From 631b1bad70ad7179aa5891da5e5f4e747f76bf71 Mon Sep 17 00:00:00 2001
From: Stefan Kebekus <kebekus@users.noreply.github.com>
Date: Wed, 8 May 2024 07:15:34 +0200
Subject: [PATCH] Update complexHarmonic.lean
---
Nevanlinna/complexHarmonic.lean | 12 +++++++++++-
1 file changed, 11 insertions(+), 1 deletion(-)
diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean
index 506339a..6ffe7c5 100644
--- a/Nevanlinna/complexHarmonic.lean
+++ b/Nevanlinna/complexHarmonic.lean
@@ -39,7 +39,17 @@ theorem holomorphic_is_harmonic {f : ℂ → ℂ} (h : Differentiable ℂ f) :
· -- Laplace of f is zero
unfold Complex.laplace
rw [CauchyRiemann₄ h]
- rw [partialDeriv_smul₂ fI_is_real_differentiable]
+
+ let l : ℂ →L[ℝ] ℂ := by
+ --
+ sorry --(fun x ↦ Complex.I • x)
+ have : (Complex.I • Real.partialDeriv 1 f) = (l ∘ (Real.partialDeriv 1 f)) := by
+ sorry
+ rw [this]
+ rw [partialDeriv_compContLin]
+
+ --rw [partialDeriv_smul₂ fI_is_real_differentiable]
+
rw [partialDeriv_comm f_is_real_C2 Complex.I 1]
rw [CauchyRiemann₄ h]
rw [partialDeriv_smul₂ fI_is_real_differentiable]