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

fd4551cf

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Analysis.Complex.CauchyIntegral
-import Analysis.Calculus.FderivAnalytic
+import Analysis.Calculus.FDeriv.Analytic
 import Analysis.NormedSpace.Completion
 
 #align_import analysis.complex.liouville from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"

fd4551cf

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 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.Analysis.Complex.CauchyIntegral
-import Mathbin.Analysis.Calculus.FderivAnalytic
-import Mathbin.Analysis.NormedSpace.Completion
+import Analysis.Complex.CauchyIntegral
+import Analysis.Calculus.FderivAnalytic
+import Analysis.NormedSpace.Completion
 
 #align_import analysis.complex.liouville from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"

fd4551cf

bump to nightly-2023-09-20-06

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

e28e6964

Diff

@@ -102,7 +102,7 @@ theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb :
   clear z w; intro c
   obtain ⟨C, C₀, hC⟩ : ∃ C > (0 : ℝ), ∀ z, ‖f z‖ ≤ C :=
     by
-    rcases bounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩
+    rcases isBounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩
     exact
       ⟨max C 1, lt_max_iff.2 (Or.inr zero_lt_one), fun z =>
         (hC (f z) (mem_range_self _)).trans (le_max_left _ _)⟩

fd4551cf

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 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.complex.liouville
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Complex.CauchyIntegral
 import Mathbin.Analysis.Calculus.FderivAnalytic
 import Mathbin.Analysis.NormedSpace.Completion
 
+#align_import analysis.complex.liouville from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Liouville's theorem

fd4551cf

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -38,11 +38,11 @@ universe u v
 variable {E : Type u} [NormedAddCommGroup E] [NormedSpace ℂ E] {F : Type v} [NormedAddCommGroup F]
   [NormedSpace ℂ F]
 
--- mathport name: «expr ̂»
 local postfix:100 "̂" => UniformSpace.Completion
 
 namespace Complex
 
+#print Complex.deriv_eq_smul_circleIntegral /-
 /-- If `f` is complex differentiable on an open disc with center `c` and radius `R > 0` and is
 continuous on its closure, then `f' c` can be represented as an integral over the corresponding
 circle.
@@ -58,7 +58,9 @@ theorem deriv_eq_smul_circleIntegral [CompleteSpace F] {R : ℝ} {c : ℂ} {f :
   refine' (hf.has_fpower_series_on_ball hR).HasFPowerSeriesAt.deriv.trans _
   simp only [cauchyPowerSeries_apply, one_div, zpow_neg, pow_one, smul_smul, zpow_two, mul_inv]
 #align complex.deriv_eq_smul_circle_integral Complex.deriv_eq_smul_circleIntegral
+-/
 
+#print Complex.norm_deriv_le_aux /-
 theorem norm_deriv_le_aux [CompleteSpace F] {c : ℂ} {R C : ℝ} {f : ℂ → F} (hR : 0 < R)
     (hf : DiffContOnCl ℂ f (ball c R)) (hC : ∀ z ∈ sphere c R, ‖f z‖ ≤ C) : ‖deriv f c‖ ≤ C / R :=
   by
@@ -73,7 +75,9 @@ theorem norm_deriv_le_aux [CompleteSpace F] {c : ℂ} {R C : ℝ} {f : ℂ → F
       (circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const hR.le this)
     _ = C / R := by rw [mul_div_left_comm, div_self_mul_self', div_eq_mul_inv]
 #align complex.norm_deriv_le_aux Complex.norm_deriv_le_aux
+-/
 
+#print Complex.norm_deriv_le_of_forall_mem_sphere_norm_le /-
 /-- If `f` is complex differentiable on an open disc of radius `R > 0`, is continuous on its
 closure, and its values on the boundary circle of this disc are bounded from above by `C`, then the
 norm of its derivative at the center is at most `C / R`. -/
@@ -91,7 +95,9 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
       norm_deriv_le_aux hR (e.differentiable.comp_diff_cont_on_cl hd) fun z hz =>
         (UniformSpace.Completion.norm_coe _).trans_le (hC z hz)
 #align complex.norm_deriv_le_of_forall_mem_sphere_norm_le Complex.norm_deriv_le_of_forall_mem_sphere_norm_le
+-/
 
