analysis.complex.re_im_topology ⟷ Mathlib.Analysis.Complex.ReImTopology

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

@@ -46,14 +46,14 @@ namespace Complex
 #print Complex.isHomeomorphicTrivialFiberBundle_re /-
 /-- `complex.re` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_re : IsHomeomorphicTrivialFiberBundle ℝ re :=
-  ⟨equivRealProdClm.toHomeomorph, fun z => rfl⟩
+  ⟨equivRealProdCLM.toHomeomorph, fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_re
 -/
 
 #print Complex.isHomeomorphicTrivialFiberBundle_im /-
 /-- `complex.im` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_im : IsHomeomorphicTrivialFiberBundle ℝ im :=
-  ⟨equivRealProdClm.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun z => rfl⟩
+  ⟨equivRealProdCLM.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_im
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.Complex.Basic
-import Mathbin.Topology.FiberBundle.IsHomeomorphicTrivialBundle
+import Analysis.Complex.Basic
+import Topology.FiberBundle.IsHomeomorphicTrivialBundle
 
 #align_import analysis.complex.re_im_topology from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
 

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

@@ -283,9 +283,9 @@ theorem IsClosed.reProdIm (hs : IsClosed s) (ht : IsClosed t) : IsClosed (s ×
 #align is_closed.re_prod_im IsClosed.reProdIm
 -/
 
-#print Metric.Bounded.reProdIm /-
-theorem Metric.Bounded.reProdIm (hs : Bounded s) (ht : Bounded t) : Bounded (s ×ℂ t) :=
-  antilipschitz_equivRealProd.bounded_preimage (hs.Prod ht)
-#align metric.bounded.re_prod_im Metric.Bounded.reProdIm
+#print Bornology.IsBounded.reProdIm /-
+theorem Bornology.IsBounded.reProdIm (hs : IsBounded s) (ht : IsBounded t) : IsBounded (s ×ℂ t) :=
+  antilipschitz_equivRealProd.isBounded_preimage (hs.Prod ht)
+#align metric.bounded.re_prod_im Bornology.IsBounded.reProdIm
 -/
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.complex.re_im_topology
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.Basic
 import Mathbin.Topology.FiberBundle.IsHomeomorphicTrivialBundle
 
+#align_import analysis.complex.re_im_topology from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # Closure, interior, and frontier of preimages under `re` and `im`
 

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

@@ -46,161 +46,227 @@ noncomputable section
 
 namespace Complex
 
+#print Complex.isHomeomorphicTrivialFiberBundle_re /-
 /-- `complex.re` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_re : IsHomeomorphicTrivialFiberBundle ℝ re :=
   ⟨equivRealProdClm.toHomeomorph, fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_re
+-/
 
+#print Complex.isHomeomorphicTrivialFiberBundle_im /-
 /-- `complex.im` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_im : IsHomeomorphicTrivialFiberBundle ℝ im :=
   ⟨equivRealProdClm.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_im
+-/
 
+#print Complex.isOpenMap_re /-
 theorem isOpenMap_re : IsOpenMap re :=
   isHomeomorphicTrivialFiberBundle_re.isOpenMap_proj
 #align complex.is_open_map_re Complex.isOpenMap_re
+-/
 
+#print Complex.isOpenMap_im /-
 theorem isOpenMap_im : IsOpenMap im :=
   isHomeomorphicTrivialFiberBundle_im.isOpenMap_proj
 #align complex.is_open_map_im Complex.isOpenMap_im
+-/
 
+#print Complex.quotientMap_re /-
 theorem quotientMap_re : QuotientMap re :=
   isHomeomorphicTrivialFiberBundle_re.quotientMap_proj
 #align complex.quotient_map_re Complex.quotientMap_re
+-/
 
+#print Complex.quotientMap_im /-
 theorem quotientMap_im : QuotientMap im :=
   isHomeomorphicTrivialFiberBundle_im.quotientMap_proj
 #align complex.quotient_map_im Complex.quotientMap_im
+-/
 
+#print Complex.interior_preimage_re /-
 theorem interior_preimage_re (s : Set ℝ) : interior (re ⁻¹' s) = re ⁻¹' interior s :=
   (isOpenMap_re.preimage_interior_eq_interior_preimage continuous_re _).symm
 #align complex.interior_preimage_re Complex.interior_preimage_re
+-/
 
+#print Complex.interior_preimage_im /-
 theorem interior_preimage_im (s : Set ℝ) : interior (im ⁻¹' s) = im ⁻¹' interior s :=
   (isOpenMap_im.preimage_interior_eq_interior_preimage continuous_im _).symm
 #align complex.interior_preimage_im Complex.interior_preimage_im
+-/
 
+#print Complex.closure_preimage_re /-
 theorem closure_preimage_re (s : Set ℝ) : closure (re ⁻¹' s) = re ⁻¹' closure s :=
   (isOpenMap_re.preimage_closure_eq_closure_preimage continuous_re _).symm
 #align complex.closure_preimage_re Complex.closure_preimage_re
+-/
 
+#print Complex.closure_preimage_im /-
 theorem closure_preimage_im (s : Set ℝ) : closure (im ⁻¹' s) = im ⁻¹' closure s :=
   (isOpenMap_im.preimage_closure_eq_closure_preimage continuous_im _).symm
 #align complex.closure_preimage_im Complex.closure_preimage_im
+-/
 
+#print Complex.frontier_preimage_re /-
 theorem frontier_preimage_re (s : Set ℝ) : frontier (re ⁻¹' s) = re ⁻¹' frontier s :=
   (isOpenMap_re.preimage_frontier_eq_frontier_preimage continuous_re _).symm
 #align complex.frontier_preimage_re Complex.frontier_preimage_re
+-/
 
+#print Complex.frontier_preimage_im /-
 theorem frontier_preimage_im (s : Set ℝ) : frontier (im ⁻¹' s) = im ⁻¹' frontier s :=
   (isOpenMap_im.preimage_frontier_eq_frontier_preimage continuous_im _).symm
 #align complex.frontier_preimage_im Complex.frontier_preimage_im
+-/
 
+#print Complex.interior_setOf_re_le /-
 @[simp]
 theorem interior_setOf_re_le (a : ℝ) : interior {z : ℂ | z.re ≤ a} = {z | z.re < a} := by
   simpa only [interior_Iic] using interior_preimage_re (Iic a)
 #align complex.interior_set_of_re_le Complex.interior_setOf_re_le
+-/
 
+#print Complex.interior_setOf_im_le /-
 @[simp]
 theorem interior_setOf_im_le (a : ℝ) : interior {z : ℂ | z.im ≤ a} = {z | z.im < a} := by
   simpa only [interior_Iic] using interior_preimage_im (Iic a)
 #align complex.interior_set_of_im_le Complex.interior_setOf_im_le
+-/
 
+#print Complex.interior_setOf_le_re /-
 @[simp]
 theorem interior_setOf_le_re (a : ℝ) : interior {z : ℂ | a ≤ z.re} = {z | a < z.re} := by
   simpa only [interior_Ici] using interior_preimage_re (Ici a)
 #align complex.interior_set_of_le_re Complex.interior_setOf_le_re
+-/
 
+#print Complex.interior_setOf_le_im /-
 @[simp]
 theorem interior_setOf_le_im (a : ℝ) : interior {z : ℂ | a ≤ z.im} = {z | a < z.im} := by
   simpa only [interior_Ici] using interior_preimage_im (Ici a)
 #align complex.interior_set_of_le_im Complex.interior_setOf_le_im
+-/
 
+#print Complex.closure_setOf_re_lt /-
 @[simp]
 theorem closure_setOf_re_lt (a : ℝ) : closure {z : ℂ | z.re < a} = {z | z.re ≤ a} := by
   simpa only [closure_Iio] using closure_preimage_re (Iio a)
 #align complex.closure_set_of_re_lt Complex.closure_setOf_re_lt
+-/
 
+#print Complex.closure_setOf_im_lt /-
 @[simp]
 theorem closure_setOf_im_lt (a : ℝ) : closure {z : ℂ | z.im < a} = {z | z.im ≤ a} := by
   simpa only [closure_Iio] using closure_preimage_im (Iio a)
 #align complex.closure_set_of_im_lt Complex.closure_setOf_im_lt
+-/
 
+#print Complex.closure_setOf_lt_re /-
 @[simp]
 theorem closure_setOf_lt_re (a : ℝ) : closure {z : ℂ | a < z.re} = {z | a ≤ z.re} := by
   simpa only [closure_Ioi] using closure_preimage_re (Ioi a)
 #align complex.closure_set_of_lt_re Complex.closure_setOf_lt_re
+-/
 
