4151)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

7f9830ea

`analysis.special_functions.complex.circle` ⟷ `Mathlib.Analysis.SpecialFunctions.Complex.Circle`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 748

analysis.special_functions.complex.circle ⟷ Mathlib.Analysis.SpecialFunctions.Complex.Circle

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 748

`analysis.special_functions.complex.circle` ⟷ `Mathlib.Analysis.SpecialFunctions.Complex.Circle`