analysis.complex.upper_half_plane.functions_bounded_at_infty

Changes since the initial port

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

Changes in mathlib3

f2ce6086

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

9240e8be

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck, David Loeffler
 -/
-import Mathbin.Algebra.Module.Submodule.Basic
-import Mathbin.Analysis.Complex.UpperHalfPlane.Basic
-import Mathbin.Order.Filter.ZeroAndBoundedAtFilter
+import Algebra.Module.Submodule.Basic
+import Analysis.Complex.UpperHalfPlane.Basic
+import Order.Filter.ZeroAndBoundedAtFilter
 
 #align_import analysis.complex.upper_half_plane.functions_bounded_at_infty from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"

9240e8be

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck, David Loeffler
-
-! This file was ported from Lean 3 source module analysis.complex.upper_half_plane.functions_bounded_at_infty
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Module.Submodule.Basic
 import Mathbin.Analysis.Complex.UpperHalfPlane.Basic
 import Mathbin.Order.Filter.ZeroAndBoundedAtFilter
 
+#align_import analysis.complex.upper_half_plane.functions_bounded_at_infty from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 # Bounded at infinity

9240e8be

bump to nightly-2023-06-30-03

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

397a8f48

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck, David Loeffler
 
 ! This file was ported from Lean 3 source module analysis.complex.upper_half_plane.functions_bounded_at_infty
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Order.Filter.ZeroAndBoundedAtFilter
 /-!
 # Bounded at infinity
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 For complex valued functions on the upper half plane, this file defines the filter `at_im_infty`
 required for defining when functions are bounded at infinity and zero at infinity.
 Both of which are relevant for defining modular forms.

f2ce6086

bump to nightly-2023-06-28-15

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

bf9f9bdc

Diff

@@ -30,15 +30,20 @@ noncomputable section
 
 namespace UpperHalfPlane
 
+#print UpperHalfPlane.atImInfty /-
 /-- Filter for approaching `i∞`. -/
 def atImInfty :=
   Filter.atTop.comap UpperHalfPlane.im
 #align upper_half_plane.at_im_infty UpperHalfPlane.atImInfty
+-/
 
+#print UpperHalfPlane.atImInfty_basis /-
 theorem atImInfty_basis : atImInfty.HasBasis (fun _ => True) fun i : ℝ => im ⁻¹' Set.Ici i :=
   Filter.HasBasis.comap UpperHalfPlane.im Filter.atTop_basis
 #align upper_half_plane.at_im_infty_basis UpperHalfPlane.atImInfty_basis
+-/
 
+#print UpperHalfPlane.atImInfty_mem /-
 theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → z ∈ S :=
   by
   simp only [at_im_infty, Filter.mem_comap', Filter.mem_atTop_sets, ge_iff_le, Set.mem_setOf_eq,
@@ -48,43 +53,59 @@ theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : 
   refine' ⟨A, fun b hb x hx => h x _⟩
   rwa [hx]
 #align upper_half_plane.at_im_infty_mem UpperHalfPlane.atImInfty_mem
+-/
 
+#print UpperHalfPlane.IsBoundedAtImInfty /-
 /-- A function ` f : ℍ → α` is bounded at infinity if it is bounded along `at_im_infty`. -/
 def IsBoundedAtImInfty {α : Type _} [Norm α] (f : ℍ → α) : Prop :=
   BoundedAtFilter atImInfty f
 #align upper_half_plane.is_bounded_at_im_infty UpperHalfPlane.IsBoundedAtImInfty
+-/
 
+#print UpperHalfPlane.IsZeroAtImInfty /-
 /-- A function ` f : ℍ → α` is zero at infinity it is zero along `at_im_infty`. -/
 def IsZeroAtImInfty {α : Type _} [Zero α] [TopologicalSpace α] (f : ℍ → α) : Prop :=
   ZeroAtFilter atImInfty f
 #align upper_half_plane.is_zero_at_im_infty UpperHalfPlane.IsZeroAtImInfty
+-/
 