+#print Complex.closure_setOf_lt_im /-
 @[simp]
 theorem closure_setOf_lt_im (a : ℝ) : closure {z : ℂ | a < z.im} = {z | a ≤ z.im} := by
   simpa only [closure_Ioi] using closure_preimage_im (Ioi a)
 #align complex.closure_set_of_lt_im Complex.closure_setOf_lt_im
+-/
 
+#print Complex.frontier_setOf_re_le /-
 @[simp]
 theorem frontier_setOf_re_le (a : ℝ) : frontier {z : ℂ | z.re ≤ a} = {z | z.re = a} := by
   simpa only [frontier_Iic] using frontier_preimage_re (Iic a)
 #align complex.frontier_set_of_re_le Complex.frontier_setOf_re_le
+-/
 
+#print Complex.frontier_setOf_im_le /-
 @[simp]
 theorem frontier_setOf_im_le (a : ℝ) : frontier {z : ℂ | z.im ≤ a} = {z | z.im = a} := by
   simpa only [frontier_Iic] using frontier_preimage_im (Iic a)
 #align complex.frontier_set_of_im_le Complex.frontier_setOf_im_le
+-/
 
+#print Complex.frontier_setOf_le_re /-
 @[simp]
 theorem frontier_setOf_le_re (a : ℝ) : frontier {z : ℂ | a ≤ z.re} = {z | z.re = a} := by
   simpa only [frontier_Ici] using frontier_preimage_re (Ici a)
 #align complex.frontier_set_of_le_re Complex.frontier_setOf_le_re
+-/
 
+#print Complex.frontier_setOf_le_im /-
 @[simp]
 theorem frontier_setOf_le_im (a : ℝ) : frontier {z : ℂ | a ≤ z.im} = {z | z.im = a} := by
   simpa only [frontier_Ici] using frontier_preimage_im (Ici a)
 #align complex.frontier_set_of_le_im Complex.frontier_setOf_le_im
+-/
 
+#print Complex.frontier_setOf_re_lt /-
 @[simp]
 theorem frontier_setOf_re_lt (a : ℝ) : frontier {z : ℂ | z.re < a} = {z | z.re = a} := by
   simpa only [frontier_Iio] using frontier_preimage_re (Iio a)
 #align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_lt
+-/
 
+#print Complex.frontier_setOf_im_lt /-
 @[simp]
 theorem frontier_setOf_im_lt (a : ℝ) : frontier {z : ℂ | z.im < a} = {z | z.im = a} := by
   simpa only [frontier_Iio] using frontier_preimage_im (Iio a)
 #align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_lt
+-/
 
+#print Complex.frontier_setOf_lt_re /-
 @[simp]
 theorem frontier_setOf_lt_re (a : ℝ) : frontier {z : ℂ | a < z.re} = {z | z.re = a} := by
   simpa only [frontier_Ioi] using frontier_preimage_re (Ioi a)
 #align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_re
+-/
 
+#print Complex.frontier_setOf_lt_im /-
 @[simp]
 theorem frontier_setOf_lt_im (a : ℝ) : frontier {z : ℂ | a < z.im} = {z | z.im = a} := by
   simpa only [frontier_Ioi] using frontier_preimage_im (Ioi a)
 #align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_im
+-/
 
+#print Complex.closure_reProdIm /-
 theorem closure_reProdIm (s t : Set ℝ) : closure (s ×ℂ t) = closure s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t
 #align complex.closure_re_prod_im Complex.closure_reProdIm
+-/
 
+#print Complex.interior_reProdIm /-
 theorem interior_reProdIm (s t : Set ℝ) : interior (s ×ℂ t) = interior s ×ℂ interior t := by
   rw [re_prod_im, re_prod_im, interior_inter, interior_preimage_re, interior_preimage_im]
 #align complex.interior_re_prod_im Complex.interior_reProdIm
+-/
 
+#print Complex.frontier_reProdIm /-
 theorem frontier_reProdIm (s t : Set ℝ) :
     frontier (s ×ℂ t) = closure s ×ℂ frontier t ∪ frontier s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_frontier] using frontier_prod_eq s t
 #align complex.frontier_re_prod_im Complex.frontier_reProdIm
+-/
 
+#print Complex.frontier_setOf_le_re_and_le_im /-
 theorem frontier_setOf_le_re_and_le_im (a b : ℝ) :
     frontier {z | a ≤ re z ∧ b ≤ im z} = {z | a ≤ re z ∧ im z = b ∨ re z = a ∧ b ≤ im z} := by
   simpa only [closure_Ici, frontier_Ici] using frontier_re_prod_im (Ici a) (Ici b)
 #align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_im
+-/
 
+#print Complex.frontier_setOf_le_re_and_im_le /-
 theorem frontier_setOf_le_re_and_im_le (a b : ℝ) :
     frontier {z | a ≤ re z ∧ im z ≤ b} = {z | a ≤ re z ∧ im z = b ∨ re z = a ∧ im z ≤ b} := by
   simpa only [closure_Ici, closure_Iic, frontier_Ici, frontier_Iic] using
     frontier_re_prod_im (Ici a) (Iic b)
 #align complex.frontier_set_of_le_re_and_im_le Complex.frontier_setOf_le_re_and_im_le
+-/
 
 end Complex
 
@@ -208,15 +274,21 @@ open Complex Metric
 
 variable {s t : Set ℝ}
 
+#print IsOpen.reProdIm /-
 theorem IsOpen.reProdIm (hs : IsOpen s) (ht : IsOpen t) : IsOpen (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_open.re_prod_im IsOpen.reProdIm
+-/
 
+#print IsClosed.reProdIm /-
 theorem IsClosed.reProdIm (hs : IsClosed s) (ht : IsClosed t) : IsClosed (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_closed.re_prod_im IsClosed.reProdIm
+-/
 
+#print Metric.Bounded.reProdIm /-
 theorem Metric.Bounded.reProdIm (hs : Bounded s) (ht : Bounded t) : Bounded (s ×ℂ t) :=
   antilipschitz_equivRealProd.bounded_preimage (hs.Prod ht)
 #align metric.bounded.re_prod_im Metric.Bounded.reProdIm
+-/
 

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

@@ -97,82 +97,82 @@ theorem frontier_preimage_im (s : Set ℝ) : frontier (im ⁻¹' s) = im ⁻¹'
 #align complex.frontier_preimage_im Complex.frontier_preimage_im
 
 @[simp]
-theorem interior_setOf_re_le (a : ℝ) : interior { z : ℂ | z.re ≤ a } = { z | z.re < a } := by
+theorem interior_setOf_re_le (a : ℝ) : interior {z : ℂ | z.re ≤ a} = {z | z.re < a} := by
   simpa only [interior_Iic] using interior_preimage_re (Iic a)
 #align complex.interior_set_of_re_le Complex.interior_setOf_re_le
 
 @[simp]
-theorem interior_setOf_im_le (a : ℝ) : interior { z : ℂ | z.im ≤ a } = { z | z.im < a } := by
+theorem interior_setOf_im_le (a : ℝ) : interior {z : ℂ | z.im ≤ a} = {z | z.im < a} := by
   simpa only [interior_Iic] using interior_preimage_im (Iic a)
 #align complex.interior_set_of_im_le Complex.interior_setOf_im_le
 
 @[simp]
-theorem interior_setOf_le_re (a : ℝ) : interior { z : ℂ | a ≤ z.re } = { z | a < z.re } := by
+theorem interior_setOf_le_re (a : ℝ) : interior {z : ℂ | a ≤ z.re} = {z | a < z.re} := by
   simpa only [interior_Ici] using interior_preimage_re (Ici a)
 #align complex.interior_set_of_le_re Complex.interior_setOf_le_re
 
 @[simp]
-theorem interior_setOf_le_im (a : ℝ) : interior { z : ℂ | a ≤ z.im } = { z | a < z.im } := by
+theorem interior_setOf_le_im (a : ℝ) : interior {z : ℂ | a ≤ z.im} = {z | a < z.im} := by
   simpa only [interior_Ici] using interior_preimage_im (Ici a)
 #align complex.interior_set_of_le_im Complex.interior_setOf_le_im
 