+#print Complex.liouville_theorem_aux /-
 /-- An auxiliary lemma for Liouville's theorem `differentiable.apply_eq_apply_of_bounded`. -/
 theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb : Bounded (range f))
     (z w : ℂ) : f z = f w := by
@@ -109,6 +115,7 @@ theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb :
       norm_deriv_le_of_forall_mem_sphere_norm_le (div_pos C₀ ε₀) hf.diff_cont_on_cl fun z _ => hC z
     _ = ε := div_div_cancel' C₀.lt.ne'
 #align complex.liouville_theorem_aux Complex.liouville_theorem_aux
+-/
 
 end Complex
 
@@ -116,6 +123,7 @@ namespace Differentiable
 
 open Complex
 
+#print Differentiable.apply_eq_apply_of_bounded /-
 /-- **Liouville's theorem**: a complex differentiable bounded function `f : E → F` is a constant. -/
 theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : Bounded (range f))
     (z w : E) : f z = f w :=
@@ -126,18 +134,23 @@ theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb
   exacts [hf.comp ((differentiable_id.smul_const (w - z)).AddConst z),
     hb.mono (range_comp_subset_range _ _)]
 #align differentiable.apply_eq_apply_of_bounded Differentiable.apply_eq_apply_of_bounded
+-/
 
+#print Differentiable.exists_const_forall_eq_of_bounded /-
 /-- **Liouville's theorem**: a complex differentiable bounded function is a constant. -/
 theorem exists_const_forall_eq_of_bounded {f : E → F} (hf : Differentiable ℂ f)
     (hb : Bounded (range f)) : ∃ c, ∀ z, f z = c :=
   ⟨f 0, fun z => hf.apply_eq_apply_of_bounded hb _ _⟩
 #align differentiable.exists_const_forall_eq_of_bounded Differentiable.exists_const_forall_eq_of_bounded
+-/
 
+#print Differentiable.exists_eq_const_of_bounded /-
 /-- **Liouville's theorem**: a complex differentiable bounded function is a constant. -/
 theorem exists_eq_const_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : Bounded (range f)) :
     ∃ c, f = const E c :=
   (hf.exists_const_forall_eq_of_bounded hb).imp fun c => funext
 #align differentiable.exists_eq_const_of_bounded Differentiable.exists_eq_const_of_bounded
+-/
 
 end Differentiable

fd4551cf

bump to nightly-2023-06-11-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

6960a941

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.complex.liouville
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Analysis.NormedSpace.Completion
 /-!
 # Liouville's theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove Liouville's theorem: if `f : E → F` is complex differentiable on the whole
 space and its range is bounded, then the function is a constant. Various versions of this theorem
 are formalized in `differentiable.apply_eq_apply_of_bounded`,

f2ce6086

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -69,7 +69,6 @@ theorem norm_deriv_le_aux [CompleteSpace F] {c : ℂ} {R C : ℝ} {f : ℂ → F
     _ ≤ R * (C / (R * R)) :=
       (circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const hR.le this)
     _ = C / R := by rw [mul_div_left_comm, div_self_mul_self', div_eq_mul_inv]
-    
 #align complex.norm_deriv_le_aux Complex.norm_deriv_le_aux
 
 /-- If `f` is complex differentiable on an open disc of radius `R > 0`, is continuous on its
@@ -88,7 +87,6 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
     _ ≤ C / R :=
       norm_deriv_le_aux hR (e.differentiable.comp_diff_cont_on_cl hd) fun z hz =>
         (UniformSpace.Completion.norm_coe _).trans_le (hC z hz)
-    
 #align complex.norm_deriv_le_of_forall_mem_sphere_norm_le Complex.norm_deriv_le_of_forall_mem_sphere_norm_le
 
 /-- An auxiliary lemma for Liouville's theorem `differentiable.apply_eq_apply_of_bounded`. -/
@@ -107,7 +105,6 @@ theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb :
     ‖deriv f c‖ ≤ C / (C / ε) :=
       norm_deriv_le_of_forall_mem_sphere_norm_le (div_pos C₀ ε₀) hf.diff_cont_on_cl fun z _ => hC z
     _ = ε := div_div_cancel' C₀.lt.ne'
-    
 #align complex.liouville_theorem_aux Complex.liouville_theorem_aux
 
 end Complex

f2ce6086

bump to nightly-2023-06-01-18

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

cb717cb8

Diff

@@ -52,7 +52,7 @@ theorem deriv_eq_smul_circleIntegral [CompleteSpace F] {R : ℝ} {c : ℂ} {f :
     deriv f c = (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c) ^ (-2 : ℤ) • f z :=
   by
   lift R to ℝ≥0 using hR.le
-  refine' (hf.has_fpower_series_on_ball hR).HasFpowerSeriesAt.deriv.trans _
+  refine' (hf.has_fpower_series_on_ball hR).HasFPowerSeriesAt.deriv.trans _
   simp only [cauchyPowerSeries_apply, one_div, zpow_neg, pow_one, smul_smul, zpow_two, mul_inv]
 #align complex.deriv_eq_smul_circle_integral Complex.deriv_eq_smul_circleIntegral