+#print UpperHalfPlane.zero_form_isBoundedAtImInfty /-
 theorem zero_form_isBoundedAtImInfty {α : Type _} [NormedField α] :
     IsBoundedAtImInfty (0 : ℍ → α) :=
   const_boundedAtFilter atImInfty (0 : α)
 #align upper_half_plane.zero_form_is_bounded_at_im_infty UpperHalfPlane.zero_form_isBoundedAtImInfty
+-/
 
+#print UpperHalfPlane.zeroAtImInftySubmodule /-
 /-- Module of functions that are zero at infinity. -/
 def zeroAtImInftySubmodule (α : Type _) [NormedField α] : Submodule α (ℍ → α) :=
   zeroAtFilterSubmodule atImInfty
 #align upper_half_plane.zero_at_im_infty_submodule UpperHalfPlane.zeroAtImInftySubmodule
+-/
 
+#print UpperHalfPlane.boundedAtImInftySubalgebra /-
 /-- ubalgebra of functions that are bounded at infinity. -/
 def boundedAtImInftySubalgebra (α : Type _) [NormedField α] : Subalgebra α (ℍ → α) :=
   boundedFilterSubalgebra atImInfty
 #align upper_half_plane.bounded_at_im_infty_subalgebra UpperHalfPlane.boundedAtImInftySubalgebra
+-/
 
+#print UpperHalfPlane.IsBoundedAtImInfty.mul /-
 theorem IsBoundedAtImInfty.mul {f g : ℍ → ℂ} (hf : IsBoundedAtImInfty f)
     (hg : IsBoundedAtImInfty g) : IsBoundedAtImInfty (f * g) := by
   simpa only [Pi.one_apply, mul_one, norm_eq_abs] using hf.mul hg
 #align upper_half_plane.is_bounded_at_im_infty.mul UpperHalfPlane.IsBoundedAtImInfty.mul
+-/
 
+#print UpperHalfPlane.bounded_mem /-
 theorem bounded_mem (f : ℍ → ℂ) :
     IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ M := by
   simp [is_bounded_at_im_infty, bounded_at_filter, Asymptotics.isBigO_iff, Filter.Eventually,
     at_im_infty_mem]
 #align upper_half_plane.bounded_mem UpperHalfPlane.bounded_mem
+-/
 
+#print UpperHalfPlane.zero_at_im_infty /-
 theorem zero_at_im_infty (f : ℍ → ℂ) :
     IsZeroAtImInfty f ↔ ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ ε :=
   by
@@ -108,6 +129,7 @@ theorem zero_at_im_infty (f : ℍ → ℂ) :
       linarith
     apply hzs
 #align upper_half_plane.zero_at_im_infty UpperHalfPlane.zero_at_im_infty
+-/
 
 end UpperHalfPlane

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -24,7 +24,7 @@ Both of which are relevant for defining modular forms.
 
 open Complex Filter
 
-open Topology UpperHalfPlane
+open scoped Topology UpperHalfPlane
 
 noncomputable section

f2ce6086

bump to nightly-2023-04-12-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

0809e5be

Diff

@@ -81,7 +81,7 @@ theorem IsBoundedAtImInfty.mul {f g : ℍ → ℂ} (hf : IsBoundedAtImInfty f)
 
 theorem bounded_mem (f : ℍ → ℂ) :
     IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ M := by
-  simp [is_bounded_at_im_infty, bounded_at_filter, Asymptotics.isO_iff, Filter.Eventually,
+  simp [is_bounded_at_im_infty, bounded_at_filter, Asymptotics.isBigO_iff, Filter.Eventually,
     at_im_infty_mem]
 #align upper_half_plane.bounded_mem UpperHalfPlane.bounded_mem

f2ce6086

bump to nightly-2023-03-13-14

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

a0c9db6f

Diff

@@ -80,15 +80,13 @@ theorem IsBoundedAtImInfty.mul {f g : ℍ → ℂ} (hf : IsBoundedAtImInfty f)
 #align upper_half_plane.is_bounded_at_im_infty.mul UpperHalfPlane.IsBoundedAtImInfty.mul
 
 theorem bounded_mem (f : ℍ → ℂ) :
-    IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → Complex.AbsTheory.Complex.abs (f z) ≤ M :=
-  by
+    IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ M := by
   simp [is_bounded_at_im_infty, bounded_at_filter, Asymptotics.isO_iff, Filter.Eventually,
     at_im_infty_mem]
 #align upper_half_plane.bounded_mem UpperHalfPlane.bounded_mem
 