 @[simp]
-theorem closure_setOf_re_lt (a : ℝ) : closure { z : ℂ | z.re < a } = { z | z.re ≤ a } := by
+theorem closure_setOf_re_lt (a : ℝ) : closure {z : ℂ | z.re < a} = {z | z.re ≤ a} := by
   simpa only [closure_Iio] using closure_preimage_re (Iio a)
 #align complex.closure_set_of_re_lt Complex.closure_setOf_re_lt
 
 @[simp]
-theorem closure_setOf_im_lt (a : ℝ) : closure { z : ℂ | z.im < a } = { z | z.im ≤ a } := by
+theorem closure_setOf_im_lt (a : ℝ) : closure {z : ℂ | z.im < a} = {z | z.im ≤ a} := by
   simpa only [closure_Iio] using closure_preimage_im (Iio a)
 #align complex.closure_set_of_im_lt Complex.closure_setOf_im_lt
 
 @[simp]
-theorem closure_setOf_lt_re (a : ℝ) : closure { z : ℂ | a < z.re } = { z | a ≤ z.re } := by
+theorem closure_setOf_lt_re (a : ℝ) : closure {z : ℂ | a < z.re} = {z | a ≤ z.re} := by
   simpa only [closure_Ioi] using closure_preimage_re (Ioi a)
 #align complex.closure_set_of_lt_re Complex.closure_setOf_lt_re
 
 @[simp]
-theorem closure_setOf_lt_im (a : ℝ) : closure { z : ℂ | a < z.im } = { z | a ≤ z.im } := by
+theorem closure_setOf_lt_im (a : ℝ) : closure {z : ℂ | a < z.im} = {z | a ≤ z.im} := by
   simpa only [closure_Ioi] using closure_preimage_im (Ioi a)
 #align complex.closure_set_of_lt_im Complex.closure_setOf_lt_im
 
 @[simp]
-theorem frontier_setOf_re_le (a : ℝ) : frontier { z : ℂ | z.re ≤ a } = { z | z.re = a } := by
+theorem frontier_setOf_re_le (a : ℝ) : frontier {z : ℂ | z.re ≤ a} = {z | z.re = a} := by
   simpa only [frontier_Iic] using frontier_preimage_re (Iic a)
 #align complex.frontier_set_of_re_le Complex.frontier_setOf_re_le
 
 @[simp]
-theorem frontier_setOf_im_le (a : ℝ) : frontier { z : ℂ | z.im ≤ a } = { z | z.im = a } := by
+theorem frontier_setOf_im_le (a : ℝ) : frontier {z : ℂ | z.im ≤ a} = {z | z.im = a} := by
   simpa only [frontier_Iic] using frontier_preimage_im (Iic a)
 #align complex.frontier_set_of_im_le Complex.frontier_setOf_im_le
 
 @[simp]
-theorem frontier_setOf_le_re (a : ℝ) : frontier { z : ℂ | a ≤ z.re } = { z | z.re = a } := by
+theorem frontier_setOf_le_re (a : ℝ) : frontier {z : ℂ | a ≤ z.re} = {z | z.re = a} := by
   simpa only [frontier_Ici] using frontier_preimage_re (Ici a)
 #align complex.frontier_set_of_le_re Complex.frontier_setOf_le_re
 
 @[simp]
-theorem frontier_setOf_le_im (a : ℝ) : frontier { z : ℂ | a ≤ z.im } = { z | z.im = a } := by
+theorem frontier_setOf_le_im (a : ℝ) : frontier {z : ℂ | a ≤ z.im} = {z | z.im = a} := by
   simpa only [frontier_Ici] using frontier_preimage_im (Ici a)
 #align complex.frontier_set_of_le_im Complex.frontier_setOf_le_im
 
 @[simp]
-theorem frontier_setOf_re_lt (a : ℝ) : frontier { z : ℂ | z.re < a } = { z | z.re = a } := by
+theorem frontier_setOf_re_lt (a : ℝ) : frontier {z : ℂ | z.re < a} = {z | z.re = a} := by
   simpa only [frontier_Iio] using frontier_preimage_re (Iio a)
 #align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_lt
 
 @[simp]
-theorem frontier_setOf_im_lt (a : ℝ) : frontier { z : ℂ | z.im < a } = { z | z.im = a } := by
+theorem frontier_setOf_im_lt (a : ℝ) : frontier {z : ℂ | z.im < a} = {z | z.im = a} := by
   simpa only [frontier_Iio] using frontier_preimage_im (Iio a)
 #align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_lt
 
 @[simp]
-theorem frontier_setOf_lt_re (a : ℝ) : frontier { z : ℂ | a < z.re } = { z | z.re = a } := by
+theorem frontier_setOf_lt_re (a : ℝ) : frontier {z : ℂ | a < z.re} = {z | z.re = a} := by
   simpa only [frontier_Ioi] using frontier_preimage_re (Ioi a)
 #align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_re
 
 @[simp]
-theorem frontier_setOf_lt_im (a : ℝ) : frontier { z : ℂ | a < z.im } = { z | z.im = a } := by
+theorem frontier_setOf_lt_im (a : ℝ) : frontier {z : ℂ | a < z.im} = {z | z.im = a} := by
   simpa only [frontier_Ioi] using frontier_preimage_im (Ioi a)
 #align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_im
 
@@ -192,12 +192,12 @@ theorem frontier_reProdIm (s t : Set ℝ) :
 #align complex.frontier_re_prod_im Complex.frontier_reProdIm
 
 theorem frontier_setOf_le_re_and_le_im (a b : ℝ) :
-    frontier { z | a ≤ re z ∧ b ≤ im z } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ b ≤ im z } := by
+    frontier {z | a ≤ re z ∧ b ≤ im z} = {z | a ≤ re z ∧ im z = b ∨ re z = a ∧ b ≤ im z} := by
   simpa only [closure_Ici, frontier_Ici] using frontier_re_prod_im (Ici a) (Ici b)
 #align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_im
 
 theorem frontier_setOf_le_re_and_im_le (a b : ℝ) :
-    frontier { z | a ≤ re z ∧ im z ≤ b } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ im z ≤ b } := by
+    frontier {z | a ≤ re z ∧ im z ≤ b} = {z | a ≤ re z ∧ im z = b ∨ re z = a ∧ im z ≤ b} := by
   simpa only [closure_Ici, closure_Iic, frontier_Ici, frontier_Iic] using
     frontier_re_prod_im (Ici a) (Iic b)
 #align complex.frontier_set_of_le_re_and_im_le Complex.frontier_setOf_le_re_and_im_le

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

@@ -46,354 +46,156 @@ noncomputable section
 
 namespace Complex
 
-/- warning: complex.is_homeomorphic_trivial_fiber_bundle_re -> Complex.isHomeomorphicTrivialFiberBundle_re is a dubious translation:
-lean 3 declaration is
-  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.re
-but is expected to have type
-  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.re
-Case conversion may be inaccurate. Consider using '#align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_reₓ'. -/
 /-- `complex.re` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_re : IsHomeomorphicTrivialFiberBundle ℝ re :=
   ⟨equivRealProdClm.toHomeomorph, fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_re
 
-/- warning: complex.is_homeomorphic_trivial_fiber_bundle_im -> Complex.isHomeomorphicTrivialFiberBundle_im is a dubious translation:
-lean 3 declaration is
-  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.im
-but is expected to have type
-  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.im
-Case conversion may be inaccurate. Consider using '#align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_imₓ'. -/
 /-- `complex.im` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_im : IsHomeomorphicTrivialFiberBundle ℝ im :=
   ⟨equivRealProdClm.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_im
 
-/- warning: complex.is_open_map_re -> Complex.isOpenMap_re is a dubious translation:
-lean 3 declaration is
-  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
-but is expected to have type
-  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
-Case conversion may be inaccurate. Consider using '#align complex.is_open_map_re Complex.isOpenMap_reₓ'. -/
 theorem isOpenMap_re : IsOpenMap re :=
   isHomeomorphicTrivialFiberBundle_re.isOpenMap_proj
 #align complex.is_open_map_re Complex.isOpenMap_re
 
-/- warning: complex.is_open_map_im -> Complex.isOpenMap_im is a dubious translation:
-lean 3 declaration is
-  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
-but is expected to have type
-  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
-Case conversion may be inaccurate. Consider using '#align complex.is_open_map_im Complex.isOpenMap_imₓ'. -/
 theorem isOpenMap_im : IsOpenMap im :=
   isHomeomorphicTrivialFiberBundle_im.isOpenMap_proj
 #align complex.is_open_map_im Complex.isOpenMap_im
 