f2ce6086

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -123,7 +123,7 @@ theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb
   set g : ℂ → F := f ∘ fun t : ℂ => t • (w - z) + z
   suffices g 0 = g 1 by simpa [g]
   apply liouville_theorem_aux
-  exacts[hf.comp ((differentiable_id.smul_const (w - z)).AddConst z),
+  exacts [hf.comp ((differentiable_id.smul_const (w - z)).AddConst z),
     hb.mono (range_comp_subset_range _ _)]
 #align differentiable.apply_eq_apply_of_bounded Differentiable.apply_eq_apply_of_bounded

f2ce6086

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -28,7 +28,7 @@ The proof is based on the Cauchy integral formula for the derivative of an analy
 
 open TopologicalSpace Metric Set Filter Asymptotics Function MeasureTheory
 
-open Topology Filter NNReal Real
+open scoped Topology Filter NNReal Real
 
 universe u v

f2ce6086

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -83,8 +83,7 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
     e.has_fderiv_at.comp_has_deriv_at c
       (hd.differentiable_at is_open_ball <| mem_ball_self hR).HasDerivAt
   calc
-    ‖deriv f c‖ = ‖deriv (e ∘ f) c‖ := by
-      rw [this.deriv]
+    ‖deriv f c‖ = ‖deriv (e ∘ f) c‖ := by rw [this.deriv];
       exact (UniformSpace.Completion.norm_coe _).symm
     _ ≤ C / R :=
       norm_deriv_le_aux hR (e.differentiable.comp_diff_cont_on_cl hd) fun z hz =>
@@ -95,10 +94,8 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
 /-- An auxiliary lemma for Liouville's theorem `differentiable.apply_eq_apply_of_bounded`. -/
 theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb : Bounded (range f))
     (z w : ℂ) : f z = f w := by
-  suffices : ∀ c, deriv f c = 0
-  exact is_const_of_deriv_eq_zero hf this z w
-  clear z w
-  intro c
+  suffices : ∀ c, deriv f c = 0; exact is_const_of_deriv_eq_zero hf this z w
+  clear z w; intro c
   obtain ⟨C, C₀, hC⟩ : ∃ C > (0 : ℝ), ∀ z, ‖f z‖ ≤ C :=
     by
     rcases bounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩

f2ce6086

bump to nightly-2023-03-10-14

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

24f14899

Diff

@@ -49,7 +49,7 @@ TODO: add a version for `w ∈ metric.ball c R`.
 TODO: add a version for higher derivatives. -/
 theorem deriv_eq_smul_circleIntegral [CompleteSpace F] {R : ℝ} {c : ℂ} {f : ℂ → F} (hR : 0 < R)
     (hf : DiffContOnCl ℂ f (ball c R)) :
-    deriv f c = (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - c) ^ (-2 : ℤ) • f z :=
+    deriv f c = (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c) ^ (-2 : ℤ) • f z :=
   by
   lift R to ℝ≥0 using hR.le
   refine' (hf.has_fpower_series_on_ball hR).HasFpowerSeriesAt.deriv.trans _

f2ce6086

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -67,7 +67,7 @@ theorem norm_deriv_le_aux [CompleteSpace F] {c : ℂ} {R C : ℝ} {f : ℂ → F
     ‖deriv f c‖ = ‖(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c) ^ (-2 : ℤ) • f z‖ :=
       congr_arg norm (deriv_eq_smul_circle_integral hR hf)
     _ ≤ R * (C / (R * R)) :=
-      circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const hR.le this
+      (circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const hR.le this)
     _ = C / R := by rw [mul_div_left_comm, div_self_mul_self', div_eq_mul_inv]
     
 #align complex.norm_deriv_le_aux Complex.norm_deriv_le_aux

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

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -111,7 +111,7 @@ open Complex
 theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : IsBounded (range f))
     (z w : E) : f z = f w := by
   set g : ℂ → F := f ∘ fun t : ℂ => t • (w - z) + z
-  suffices g 0 = g 1 by simpa
+  suffices g 0 = g 1 by simpa [g]
   apply liouville_theorem_aux
   exacts [hf.comp ((differentiable_id.smul_const (w - z)).add_const z),
     hb.subset (range_comp_subset_range _ _)]

f2ce6086

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -87,7 +87,7 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
 /-- An auxiliary lemma for Liouville's theorem `Differentiable.apply_eq_apply_of_bounded`. -/
 theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb : IsBounded (range f))
     (z w : ℂ) : f z = f w := by
-  suffices : ∀ c, deriv f c = 0; exact is_const_of_deriv_eq_zero hf this z w
+  suffices ∀ c, deriv f c = 0 from is_const_of_deriv_eq_zero hf this z w
   clear z w; intro c
   obtain ⟨C, C₀, hC⟩ : ∃ C > (0 : ℝ), ∀ z, ‖f z‖ ≤ C := by
     rcases isBounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩

f2ce6086

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -22,9 +22,6 @@ The proof is based on the Cauchy integral formula for the derivative of an analy
 `Complex.deriv_eq_smul_circleIntegral`.
 -/
 
-
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 open TopologicalSpace Metric Set Filter Asymptotics Function MeasureTheory Bornology
 
 open scoped Topology Filter NNReal Real

f2ce6086

feat: corollaries of Liouville's theorem with limits at infinity (#8244)

If f : E → F is differentiable (over ℂ) and Tendsto f (cocompact E) (𝓝 c) then f = Function.const E c. This is useful to make the proof of the fundamental theorem of algebra slightly more conceptual, as well as to simplify the proof that the spectrum of an element in a Banach algebra over ℂ is nonempty.

depends on: #8234

b000223a

Diff

@@ -132,4 +132,25 @@ theorem exists_eq_const_of_bounded {f : E → F} (hf : Differentiable ℂ f)
   (hf.exists_const_forall_eq_of_bounded hb).imp fun _ => funext
 #align differentiable.exists_eq_const_of_bounded Differentiable.exists_eq_const_of_bounded
 
+/-- A corollary of Liouville's theorem where the function tends to a finite value at infinity
+(i.e., along `Filter.cocompact`, which in proper spaces coincides with `Bornology.cobounded`). -/
+theorem eq_const_of_tendsto_cocompact [Nontrivial E] {f : E → F} (hf : Differentiable ℂ f) {c : F}
+    (hb : Tendsto f (cocompact E) (𝓝 c)) : f = Function.const E c := by
+  have h_bdd : Bornology.IsBounded (Set.range f) := by
+    obtain ⟨s, hs, hs_bdd⟩ := Metric.exists_isBounded_image_of_tendsto hb
+    obtain ⟨t, ht, hts⟩ := mem_cocompact.mp hs
+    apply ht.image hf.continuous |>.isBounded.union hs_bdd |>.subset
+    simpa [Set.image_union, Set.image_univ] using Set.image_subset _ <| calc
+      Set.univ = t ∪ tᶜ := t.union_compl_self.symm
+      _        ⊆ t ∪ s  := by gcongr
+  obtain ⟨c', hc'⟩ := hf.exists_eq_const_of_bounded h_bdd
+  convert hc'
+  exact tendsto_nhds_unique hb (by simpa [hc'] using tendsto_const_nhds)
+
+/-- A corollary of Liouville's theorem where the function tends to a finite value at infinity
+(i.e., along `Filter.cocompact`, which in proper spaces coincides with `Bornology.cobounded`). -/
+theorem apply_eq_of_tendsto_cocompact [Nontrivial E] {f : E → F} (hf : Differentiable ℂ f) {c : F}
+    (x : E) (hb : Tendsto f (cocompact E) (𝓝 c)) : f x = c :=
+  congr($(hf.eq_const_of_tendsto_cocompact hb) x)
+
 end Differentiable

f2ce6086

refactor(Topology/MetricSpace): remove Metric.Bounded (#7240)

Use Bornology.IsBounded instead.

