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Update complexHarmonic.lean

This commit is contained in:
Stefan Kebekus 2024-05-03 15:54:51 +02:00
parent bfdc7f6d2a
commit a55b084031
1 changed files with 9 additions and 7 deletions
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Nevanlinna/complexHarmonic.lean
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@ -1,3 +1,4 @@
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.TaylorSeries
import Mathlib.Analysis.Calculus.LineDeriv.Basic
@ -21,17 +22,18 @@ def Harmonic (f : ℂ → ℂ) : Prop :=
#check second_derivative_symmetric
lemma zwoDiff (f : ℝ × ℝ → ℝ) (h : ContDiff ℝ 2 f) : ∀ z a b : ℂ, 0 = 1 := by
lemma zwoDiff (f : ℝ × ℝ → ℝ) (h : ContDiff ℝ 2 f) : ∀ z a b : ℝ × ℝ, 0 = 1 := by
intro z a b
let fx := fun w ↦ (fderiv ℝ f w) 1
let fxx := fun w ↦ (fderiv ℝ fx w) 1
let f2 := (fderiv ℝ (fun w => fderiv ℝ f w) z) 1 1
have : iteratedFDeriv ℝ (1 + 1) f = 0 := by
rw [iteratedFDeriv_succ_eq_comp_left]
let fx := fun w ↦ (fderiv ℝ f w) a
let fxx := fun w ↦ (fderiv ℝ fx w) a
let f2 := (fderiv ℝ (fun w => fderiv ℝ f w) z) a a
have : iteratedFDeriv ℝ 1 f z ![a] = 0 := by
rw [iteratedFDeriv_succ_apply_left]
simp
let g := iteratedFDeriv ℝ 0 f
simp at g
sorry
have : f2 = fxx z := by