-/- warning: complex.quotient_map_re -> Complex.quotientMap_re is a dubious translation:
-lean 3 declaration is
-  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
-but is expected to have type
-  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
-Case conversion may be inaccurate. Consider using '#align complex.quotient_map_re Complex.quotientMap_reₓ'. -/
 theorem quotientMap_re : QuotientMap re :=
   isHomeomorphicTrivialFiberBundle_re.quotientMap_proj
 #align complex.quotient_map_re Complex.quotientMap_re
 
-/- warning: complex.quotient_map_im -> Complex.quotientMap_im is a dubious translation:
-lean 3 declaration is
-  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
-but is expected to have type
-  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
-Case conversion may be inaccurate. Consider using '#align complex.quotient_map_im Complex.quotientMap_imₓ'. -/
 theorem quotientMap_im : QuotientMap im :=
   isHomeomorphicTrivialFiberBundle_im.quotientMap_proj
 #align complex.quotient_map_im Complex.quotientMap_im
 
-/- warning: complex.interior_preimage_re -> Complex.interior_preimage_re is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.interior_preimage_re Complex.interior_preimage_reₓ'. -/
 theorem interior_preimage_re (s : Set ℝ) : interior (re ⁻¹' s) = re ⁻¹' interior s :=
   (isOpenMap_re.preimage_interior_eq_interior_preimage continuous_re _).symm
 #align complex.interior_preimage_re Complex.interior_preimage_re
 
-/- warning: complex.interior_preimage_im -> Complex.interior_preimage_im is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.interior_preimage_im Complex.interior_preimage_imₓ'. -/
 theorem interior_preimage_im (s : Set ℝ) : interior (im ⁻¹' s) = im ⁻¹' interior s :=
   (isOpenMap_im.preimage_interior_eq_interior_preimage continuous_im _).symm
 #align complex.interior_preimage_im Complex.interior_preimage_im
 
-/- warning: complex.closure_preimage_re -> Complex.closure_preimage_re is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.closure_preimage_re Complex.closure_preimage_reₓ'. -/
 theorem closure_preimage_re (s : Set ℝ) : closure (re ⁻¹' s) = re ⁻¹' closure s :=
   (isOpenMap_re.preimage_closure_eq_closure_preimage continuous_re _).symm
 #align complex.closure_preimage_re Complex.closure_preimage_re
 
-/- warning: complex.closure_preimage_im -> Complex.closure_preimage_im is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.closure_preimage_im Complex.closure_preimage_imₓ'. -/
 theorem closure_preimage_im (s : Set ℝ) : closure (im ⁻¹' s) = im ⁻¹' closure s :=
   (isOpenMap_im.preimage_closure_eq_closure_preimage continuous_im _).symm
 #align complex.closure_preimage_im Complex.closure_preimage_im
 
-/- warning: complex.frontier_preimage_re -> Complex.frontier_preimage_re is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_preimage_re Complex.frontier_preimage_reₓ'. -/
 theorem frontier_preimage_re (s : Set ℝ) : frontier (re ⁻¹' s) = re ⁻¹' frontier s :=
   (isOpenMap_re.preimage_frontier_eq_frontier_preimage continuous_re _).symm
 #align complex.frontier_preimage_re Complex.frontier_preimage_re
 
-/- warning: complex.frontier_preimage_im -> Complex.frontier_preimage_im is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-but is expected to have type
-  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_preimage_im Complex.frontier_preimage_imₓ'. -/
 theorem frontier_preimage_im (s : Set ℝ) : frontier (im ⁻¹' s) = im ⁻¹' frontier s :=
   (isOpenMap_im.preimage_frontier_eq_frontier_preimage continuous_im _).symm
 #align complex.frontier_preimage_im Complex.frontier_preimage_im
 
-/- warning: complex.interior_set_of_re_le -> Complex.interior_setOf_re_le is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_re_le Complex.interior_setOf_re_leₓ'. -/
 @[simp]
 theorem interior_setOf_re_le (a : ℝ) : interior { z : ℂ | z.re ≤ a } = { z | z.re < a } := by
   simpa only [interior_Iic] using interior_preimage_re (Iic a)
 #align complex.interior_set_of_re_le Complex.interior_setOf_re_le
 
-/- warning: complex.interior_set_of_im_le -> Complex.interior_setOf_im_le is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_im_le Complex.interior_setOf_im_leₓ'. -/
 @[simp]
 theorem interior_setOf_im_le (a : ℝ) : interior { z : ℂ | z.im ≤ a } = { z | z.im < a } := by
   simpa only [interior_Iic] using interior_preimage_im (Iic a)
 #align complex.interior_set_of_im_le Complex.interior_setOf_im_le
 
-/- warning: complex.interior_set_of_le_re -> Complex.interior_setOf_le_re is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))
-Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_le_re Complex.interior_setOf_le_reₓ'. -/
 @[simp]
 theorem interior_setOf_le_re (a : ℝ) : interior { z : ℂ | a ≤ z.re } = { z | a < z.re } := by
   simpa only [interior_Ici] using interior_preimage_re (Ici a)
 #align complex.interior_set_of_le_re Complex.interior_setOf_le_re
 
-/- warning: complex.interior_set_of_le_im -> Complex.interior_setOf_le_im is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))
-Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_le_im Complex.interior_setOf_le_imₓ'. -/
 @[simp]
 theorem interior_setOf_le_im (a : ℝ) : interior { z : ℂ | a ≤ z.im } = { z | a < z.im } := by
   simpa only [interior_Ici] using interior_preimage_im (Ici a)
 #align complex.interior_set_of_le_im Complex.interior_setOf_le_im
 
-/- warning: complex.closure_set_of_re_lt -> Complex.closure_setOf_re_lt is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_re_lt Complex.closure_setOf_re_ltₓ'. -/
 @[simp]
 theorem closure_setOf_re_lt (a : ℝ) : closure { z : ℂ | z.re < a } = { z | z.re ≤ a } := by
   simpa only [closure_Iio] using closure_preimage_re (Iio a)
 #align complex.closure_set_of_re_lt Complex.closure_setOf_re_lt
 
-/- warning: complex.closure_set_of_im_lt -> Complex.closure_setOf_im_lt is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_im_lt Complex.closure_setOf_im_ltₓ'. -/
 @[simp]
 theorem closure_setOf_im_lt (a : ℝ) : closure { z : ℂ | z.im < a } = { z | z.im ≤ a } := by
   simpa only [closure_Iio] using closure_preimage_im (Iio a)
 #align complex.closure_set_of_im_lt Complex.closure_setOf_im_lt
 
-/- warning: complex.closure_set_of_lt_re -> Complex.closure_setOf_lt_re is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))
-Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_lt_re Complex.closure_setOf_lt_reₓ'. -/
 @[simp]
 theorem closure_setOf_lt_re (a : ℝ) : closure { z : ℂ | a < z.re } = { z | a ≤ z.re } := by
   simpa only [closure_Ioi] using closure_preimage_re (Ioi a)
 #align complex.closure_set_of_lt_re Complex.closure_setOf_lt_re
 
-/- warning: complex.closure_set_of_lt_im -> Complex.closure_setOf_lt_im is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))
-Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_lt_im Complex.closure_setOf_lt_imₓ'. -/
 @[simp]
 theorem closure_setOf_lt_im (a : ℝ) : closure { z : ℂ | a < z.im } = { z | a ≤ z.im } := by
   simpa only [closure_Ioi] using closure_preimage_im (Ioi a)
 #align complex.closure_set_of_lt_im Complex.closure_setOf_lt_im
 
-/- warning: complex.frontier_set_of_re_le -> Complex.frontier_setOf_re_le is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_re_le Complex.frontier_setOf_re_leₓ'. -/
 @[simp]
 theorem frontier_setOf_re_le (a : ℝ) : frontier { z : ℂ | z.re ≤ a } = { z | z.re = a } := by
   simpa only [frontier_Iic] using frontier_preimage_re (Iic a)
 #align complex.frontier_set_of_re_le Complex.frontier_setOf_re_le
 
-/- warning: complex.frontier_set_of_im_le -> Complex.frontier_setOf_im_le is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_im_le Complex.frontier_setOf_im_leₓ'. -/
 @[simp]
 theorem frontier_setOf_im_le (a : ℝ) : frontier { z : ℂ | z.im ≤ a } = { z | z.im = a } := by
   simpa only [frontier_Iic] using frontier_preimage_im (Iic a)
 #align complex.frontier_set_of_im_le Complex.frontier_setOf_im_le
 