 theorem zero_at_im_infty (f : ℍ → ℂ) :
-    IsZeroAtImInfty f ↔
-      ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → Complex.AbsTheory.Complex.abs (f z) ≤ ε :=
+    IsZeroAtImInfty f ↔ ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ ε :=
   by
   rw [is_zero_at_im_infty, zero_at_filter, tendsto_iff_forall_eventually_mem]
   constructor

f2ce6086

bump to nightly-2023-03-10-14

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

24f14899

Diff

@@ -80,13 +80,15 @@ theorem IsBoundedAtImInfty.mul {f g : ℍ → ℂ} (hf : IsBoundedAtImInfty f)
 #align upper_half_plane.is_bounded_at_im_infty.mul UpperHalfPlane.IsBoundedAtImInfty.mul
 
 theorem bounded_mem (f : ℍ → ℂ) :
-    IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ M := by
+    IsBoundedAtImInfty f ↔ ∃ M A : ℝ, ∀ z : ℍ, A ≤ im z → Complex.AbsTheory.Complex.abs (f z) ≤ M :=
+  by
   simp [is_bounded_at_im_infty, bounded_at_filter, Asymptotics.isO_iff, Filter.Eventually,
     at_im_infty_mem]
 #align upper_half_plane.bounded_mem UpperHalfPlane.bounded_mem
 
 theorem zero_at_im_infty (f : ℍ → ℂ) :
-    IsZeroAtImInfty f ↔ ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ ε :=
+    IsZeroAtImInfty f ↔
+      ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → Complex.AbsTheory.Complex.abs (f z) ≤ ε :=
   by
   rw [is_zero_at_im_infty, zero_at_filter, tendsto_iff_forall_eventually_mem]
   constructor

f2ce6086

bump to nightly-2023-03-09-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

a3ca2eeb

Diff

@@ -50,7 +50,7 @@ theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : 
 #align upper_half_plane.at_im_infty_mem UpperHalfPlane.atImInfty_mem
 
 /-- A function ` f : ℍ → α` is bounded at infinity if it is bounded along `at_im_infty`. -/
-def IsBoundedAtImInfty {α : Type _} [HasNorm α] (f : ℍ → α) : Prop :=
+def IsBoundedAtImInfty {α : Type _} [Norm α] (f : ℍ → α) : Prop :=
   BoundedAtFilter atImInfty f
 #align upper_half_plane.is_bounded_at_im_infty UpperHalfPlane.IsBoundedAtImInfty

f2ce6086

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

f2ce6086

feat: generalize boundedFilterSubalgebra (#10519)

This previously only worked for normed fields, now it works for seminormed algebras. There is no particular motivation for this beyond seeing where NormedSpace is too strong.

03e3005a

Diff

@@ -55,12 +55,12 @@ theorem zero_form_isBoundedAtImInfty {α : Type*} [NormedField α] :
 
 /-- Module of functions that are zero at infinity. -/
 def zeroAtImInftySubmodule (α : Type*) [NormedField α] : Submodule α (ℍ → α) :=
-  zeroAtFilterSubmodule atImInfty
+  zeroAtFilterSubmodule _ atImInfty
 #align upper_half_plane.zero_at_im_infty_submodule UpperHalfPlane.zeroAtImInftySubmodule
 
 /-- Subalgebra of functions that are bounded at infinity. -/
 def boundedAtImInftySubalgebra (α : Type*) [NormedField α] : Subalgebra α (ℍ → α) :=
-  boundedFilterSubalgebra atImInfty
+  boundedFilterSubalgebra _ atImInfty
 #align upper_half_plane.bounded_at_im_infty_subalgebra UpperHalfPlane.boundedAtImInftySubalgebra
 
 nonrec theorem IsBoundedAtImInfty.mul {f g : ℍ → ℂ} (hf : IsBoundedAtImInfty f)

f2ce6086

chore: remove trailing space in backticks (#7617)

This will improve spaces in the mathlib4 docs.

