From e1b948ad2cd9d4aa9deb242cb45c83df367fb151 Mon Sep 17 00:00:00 2001
From: Stefan Kebekus <kebekus@users.noreply.github.com>
Date: Tue, 22 Oct 2024 17:12:59 +0200
Subject: [PATCH] =?UTF-8?q?Update,=20working,=20=E2=80=A6?=
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---
 Nevanlinna/stronglyMeromorphic.lean | 76 ++++++++++++++++++++---------
 lake-manifest.json                  | 12 ++---
 2 files changed, 58 insertions(+), 30 deletions(-)

diff --git a/Nevanlinna/stronglyMeromorphic.lean b/Nevanlinna/stronglyMeromorphic.lean
index 8d0f6b7..4140e50 100644
--- a/Nevanlinna/stronglyMeromorphic.lean
+++ b/Nevanlinna/stronglyMeromorphic.lean
@@ -81,41 +81,49 @@ theorem AnalyticAt.stronglyMeromorphicAt
     tauto
 
 
-theorem MeromorphicAt.order_neq_top_iff
-  {f : ℂ → ℂ}
-  {z₀ : ℂ}
-  (hf : MeromorphicAt f z₀) :
-  hf.order ≠ ⊤ ↔ ∃ (g : ℂ → ℂ), AnalyticAt ℂ g z₀ ∧ g z₀ ≠ 0 ∧ ∀ᶠ (z : ℂ) in nhdsWithin z₀ {z₀}ᶜ, f z = (z - z₀) ^ (hf.order.untop' 0) • g z := by
-
-  rw [← hf.order_eq_int_iff (hf.order.untop' 0)]
-  constructor
-  · intro h₁f
-    apply?
-    exact Eq.symm (ENat.coe_toNat h₁f)
-  · intro h₁f
-    exact ENat.coe_toNat_eq_self.mp (id (Eq.symm h₁f))
-
-
 /- Make strongly MeromorphicAt -/
 noncomputable def MeromorphicAt.makeStronglyMeromorphicAt
   {f : ℂ → ℂ}
   {z₀ : ℂ}
   (hf : MeromorphicAt f z₀) :
   ℂ → ℂ := by
-
-  by_cases h₁f : hf.order = ⊤
-  · exact 0
-  ·
-
   intro z
   by_cases z = z₀
-  · by_cases h₂f : hf.order = 0
-    · have : (0 : WithTop ℤ) = (0 : ℤ) := rfl
-      rw [this, hf.order_eq_int_iff] at h₂f
-      exact (Classical.choose h₂f) z₀
+  · by_cases h₁f : hf.order = (0 : ℤ)
+    · rw [hf.order_eq_int_iff] at h₁f
+      exact (Classical.choose h₁f) z₀
     · exact 0
   · exact f z
 
+lemma m₁
+  {f : ℂ → ℂ}
+  {z₀ : ℂ}
+  (hf : MeromorphicAt f z₀) :
+  ∀ z ≠ z₀, f z = hf.makeStronglyMeromorphicAt z := by
+  intro z hz
+  unfold MeromorphicAt.makeStronglyMeromorphicAt
+  simp [hz]
+
+lemma m₂
+  {f : ℂ → ℂ}
+  {z₀ : ℂ}
+  (hf : MeromorphicAt f z₀) :
+  ∀ᶠ (z : ℂ) in nhdsWithin z₀ {z₀}ᶜ, f z = hf.makeStronglyMeromorphicAt z := by
+  apply eventually_nhdsWithin_of_forall
+  exact fun x a => m₁ hf x a
+
+
+open Topology
+
+lemma Mnhds
+  {f g : ℂ → ℂ}
+  {z₀ : ℂ}
+  (h₁ : ∀ᶠ (z : ℂ) in nhdsWithin z₀ {z₀}ᶜ, f z = g z)
+  (h₂ : f z₀ = g z₀) :
+  ∀ᶠ (z : ℂ) in nhds z₀, f z = g z := by
+  rw [eventually_nhds_iff]
+  rw [eventually_nhdsWithin_iff] at h₁
+  sorry
 
 theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
   {f : ℂ → ℂ}
@@ -123,6 +131,26 @@ theorem StronglyMeromorphicAt_of_makeStronglyMeromorphic
   (hf : MeromorphicAt f z₀) :
   StronglyMeromorphicAt hf.makeStronglyMeromorphicAt z₀ := by
 
+  by_cases h₂f : hf.order = ⊤
+  · rw [MeromorphicAt.order_eq_top_iff] at h₂f
+    let Z : ℂ → ℂ := fun z ↦ 0
+    have : hf.makeStronglyMeromorphicAt =ᶠ[𝓝 z₀] 0 := by
+      --unfold Filter.EventuallyEq
+      apply Mnhds
+      · apply eventually_nhdsWithin_of_forall
+        intro x hx
+
+        sorry
+
+
+      sorry
+
+
+
+    apply AnalyticAt.stronglyMeromorphicAt
+    rw [analyticAt_congr this]
+    apply analyticAt_const
+
 
 
   by_cases h₂f : hf.order = 0
diff --git a/lake-manifest.json b/lake-manifest.json
index 66bfdc5..22c26ed 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -5,7 +5,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "9efd9c267ad7a71c5e3a83e8fbbd446fe61ef119",
+   "rev": "7c5548eeeb1748da5c2872dbd866d3acbaea4b3f",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -15,7 +15,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "fa3d73a2cf077f4b14c7840352ac7b08aeb6eb41",
+   "rev": "1357f4f49450abb9dfd4783e38219f4ce84f9785",
    "name": "Qq",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -35,10 +35,10 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "cd20dae87c48495f0220663014dff11671597fcf",
+   "rev": "baa65c6339a56bd22b7292aa4511c54b3cc7a6af",
    "name": "proofwidgets",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v0.0.43-pre",
+   "inputRev": "v0.0.43",
    "inherited": true,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover/lean4-cli",
@@ -65,7 +65,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "4b61d4abc1659f15ffda5ec24fdebc229d51d066",
+   "rev": "7bedaed1ef024add1e171cc17706b012a9a37802",
    "name": "LeanSearchClient",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -75,7 +75,7 @@
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "5ab87a979ed4fbe6219ecaf7ca251345ab04ec8f",
+   "rev": "818db408b33f801f4094614250e6b3cfb9e065c8",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
    "inputRev": null,