98e78f90

Diff

@@ -25,7 +25,7 @@ The proof is based on the Cauchy integral formula for the derivative of an analy
 
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
-open TopologicalSpace Metric Set Filter Asymptotics Function MeasureTheory
+open TopologicalSpace Metric Set Filter Asymptotics Function MeasureTheory Bornology
 
 open scoped Topology Filter NNReal Real
 
@@ -88,12 +88,12 @@ theorem norm_deriv_le_of_forall_mem_sphere_norm_le {c : ℂ} {R C : ℝ} {f : 
 #align complex.norm_deriv_le_of_forall_mem_sphere_norm_le Complex.norm_deriv_le_of_forall_mem_sphere_norm_le
 
 /-- An auxiliary lemma for Liouville's theorem `Differentiable.apply_eq_apply_of_bounded`. -/
-theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb : Bounded (range f))
+theorem liouville_theorem_aux {f : ℂ → F} (hf : Differentiable ℂ f) (hb : IsBounded (range f))
     (z w : ℂ) : f z = f w := by
   suffices : ∀ c, deriv f c = 0; exact is_const_of_deriv_eq_zero hf this z w
   clear z w; intro c
   obtain ⟨C, C₀, hC⟩ : ∃ C > (0 : ℝ), ∀ z, ‖f z‖ ≤ C := by
-    rcases bounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩
+    rcases isBounded_iff_forall_norm_le.1 hb with ⟨C, hC⟩
     exact
       ⟨max C 1, lt_max_iff.2 (Or.inr zero_lt_one), fun z =>
         (hC (f z) (mem_range_self _)).trans (le_max_left _ _)⟩
@@ -111,24 +111,24 @@ namespace Differentiable
 open Complex
 
 /-- **Liouville's theorem**: a complex differentiable bounded function `f : E → F` is a constant. -/
-theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : Bounded (range f))
+theorem apply_eq_apply_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : IsBounded (range f))
     (z w : E) : f z = f w := by
   set g : ℂ → F := f ∘ fun t : ℂ => t • (w - z) + z
   suffices g 0 = g 1 by simpa
   apply liouville_theorem_aux
   exacts [hf.comp ((differentiable_id.smul_const (w - z)).add_const z),
-    hb.mono (range_comp_subset_range _ _)]
+    hb.subset (range_comp_subset_range _ _)]
 #align differentiable.apply_eq_apply_of_bounded Differentiable.apply_eq_apply_of_bounded
 
 /-- **Liouville's theorem**: a complex differentiable bounded function is a constant. -/
 theorem exists_const_forall_eq_of_bounded {f : E → F} (hf : Differentiable ℂ f)
-    (hb : Bounded (range f)) : ∃ c, ∀ z, f z = c :=
+    (hb : IsBounded (range f)) : ∃ c, ∀ z, f z = c :=
   ⟨f 0, fun _ => hf.apply_eq_apply_of_bounded hb _ _⟩
 #align differentiable.exists_const_forall_eq_of_bounded Differentiable.exists_const_forall_eq_of_bounded
 
 /-- **Liouville's theorem**: a complex differentiable bounded function is a constant. -/
-theorem exists_eq_const_of_bounded {f : E → F} (hf : Differentiable ℂ f) (hb : Bounded (range f)) :
-    ∃ c, f = const E c :=
+theorem exists_eq_const_of_bounded {f : E → F} (hf : Differentiable ℂ f)
+    (hb : IsBounded (range f)) : ∃ c, f = const E c :=
   (hf.exists_const_forall_eq_of_bounded hb).imp fun _ => funext
 #align differentiable.exists_eq_const_of_bounded Differentiable.exists_eq_const_of_bounded

f2ce6086

chore: regularize HPow.hPow porting notes (#6465)

0f85d19f

Diff

@@ -23,7 +23,7 @@ The proof is based on the Cauchy integral formula for the derivative of an analy
 -/
 
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 open TopologicalSpace Metric Set Filter Asymptotics Function MeasureTheory

f2ce6086

chore(Deriv): rename some files (#6167)

Move some files to Analysis/Calculus/FDeriv

7433944e

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
 import Mathlib.Analysis.Complex.CauchyIntegral
-import Mathlib.Analysis.Calculus.FDerivAnalytic
+import Mathlib.Analysis.Calculus.FDeriv.Analytic
 import Mathlib.Analysis.NormedSpace.Completion
 
 #align_import analysis.complex.liouville from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"

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 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module analysis.complex.liouville
-! 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.Analysis.Complex.CauchyIntegral
 import Mathlib.Analysis.Calculus.FDerivAnalytic
 import Mathlib.Analysis.NormedSpace.Completion
 
+#align_import analysis.complex.liouville from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Liouville's theorem

f2ce6086

feat: port Analysis.Complex.Liouville (#4894)

03854c5d

`analysis.complex.liouville` ⟷ `Mathlib.Analysis.Complex.Liouville`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 1081

analysis.complex.liouville ⟷ Mathlib.Analysis.Complex.Liouville

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 12 + 1081

`analysis.complex.liouville` ⟷ `Mathlib.Analysis.Complex.Liouville`