-/- warning: complex.frontier_set_of_le_re -> Complex.frontier_setOf_le_re is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re Complex.frontier_setOf_le_reₓ'. -/
 @[simp]
 theorem frontier_setOf_le_re (a : ℝ) : frontier { z : ℂ | a ≤ z.re } = { z | z.re = a } := by
   simpa only [frontier_Ici] using frontier_preimage_re (Ici a)
 #align complex.frontier_set_of_le_re Complex.frontier_setOf_le_re
 
-/- warning: complex.frontier_set_of_le_im -> Complex.frontier_setOf_le_im is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_im Complex.frontier_setOf_le_imₓ'. -/
 @[simp]
 theorem frontier_setOf_le_im (a : ℝ) : frontier { z : ℂ | a ≤ z.im } = { z | z.im = a } := by
   simpa only [frontier_Ici] using frontier_preimage_im (Ici a)
 #align complex.frontier_set_of_le_im Complex.frontier_setOf_le_im
 
-/- warning: complex.frontier_set_of_re_lt -> Complex.frontier_setOf_re_lt is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_ltₓ'. -/
 @[simp]
 theorem frontier_setOf_re_lt (a : ℝ) : frontier { z : ℂ | z.re < a } = { z | z.re = a } := by
   simpa only [frontier_Iio] using frontier_preimage_re (Iio a)
 #align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_lt
 
-/- warning: complex.frontier_set_of_im_lt -> Complex.frontier_setOf_im_lt is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_ltₓ'. -/
 @[simp]
 theorem frontier_setOf_im_lt (a : ℝ) : frontier { z : ℂ | z.im < a } = { z | z.im = a } := by
   simpa only [frontier_Iio] using frontier_preimage_im (Iio a)
 #align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_lt
 
-/- warning: complex.frontier_set_of_lt_re -> Complex.frontier_setOf_lt_re is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_reₓ'. -/
 @[simp]
 theorem frontier_setOf_lt_re (a : ℝ) : frontier { z : ℂ | a < z.re } = { z | z.re = a } := by
   simpa only [frontier_Ioi] using frontier_preimage_re (Ioi a)
 #align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_re
 
-/- warning: complex.frontier_set_of_lt_im -> Complex.frontier_setOf_lt_im is a dubious translation:
-lean 3 declaration is
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-but is expected to have type
-  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_imₓ'. -/
 @[simp]
 theorem frontier_setOf_lt_im (a : ℝ) : frontier { z : ℂ | a < z.im } = { z | z.im = a } := by
   simpa only [frontier_Ioi] using frontier_preimage_im (Ioi a)
 #align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_im
 
-/- warning: complex.closure_re_prod_im -> Complex.closure_reProdIm is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
-but is expected to have type
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
-Case conversion may be inaccurate. Consider using '#align complex.closure_re_prod_im Complex.closure_reProdImₓ'. -/
 theorem closure_reProdIm (s t : Set ℝ) : closure (s ×ℂ t) = closure s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t
 #align complex.closure_re_prod_im Complex.closure_reProdIm
 
-/- warning: complex.interior_re_prod_im -> Complex.interior_reProdIm is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
-but is expected to have type
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
-Case conversion may be inaccurate. Consider using '#align complex.interior_re_prod_im Complex.interior_reProdImₓ'. -/
 theorem interior_reProdIm (s t : Set ℝ) : interior (s ×ℂ t) = interior s ×ℂ interior t := by
   rw [re_prod_im, re_prod_im, interior_inter, interior_preimage_re, interior_preimage_im]
 #align complex.interior_re_prod_im Complex.interior_reProdIm
 
-/- warning: complex.frontier_re_prod_im -> Complex.frontier_reProdIm is a dubious translation:
-lean 3 declaration is
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Union.union.{0} (Set.{0} Complex) (Set.hasUnion.{0} Complex) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)) (Complex.Set.reProdIm (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)))
-but is expected to have type
-  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Union.union.{0} (Set.{0} Complex) (Set.instUnionSet.{0} Complex) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)) (Complex.Set.reProdIm (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_re_prod_im Complex.frontier_reProdImₓ'. -/
 theorem frontier_reProdIm (s t : Set ℝ) :
     frontier (s ×ℂ t) = closure s ×ℂ frontier t ∪ frontier s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_frontier] using frontier_prod_eq s t
 #align complex.frontier_re_prod_im Complex.frontier_reProdIm
 
-/- warning: complex.frontier_set_of_le_re_and_le_im -> Complex.frontier_setOf_le_re_and_le_im is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (LE.le.{0} Real Real.hasLe b (Complex.im z))))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.hasLe b (Complex.im z)))))
-but is expected to have type
-  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (LE.le.{0} Real Real.instLEReal b (Complex.im z))))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.instLEReal b (Complex.im z)))))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_imₓ'. -/
 theorem frontier_setOf_le_re_and_le_im (a b : ℝ) :
     frontier { z | a ≤ re z ∧ b ≤ im z } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ b ≤ im z } := by
   simpa only [closure_Ici, frontier_Ici] using frontier_re_prod_im (Ici a) (Ici b)
 #align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_im
 
-/- warning: complex.frontier_set_of_le_re_and_im_le -> Complex.frontier_setOf_le_re_and_im_le is a dubious translation:
-lean 3 declaration is
-  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (LE.le.{0} Real Real.hasLe (Complex.im z) b)))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.hasLe (Complex.im z) b))))
-but is expected to have type
-  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (LE.le.{0} Real Real.instLEReal (Complex.im z) b)))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.instLEReal (Complex.im z) b))))
-Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re_and_im_le Complex.frontier_setOf_le_re_and_im_leₓ'. -/
 theorem frontier_setOf_le_re_and_im_le (a b : ℝ) :
     frontier { z | a ≤ re z ∧ im z ≤ b } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ im z ≤ b } := by
   simpa only [closure_Ici, closure_Iic, frontier_Ici, frontier_Iic] using
@@ -406,32 +208,14 @@ open Complex Metric
 
 variable {s t : Set ℝ}
 
-/- warning: is_open.re_prod_im -> IsOpen.reProdIm is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsOpen.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
-but is expected to have type
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsOpen.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
-Case conversion may be inaccurate. Consider using '#align is_open.re_prod_im IsOpen.reProdImₓ'. -/
 theorem IsOpen.reProdIm (hs : IsOpen s) (ht : IsOpen t) : IsOpen (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_open.re_prod_im IsOpen.reProdIm
 
-/- warning: is_closed.re_prod_im -> IsClosed.reProdIm is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsClosed.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
-but is expected to have type
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsClosed.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
-Case conversion may be inaccurate. Consider using '#align is_closed.re_prod_im IsClosed.reProdImₓ'. -/
 theorem IsClosed.reProdIm (hs : IsClosed s) (ht : IsClosed t) : IsClosed (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_closed.re_prod_im IsClosed.reProdIm
 
-/- warning: metric.bounded.re_prod_im -> Metric.Bounded.reProdIm is a dubious translation:
-lean 3 declaration is
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (Metric.Bounded.{0} Real Real.pseudoMetricSpace s) -> (Metric.Bounded.{0} Real Real.pseudoMetricSpace t) -> (Metric.Bounded.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (Complex.Set.reProdIm s t))
-but is expected to have type
-  forall {s : Set.{0} Real} {t : Set.{0} Real}, (Metric.Bounded.{0} Real Real.pseudoMetricSpace s) -> (Metric.Bounded.{0} Real Real.pseudoMetricSpace t) -> (Metric.Bounded.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (Complex.Set.reProdIm s t))
-Case conversion may be inaccurate. Consider using '#align metric.bounded.re_prod_im Metric.Bounded.reProdImₓ'. -/
 theorem Metric.Bounded.reProdIm (hs : Bounded s) (ht : Bounded t) : Bounded (s ×ℂ t) :=
   antilipschitz_equivRealProd.bounded_preimage (hs.Prod ht)
 #align metric.bounded.re_prod_im Metric.Bounded.reProdIm

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.complex.re_im_topology
-! leanprover-community/mathlib commit 468b141b14016d54b479eb7a0fff1e360b7e3cf6
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.FiberBundle.IsHomeomorphicTrivialBundle
 /-!
 # Closure, interior, and frontier of preimages under `re` and `im`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this fact we use the fact that `ℂ` is naturally homeomorphic to `ℝ × ℝ` to deduce some
 topological properties of `complex.re` and `complex.im`.
 

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

@@ -43,156 +43,354 @@ noncomputable section
 
 namespace Complex
 
+/- warning: complex.is_homeomorphic_trivial_fiber_bundle_re -> Complex.isHomeomorphicTrivialFiberBundle_re is a dubious translation:
+lean 3 declaration is
+  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.re
+but is expected to have type
+  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_reₓ'. -/
 /-- `complex.re` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_re : IsHomeomorphicTrivialFiberBundle ℝ re :=
   ⟨equivRealProdClm.toHomeomorph, fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_re
 
+/- warning: complex.is_homeomorphic_trivial_fiber_bundle_im -> Complex.isHomeomorphicTrivialFiberBundle_im is a dubious translation:
+lean 3 declaration is
+  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.im
+but is expected to have type
+  IsHomeomorphicTrivialFiberBundle.{0, 0, 0} Real Real Complex (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (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)))))) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_imₓ'. -/
 /-- `complex.im` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_im : IsHomeomorphicTrivialFiberBundle ℝ im :=
   ⟨equivRealProdClm.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun z => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_im
 
+/- warning: complex.is_open_map_re -> Complex.isOpenMap_re is a dubious translation:
+lean 3 declaration is
+  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+but is expected to have type
+  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.is_open_map_re Complex.isOpenMap_reₓ'. -/
 theorem isOpenMap_re : IsOpenMap re :=
   isHomeomorphicTrivialFiberBundle_re.isOpenMap_proj
 #align complex.is_open_map_re Complex.isOpenMap_re
 
+/- warning: complex.is_open_map_im -> Complex.isOpenMap_im is a dubious translation:
+lean 3 declaration is
+  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+but is expected to have type
+  IsOpenMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.is_open_map_im Complex.isOpenMap_imₓ'. -/
 theorem isOpenMap_im : IsOpenMap im :=
   isHomeomorphicTrivialFiberBundle_im.isOpenMap_proj
 #align complex.is_open_map_im Complex.isOpenMap_im
 
+/- warning: complex.quotient_map_re -> Complex.quotientMap_re is a dubious translation:
+lean 3 declaration is
+  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+but is expected to have type
+  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.re
+Case conversion may be inaccurate. Consider using '#align complex.quotient_map_re Complex.quotientMap_reₓ'. -/
 theorem quotientMap_re : QuotientMap re :=
   isHomeomorphicTrivialFiberBundle_re.quotientMap_proj
 #align complex.quotient_map_re Complex.quotientMap_re
 
+/- warning: complex.quotient_map_im -> Complex.quotientMap_im is a dubious translation:
+lean 3 declaration is
+  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+but is expected to have type
+  QuotientMap.{0, 0} Complex Real (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)))))) (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Complex.im
+Case conversion may be inaccurate. Consider using '#align complex.quotient_map_im Complex.quotientMap_imₓ'. -/
 theorem quotientMap_im : QuotientMap im :=
   isHomeomorphicTrivialFiberBundle_im.quotientMap_proj
 #align complex.quotient_map_im Complex.quotientMap_im
 
+/- warning: complex.interior_preimage_re -> Complex.interior_preimage_re is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.interior_preimage_re Complex.interior_preimage_reₓ'. -/
 theorem interior_preimage_re (s : Set ℝ) : interior (re ⁻¹' s) = re ⁻¹' interior s :=
   (isOpenMap_re.preimage_interior_eq_interior_preimage continuous_re _).symm
 #align complex.interior_preimage_re Complex.interior_preimage_re
 
+/- warning: complex.interior_preimage_im -> Complex.interior_preimage_im is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.interior_preimage_im Complex.interior_preimage_imₓ'. -/
 theorem interior_preimage_im (s : Set ℝ) : interior (im ⁻¹' s) = im ⁻¹' interior s :=
   (isOpenMap_im.preimage_interior_eq_interior_preimage continuous_im _).symm
 #align complex.interior_preimage_im Complex.interior_preimage_im
 
+/- warning: complex.closure_preimage_re -> Complex.closure_preimage_re is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.closure_preimage_re Complex.closure_preimage_reₓ'. -/
 theorem closure_preimage_re (s : Set ℝ) : closure (re ⁻¹' s) = re ⁻¹' closure s :=
   (isOpenMap_re.preimage_closure_eq_closure_preimage continuous_re _).symm
 #align complex.closure_preimage_re Complex.closure_preimage_re
 
+/- warning: complex.closure_preimage_im -> Complex.closure_preimage_im is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.closure_preimage_im Complex.closure_preimage_imₓ'. -/
 theorem closure_preimage_im (s : Set ℝ) : closure (im ⁻¹' s) = im ⁻¹' closure s :=
   (isOpenMap_im.preimage_closure_eq_closure_preimage continuous_im _).symm
 #align complex.closure_preimage_im Complex.closure_preimage_im
 
+/- warning: complex.frontier_preimage_re -> Complex.frontier_preimage_re is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.re s)) (Set.preimage.{0, 0} Complex Real Complex.re (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_preimage_re Complex.frontier_preimage_reₓ'. -/
 theorem frontier_preimage_re (s : Set ℝ) : frontier (re ⁻¹' s) = re ⁻¹' frontier s :=
   (isOpenMap_re.preimage_frontier_eq_frontier_preimage continuous_re _).symm
 #align complex.frontier_preimage_re Complex.frontier_preimage_re
 
+/- warning: complex.frontier_preimage_im -> Complex.frontier_preimage_im is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+but is expected to have type
+  forall (s : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Set.preimage.{0, 0} Complex Real Complex.im s)) (Set.preimage.{0, 0} Complex Real Complex.im (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_preimage_im Complex.frontier_preimage_imₓ'. -/
 theorem frontier_preimage_im (s : Set ℝ) : frontier (im ⁻¹' s) = im ⁻¹' frontier s :=
   (isOpenMap_im.preimage_frontier_eq_frontier_preimage continuous_im _).symm
 #align complex.frontier_preimage_im Complex.frontier_preimage_im
 
+/- warning: complex.interior_set_of_re_le -> Complex.interior_setOf_re_le is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_re_le Complex.interior_setOf_re_leₓ'. -/
 @[simp]
 theorem interior_setOf_re_le (a : ℝ) : interior { z : ℂ | z.re ≤ a } = { z | z.re < a } := by
   simpa only [interior_Iic] using interior_preimage_re (Iic a)
 #align complex.interior_set_of_re_le Complex.interior_setOf_re_le
 
+/- warning: complex.interior_set_of_im_le -> Complex.interior_setOf_im_le is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_im_le Complex.interior_setOf_im_leₓ'. -/
 @[simp]
 theorem interior_setOf_im_le (a : ℝ) : interior { z : ℂ | z.im ≤ a } = { z | z.im < a } := by
   simpa only [interior_Iic] using interior_preimage_im (Iic a)
 #align complex.interior_set_of_im_le Complex.interior_setOf_im_le
 
+/- warning: complex.interior_set_of_le_re -> Complex.interior_setOf_le_re is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))
+Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_le_re Complex.interior_setOf_le_reₓ'. -/
 @[simp]
 theorem interior_setOf_le_re (a : ℝ) : interior { z : ℂ | a ≤ z.re } = { z | a < z.re } := by
   simpa only [interior_Ici] using interior_preimage_re (Ici a)
 #align complex.interior_set_of_le_re Complex.interior_setOf_le_re
 
+/- warning: complex.interior_set_of_le_im -> Complex.interior_setOf_le_im is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.interior_set_of_le_im Complex.interior_setOf_le_imₓ'. -/
 @[simp]
 theorem interior_setOf_le_im (a : ℝ) : interior { z : ℂ | a ≤ z.im } = { z | a < z.im } := by
   simpa only [interior_Ici] using interior_preimage_im (Ici a)
 #align complex.interior_set_of_le_im Complex.interior_setOf_le_im
 
+/- warning: complex.closure_set_of_re_lt -> Complex.closure_setOf_re_lt is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_re_lt Complex.closure_setOf_re_ltₓ'. -/
 @[simp]
 theorem closure_setOf_re_lt (a : ℝ) : closure { z : ℂ | z.re < a } = { z | z.re ≤ a } := by
   simpa only [closure_Iio] using closure_preimage_re (Iio a)
 #align complex.closure_set_of_re_lt Complex.closure_setOf_re_lt
 