9106dcf8

Diff

@@ -38,12 +38,12 @@ theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : 
   simp only [atImInfty_basis.mem_iff, true_and]; rfl
 #align upper_half_plane.at_im_infty_mem UpperHalfPlane.atImInfty_mem
 
-/-- A function ` f : ℍ → α` is bounded at infinity if it is bounded along `atImInfty`. -/
+/-- A function `f : ℍ → α` is bounded at infinity if it is bounded along `atImInfty`. -/
 def IsBoundedAtImInfty {α : Type*} [Norm α] (f : ℍ → α) : Prop :=
   BoundedAtFilter atImInfty f
 #align upper_half_plane.is_bounded_at_im_infty UpperHalfPlane.IsBoundedAtImInfty
 
-/-- A function ` f : ℍ → α` is zero at infinity it is zero along `atImInfty`. -/
+/-- A function `f : ℍ → α` is zero at infinity it is zero along `atImInfty`. -/
 def IsZeroAtImInfty {α : Type*} [Zero α] [TopologicalSpace α] (f : ℍ → α) : Prop :=
   ZeroAtFilter atImInfty f
 #align upper_half_plane.is_zero_at_im_infty UpperHalfPlane.IsZeroAtImInfty

f2ce6086

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -39,27 +39,27 @@ theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : 
 #align upper_half_plane.at_im_infty_mem UpperHalfPlane.atImInfty_mem
 
 /-- A function ` f : ℍ → α` is bounded at infinity if it is bounded along `atImInfty`. -/
-def IsBoundedAtImInfty {α : Type _} [Norm α] (f : ℍ → α) : Prop :=
+def IsBoundedAtImInfty {α : Type*} [Norm α] (f : ℍ → α) : Prop :=
   BoundedAtFilter atImInfty f
 #align upper_half_plane.is_bounded_at_im_infty UpperHalfPlane.IsBoundedAtImInfty
 
 /-- A function ` f : ℍ → α` is zero at infinity it is zero along `atImInfty`. -/
-def IsZeroAtImInfty {α : Type _} [Zero α] [TopologicalSpace α] (f : ℍ → α) : Prop :=
+def IsZeroAtImInfty {α : Type*} [Zero α] [TopologicalSpace α] (f : ℍ → α) : Prop :=
   ZeroAtFilter atImInfty f
 #align upper_half_plane.is_zero_at_im_infty UpperHalfPlane.IsZeroAtImInfty
 
-theorem zero_form_isBoundedAtImInfty {α : Type _} [NormedField α] :
+theorem zero_form_isBoundedAtImInfty {α : Type*} [NormedField α] :
     IsBoundedAtImInfty (0 : ℍ → α) :=
   const_boundedAtFilter atImInfty (0 : α)
 #align upper_half_plane.zero_form_is_bounded_at_im_infty UpperHalfPlane.zero_form_isBoundedAtImInfty
 
 /-- Module of functions that are zero at infinity. -/
-def zeroAtImInftySubmodule (α : Type _) [NormedField α] : Submodule α (ℍ → α) :=
+def zeroAtImInftySubmodule (α : Type*) [NormedField α] : Submodule α (ℍ → α) :=
   zeroAtFilterSubmodule atImInfty
 #align upper_half_plane.zero_at_im_infty_submodule UpperHalfPlane.zeroAtImInftySubmodule
 
 /-- Subalgebra of functions that are bounded at infinity. -/
-def boundedAtImInftySubalgebra (α : Type _) [NormedField α] : Subalgebra α (ℍ → α) :=
+def boundedAtImInftySubalgebra (α : Type*) [NormedField α] : Subalgebra α (ℍ → α) :=
   boundedFilterSubalgebra atImInfty
 #align upper_half_plane.bounded_at_im_infty_subalgebra UpperHalfPlane.boundedAtImInftySubalgebra

f2ce6086

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Chris Birkbeck. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Birkbeck, David Loeffler
-
-! This file was ported from Lean 3 source module analysis.complex.upper_half_plane.functions_bounded_at_infty
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Module.Submodule.Basic
 import Mathlib.Analysis.Complex.UpperHalfPlane.Basic
 import Mathlib.Order.Filter.ZeroAndBoundedAtFilter
 
+#align_import analysis.complex.upper_half_plane.functions_bounded_at_infty from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Bounded at infinity

f2ce6086

chore: golf FunctionsBoundedAtInfty (#5661)

Use lemmas about Filter.HasBasis to golf some proofs.

