From 4064f69c031861173f24bfbeb1a60094c2b63a09 Mon Sep 17 00:00:00 2001
From: Stefan Kebekus <kebekus@users.noreply.github.com>
Date: Wed, 15 May 2024 15:03:16 +0200
Subject: [PATCH] Update complexHarmonic.lean

---
 Nevanlinna/complexHarmonic.lean | 36 ++++++++++++++++++++++++++++++++-
 1 file changed, 35 insertions(+), 1 deletion(-)

diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean
index 94ad6d6..57ba7c7 100644
--- a/Nevanlinna/complexHarmonic.lean
+++ b/Nevanlinna/complexHarmonic.lean
@@ -1,13 +1,14 @@
-import Mathlib.Data.Fin.Tuple.Basic
 import Mathlib.Analysis.Complex.Basic
 import Mathlib.Analysis.Complex.TaylorSeries
 import Mathlib.Analysis.Calculus.LineDeriv.Basic
 import Mathlib.Analysis.Calculus.ContDiff.Defs
 import Mathlib.Analysis.Calculus.FDeriv.Basic
 import Mathlib.Analysis.Calculus.FDeriv.Symmetric
+import Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv
 import Mathlib.Data.Complex.Module
 import Mathlib.Data.Complex.Order
 import Mathlib.Data.Complex.Exponential
+import Mathlib.Data.Fin.Tuple.Basic
 import Mathlib.Analysis.RCLike.Basic
 import Mathlib.Topology.Algebra.InfiniteSum.Module
 import Mathlib.Topology.Instances.RealVectorSpace
@@ -227,6 +228,39 @@ theorem logabs_of_holomorphic_is_harmonic
       exact (AddEquivClass.map_ne_zero_iff starRingAut).mpr (h₂ z)
       exact h₂ z
     rw [this]
+    rw [laplace_add]
+    
+    have : Differentiable ℂ (Complex.log ∘ f) := by
+      intro z
+      apply DifferentiableAt.comp 
+      exact Complex.differentiableAt_log (h₃ z)
+      exact h₁ z
+
+    have : Complex.laplace (Complex.log ∘ f) = 0 := by
+      let A := holomorphic_is_harmonic this
+      funext z
+      exact A.2 z
+    rw [this]
+    simp
+
+    have : Complex.log ∘ ⇑(starRingEnd ℂ) ∘ f = ⇑(starRingEnd ℂ) ∘ Complex.log ∘ f := by
+      funext z
+      unfold Function.comp
+      rw [Complex.log_conj]
+      exact Complex.slitPlane_arg_ne_pi (h₃ z)
+    rw [this]
+
+    have : ⇑(starRingEnd ℂ) ∘ Complex.log ∘ f = Complex.conjCLE ∘ Complex.log ∘ f := by
+      rfl
+    rw [this]
+    have : ContDiff ℝ 2 (Complex.log ∘ f) := by sorry
+    have : Complex.laplace (⇑Complex.conjCLE ∘ f) = ⇑Complex.conjCLE ∘ Complex.laplace (f) := by
+      apply laplace_compContLin
+
+      sorry
+    rw [laplace_compContLin this]
+
+    sorry
 
     sorry
     sorry