+/- warning: complex.closure_set_of_im_lt -> Complex.closure_setOf_im_lt is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_im_lt Complex.closure_setOf_im_ltₓ'. -/
 @[simp]
 theorem closure_setOf_im_lt (a : ℝ) : closure { z : ℂ | z.im < a } = { z | z.im ≤ a } := by
   simpa only [closure_Iio] using closure_preimage_im (Iio a)
 #align complex.closure_set_of_im_lt Complex.closure_setOf_im_lt
 
+/- warning: complex.closure_set_of_lt_re -> Complex.closure_setOf_lt_re is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))
+Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_lt_re Complex.closure_setOf_lt_reₓ'. -/
 @[simp]
 theorem closure_setOf_lt_re (a : ℝ) : closure { z : ℂ | a < z.re } = { z | a ≤ z.re } := by
   simpa only [closure_Ioi] using closure_preimage_re (Ioi a)
 #align complex.closure_set_of_lt_re Complex.closure_setOf_lt_re
 
+/- warning: complex.closure_set_of_lt_im -> Complex.closure_setOf_lt_im is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))
+Case conversion may be inaccurate. Consider using '#align complex.closure_set_of_lt_im Complex.closure_setOf_lt_imₓ'. -/
 @[simp]
 theorem closure_setOf_lt_im (a : ℝ) : closure { z : ℂ | a < z.im } = { z | a ≤ z.im } := by
   simpa only [closure_Ioi] using closure_preimage_im (Ioi a)
 #align complex.closure_set_of_lt_im Complex.closure_setOf_lt_im
 
+/- warning: complex.frontier_set_of_re_le -> Complex.frontier_setOf_re_le is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_re_le Complex.frontier_setOf_re_leₓ'. -/
 @[simp]
 theorem frontier_setOf_re_le (a : ℝ) : frontier { z : ℂ | z.re ≤ a } = { z | z.re = a } := by
   simpa only [frontier_Iic] using frontier_preimage_re (Iic a)
 #align complex.frontier_set_of_re_le Complex.frontier_setOf_re_le
 
+/- warning: complex.frontier_set_of_im_le -> Complex.frontier_setOf_im_le is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_im_le Complex.frontier_setOf_im_leₓ'. -/
 @[simp]
 theorem frontier_setOf_im_le (a : ℝ) : frontier { z : ℂ | z.im ≤ a } = { z | z.im = a } := by
   simpa only [frontier_Iic] using frontier_preimage_im (Iic a)
 #align complex.frontier_set_of_im_le Complex.frontier_setOf_im_le
 
+/- warning: complex.frontier_set_of_le_re -> Complex.frontier_setOf_le_re is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re Complex.frontier_setOf_le_reₓ'. -/
 @[simp]
 theorem frontier_setOf_le_re (a : ℝ) : frontier { z : ℂ | a ≤ z.re } = { z | z.re = a } := by
   simpa only [frontier_Ici] using frontier_preimage_re (Ici a)
 #align complex.frontier_set_of_le_re Complex.frontier_setOf_le_re
 
+/- warning: complex.frontier_set_of_le_im -> Complex.frontier_setOf_le_im is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.hasLe a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LE.le.{0} Real Real.instLEReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_im Complex.frontier_setOf_le_imₓ'. -/
 @[simp]
 theorem frontier_setOf_le_im (a : ℝ) : frontier { z : ℂ | a ≤ z.im } = { z | z.im = a } := by
   simpa only [frontier_Ici] using frontier_preimage_im (Ici a)
 #align complex.frontier_set_of_le_im Complex.frontier_setOf_le_im
 
+/- warning: complex.frontier_set_of_re_lt -> Complex.frontier_setOf_re_lt is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.re z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_ltₓ'. -/
 @[simp]
 theorem frontier_setOf_re_lt (a : ℝ) : frontier { z : ℂ | z.re < a } = { z | z.re = a } := by
   simpa only [frontier_Iio] using frontier_preimage_re (Iio a)
 #align complex.frontier_set_of_re_lt Complex.frontier_setOf_re_lt
 
+/- warning: complex.frontier_set_of_im_lt -> Complex.frontier_setOf_im_lt is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal (Complex.im z) a))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_ltₓ'. -/
 @[simp]
 theorem frontier_setOf_im_lt (a : ℝ) : frontier { z : ℂ | z.im < a } = { z | z.im = a } := by
   simpa only [frontier_Iio] using frontier_preimage_im (Iio a)
 #align complex.frontier_set_of_im_lt Complex.frontier_setOf_im_lt
 
+/- warning: complex.frontier_set_of_lt_re -> Complex.frontier_setOf_lt_re is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.re z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.re z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_reₓ'. -/
 @[simp]
 theorem frontier_setOf_lt_re (a : ℝ) : frontier { z : ℂ | a < z.re } = { z | z.re = a } := by
   simpa only [frontier_Ioi] using frontier_preimage_re (Ioi a)
 #align complex.frontier_set_of_lt_re Complex.frontier_setOf_lt_re
 
+/- warning: complex.frontier_set_of_lt_im -> Complex.frontier_setOf_lt_im is a dubious translation:
+lean 3 declaration is
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.hasLt a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+but is expected to have type
+  forall (a : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => LT.lt.{0} Real Real.instLTReal a (Complex.im z)))) (setOf.{0} Complex (fun (z : Complex) => Eq.{1} Real (Complex.im z) a))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_imₓ'. -/
 @[simp]
 theorem frontier_setOf_lt_im (a : ℝ) : frontier { z : ℂ | a < z.im } = { z | z.im = a } := by
   simpa only [frontier_Ioi] using frontier_preimage_im (Ioi a)
 #align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_im
 
+/- warning: complex.closure_re_prod_im -> Complex.closure_reProdIm is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
+but is expected to have type
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (closure.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
+Case conversion may be inaccurate. Consider using '#align complex.closure_re_prod_im Complex.closure_reProdImₓ'. -/
 theorem closure_reProdIm (s t : Set ℝ) : closure (s ×ℂ t) = closure s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t
 #align complex.closure_re_prod_im Complex.closure_reProdIm
 
+/- warning: complex.interior_re_prod_im -> Complex.interior_reProdIm is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
+but is expected to have type
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (interior.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Complex.Set.reProdIm (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (interior.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t))
+Case conversion may be inaccurate. Consider using '#align complex.interior_re_prod_im Complex.interior_reProdImₓ'. -/
 theorem interior_reProdIm (s t : Set ℝ) : interior (s ×ℂ t) = interior s ×ℂ interior t := by
   rw [re_prod_im, re_prod_im, interior_inter, interior_preimage_re, interior_preimage_im]
 #align complex.interior_re_prod_im Complex.interior_reProdIm
 
+/- warning: complex.frontier_re_prod_im -> Complex.frontier_reProdIm is a dubious translation:
+lean 3 declaration is
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Union.union.{0} (Set.{0} Complex) (Set.hasUnion.{0} Complex) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)) (Complex.Set.reProdIm (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)))
+but is expected to have type
+  forall (s : Set.{0} Real) (t : Set.{0} Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (Complex.Set.reProdIm s t)) (Union.union.{0} (Set.{0} Complex) (Set.instUnionSet.{0} Complex) (Complex.Set.reProdIm (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)) (Complex.Set.reProdIm (frontier.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) (closure.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t)))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_re_prod_im Complex.frontier_reProdImₓ'. -/
 theorem frontier_reProdIm (s t : Set ℝ) :
     frontier (s ×ℂ t) = closure s ×ℂ frontier t ∪ frontier s ×ℂ closure t := by
   simpa only [← preimage_eq_preimage equiv_real_prod_clm.symm.to_homeomorph.surjective,
     equiv_real_prod_clm.symm.to_homeomorph.preimage_frontier] using frontier_prod_eq s t
 #align complex.frontier_re_prod_im Complex.frontier_reProdIm
 
+/- warning: complex.frontier_set_of_le_re_and_le_im -> Complex.frontier_setOf_le_re_and_le_im is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (LE.le.{0} Real Real.hasLe b (Complex.im z))))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.hasLe b (Complex.im z)))))
+but is expected to have type
+  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (LE.le.{0} Real Real.instLEReal b (Complex.im z))))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.instLEReal b (Complex.im z)))))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_imₓ'. -/
 theorem frontier_setOf_le_re_and_le_im (a b : ℝ) :
     frontier { z | a ≤ re z ∧ b ≤ im z } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ b ≤ im z } := by
   simpa only [closure_Ici, frontier_Ici] using frontier_re_prod_im (Ici a) (Ici b)
 #align complex.frontier_set_of_le_re_and_le_im Complex.frontier_setOf_le_re_and_le_im
 
+/- warning: complex.frontier_set_of_le_re_and_im_le -> Complex.frontier_setOf_le_re_and_im_le is a dubious translation:
+lean 3 declaration is
+  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (LE.le.{0} Real Real.hasLe (Complex.im z) b)))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.hasLe a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.hasLe (Complex.im z) b))))
+but is expected to have type
+  forall (a : Real) (b : Real), Eq.{1} (Set.{0} Complex) (frontier.{0} Complex (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)))))) (setOf.{0} Complex (fun (z : Complex) => And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (LE.le.{0} Real Real.instLEReal (Complex.im z) b)))) (setOf.{0} Complex (fun (z : Complex) => Or (And (LE.le.{0} Real Real.instLEReal a (Complex.re z)) (Eq.{1} Real (Complex.im z) b)) (And (Eq.{1} Real (Complex.re z) a) (LE.le.{0} Real Real.instLEReal (Complex.im z) b))))
+Case conversion may be inaccurate. Consider using '#align complex.frontier_set_of_le_re_and_im_le Complex.frontier_setOf_le_re_and_im_leₓ'. -/
 theorem frontier_setOf_le_re_and_im_le (a b : ℝ) :
     frontier { z | a ≤ re z ∧ im z ≤ b } = { z | a ≤ re z ∧ im z = b ∨ re z = a ∧ im z ≤ b } := by
   simpa only [closure_Ici, closure_Iic, frontier_Ici, frontier_Iic] using
@@ -205,14 +403,32 @@ open Complex Metric
 
 variable {s t : Set ℝ}
 
+/- warning: is_open.re_prod_im -> IsOpen.reProdIm is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsOpen.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
+but is expected to have type
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsOpen.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsOpen.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
+Case conversion may be inaccurate. Consider using '#align is_open.re_prod_im IsOpen.reProdImₓ'. -/
 theorem IsOpen.reProdIm (hs : IsOpen s) (ht : IsOpen t) : IsOpen (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_open.re_prod_im IsOpen.reProdIm
 
+/- warning: is_closed.re_prod_im -> IsClosed.reProdIm is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsClosed.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
+but is expected to have type
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) s) -> (IsClosed.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) t) -> (IsClosed.{0} Complex (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)))))) (Complex.Set.reProdIm s t))
+Case conversion may be inaccurate. Consider using '#align is_closed.re_prod_im IsClosed.reProdImₓ'. -/
 theorem IsClosed.reProdIm (hs : IsClosed s) (ht : IsClosed t) : IsClosed (s ×ℂ t) :=
   (hs.Preimage continuous_re).inter (ht.Preimage continuous_im)
 #align is_closed.re_prod_im IsClosed.reProdIm
 
+/- warning: metric.bounded.re_prod_im -> Metric.Bounded.reProdIm is a dubious translation:
+lean 3 declaration is
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (Metric.Bounded.{0} Real Real.pseudoMetricSpace s) -> (Metric.Bounded.{0} Real Real.pseudoMetricSpace t) -> (Metric.Bounded.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSemiNormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.normedField)))) (Complex.Set.reProdIm s t))
+but is expected to have type
+  forall {s : Set.{0} Real} {t : Set.{0} Real}, (Metric.Bounded.{0} Real Real.pseudoMetricSpace s) -> (Metric.Bounded.{0} Real Real.pseudoMetricSpace t) -> (Metric.Bounded.{0} Complex (SeminormedRing.toPseudoMetricSpace.{0} Complex (SeminormedCommRing.toSeminormedRing.{0} Complex (NormedCommRing.toSeminormedCommRing.{0} Complex (NormedField.toNormedCommRing.{0} Complex Complex.instNormedFieldComplex)))) (Complex.Set.reProdIm s t))
+Case conversion may be inaccurate. Consider using '#align metric.bounded.re_prod_im Metric.Bounded.reProdImₓ'. -/
 theorem Metric.Bounded.reProdIm (hs : Bounded s) (ht : Bounded t) : Bounded (s ×ℂ t) :=
   antilipschitz_equivRealProd.bounded_preimage (hs.Prod ht)
 #align metric.bounded.re_prod_im Metric.Bounded.reProdIm

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

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -42,12 +42,12 @@ namespace Complex
 
 /-- `Complex.re` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_re : IsHomeomorphicTrivialFiberBundle ℝ re :=
-  ⟨equivRealProdClm.toHomeomorph, fun _ => rfl⟩
+  ⟨equivRealProdCLM.toHomeomorph, fun _ => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_re Complex.isHomeomorphicTrivialFiberBundle_re
 
 /-- `Complex.im` turns `ℂ` into a trivial topological fiber bundle over `ℝ`. -/
 theorem isHomeomorphicTrivialFiberBundle_im : IsHomeomorphicTrivialFiberBundle ℝ im :=
-  ⟨equivRealProdClm.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun _ => rfl⟩
+  ⟨equivRealProdCLM.toHomeomorph.trans (Homeomorph.prodComm ℝ ℝ), fun _ => rfl⟩
 #align complex.is_homeomorphic_trivial_fiber_bundle_im Complex.isHomeomorphicTrivialFiberBundle_im
 
 theorem isOpenMap_re : IsOpenMap re :=
@@ -171,8 +171,8 @@ theorem frontier_setOf_lt_im (a : ℝ) : frontier { z : ℂ | a < z.im } = { z |
 #align complex.frontier_set_of_lt_im Complex.frontier_setOf_lt_im
 
 theorem closure_reProdIm (s t : Set ℝ) : closure (s ×ℂ t) = closure s ×ℂ closure t := by
-  simpa only [← preimage_eq_preimage equivRealProdClm.symm.toHomeomorph.surjective,
-    equivRealProdClm.symm.toHomeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t
+  simpa only [← preimage_eq_preimage equivRealProdCLM.symm.toHomeomorph.surjective,
+    equivRealProdCLM.symm.toHomeomorph.preimage_closure] using @closure_prod_eq _ _ _ _ s t
 #align complex.closure_re_prod_im Complex.closure_reProdIm
 
 theorem interior_reProdIm (s t : Set ℝ) : interior (s ×ℂ t) = interior s ×ℂ interior t := by
@@ -181,8 +181,8 @@ theorem interior_reProdIm (s t : Set ℝ) : interior (s ×ℂ t) = interior s ×
 
 theorem frontier_reProdIm (s t : Set ℝ) :
     frontier (s ×ℂ t) = closure s ×ℂ frontier t ∪ frontier s ×ℂ closure t := by
-  simpa only [← preimage_eq_preimage equivRealProdClm.symm.toHomeomorph.surjective,
-    equivRealProdClm.symm.toHomeomorph.preimage_frontier] using frontier_prod_eq s t
+  simpa only [← preimage_eq_preimage equivRealProdCLM.symm.toHomeomorph.surjective,
+    equivRealProdCLM.symm.toHomeomorph.preimage_frontier] using frontier_prod_eq s t
 #align complex.frontier_re_prod_im Complex.frontier_reProdIm
 
 theorem frontier_setOf_le_re_and_le_im (a b : ℝ) :

Use Bornology.IsBounded instead.

@@ -210,6 +210,6 @@ theorem IsClosed.reProdIm (hs : IsClosed s) (ht : IsClosed t) : IsClosed (s ×
   (hs.preimage continuous_re).inter (ht.preimage continuous_im)
 #align is_closed.re_prod_im IsClosed.reProdIm
 
-theorem Metric.Bounded.reProdIm (hs : Bounded s) (ht : Bounded t) : Bounded (s ×ℂ t) :=
-  antilipschitz_equivRealProd.bounded_preimage (hs.prod ht)
-#align metric.bounded.re_prod_im Metric.Bounded.reProdIm
+theorem Bornology.IsBounded.reProdIm (hs : IsBounded s) (ht : IsBounded t) : IsBounded (s ×ℂ t) :=
+  antilipschitz_equivRealProd.isBounded_preimage (hs.prod ht)
+#align metric.bounded.re_prod_im Bornology.IsBounded.reProdIm

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.complex.re_im_topology
-! leanprover-community/mathlib commit 468b141b14016d54b479eb7a0fff1e360b7e3cf6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Complex.Basic
 import Mathlib.Topology.FiberBundle.IsHomeomorphicTrivialBundle
 
+#align_import analysis.complex.re_im_topology from "leanprover-community/mathlib"@"468b141b14016d54b479eb7a0fff1e360b7e3cf6"
+
 /-!
 # Closure, interior, and frontier of preimages under `re` and `im`