8c73845e

Diff

@@ -15,13 +15,11 @@ import Mathlib.Order.Filter.ZeroAndBoundedAtFilter
 /-!
 # Bounded at infinity
 
-For complex valued functions on the upper half plane, this file defines the filter `atImInfty`
-required for defining when functions are bounded at infinity and zero at infinity.
-Both of which are relevant for defining modular forms.
-
+For complex valued functions on the upper half plane, this file defines the filter
+`UpperHalfPlane.atImInfty` required for defining when functions are bounded at infinity and zero at
+infinity. Both of which are relevant for defining modular forms.
 -/
 
-
 open Complex Filter
 
 open scoped Topology UpperHalfPlane
@@ -40,12 +38,7 @@ theorem atImInfty_basis : atImInfty.HasBasis (fun _ => True) fun i : ℝ => im 
 #align upper_half_plane.at_im_infty_basis UpperHalfPlane.atImInfty_basis
 
 theorem atImInfty_mem (S : Set ℍ) : S ∈ atImInfty ↔ ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → z ∈ S := by
-  simp only [atImInfty, Filter.mem_comap', Filter.mem_atTop_sets, ge_iff_le, Set.mem_setOf_eq,
-    UpperHalfPlane.coe_im]
-  refine' ⟨fun ⟨a, h⟩ => ⟨a, fun z hz => h (im z) hz rfl⟩, _⟩
-  rintro ⟨A, h⟩
-  refine' ⟨A, fun b hb x hx => h x _⟩
-  rwa [hx]
+  simp only [atImInfty_basis.mem_iff, true_and]; rfl
 #align upper_half_plane.at_im_infty_mem UpperHalfPlane.atImInfty_mem
 
 /-- A function ` f : ℍ → α` is bounded at infinity if it is bounded along `atImInfty`. -/
@@ -85,26 +78,9 @@ theorem bounded_mem (f : ℍ → ℂ) :
 #align upper_half_plane.bounded_mem UpperHalfPlane.bounded_mem
 
 theorem zero_at_im_infty (f : ℍ → ℂ) :
-    IsZeroAtImInfty f ↔ ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ ε := by
-  rw [IsZeroAtImInfty, ZeroAtFilter, tendsto_iff_forall_eventually_mem]
-  constructor
-  · simp_rw [Filter.Eventually, atImInfty_mem]
-    intro h ε hε
-    simpa using h (Metric.closedBall (0 : ℂ) ε) (Metric.closedBall_mem_nhds (0 : ℂ) hε)
-  · simp_rw [Metric.mem_nhds_iff]
-    intro h s hs
-    simp_rw [Filter.Eventually, atImInfty_mem]
-    obtain ⟨ε, h1, h2⟩ := hs
-    have h11 : 0 < ε / 2 := by linarith
-    obtain ⟨A, hA⟩ := h (ε / 2) h11
-    use A
-    intro z hz
-    have hzs : f z ∈ s := by
-      apply h2
-      simp only [mem_ball_zero_iff, norm_eq_abs]
-      apply lt_of_le_of_lt (hA z hz)
-      linarith
-    apply hzs
+    IsZeroAtImInfty f ↔ ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, ∀ z : ℍ, A ≤ im z → abs (f z) ≤ ε :=
+  (atImInfty_basis.tendsto_iff Metric.nhds_basis_closedBall).trans <| by
+    simp only [true_and, mem_closedBall_zero_iff]; rfl
 #align upper_half_plane.zero_at_im_infty UpperHalfPlane.zero_at_im_infty
 
 end UpperHalfPlane

f2ce6086

feat: port Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty (#5531)

ff61283e

`analysis.complex.upper_half_plane.functions_bounded_at_infty` ⟷ `Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 782

analysis.complex.upper_half_plane.functions_bounded_at_infty ⟷ Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 782

`analysis.complex.upper_half_plane.functions_bounded_at_infty` ⟷ `Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty`