Update laplace.lean

This commit is contained in:
Stefan Kebekus 2024-05-30 10:26:39 +02:00
parent 47ab90446f
commit 2544242b13
1 changed files with 14 additions and 1 deletions

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@ -11,6 +11,7 @@ import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.RCLike.Basic import Mathlib.Analysis.RCLike.Basic
import Mathlib.Order.Filter.Basic import Mathlib.Order.Filter.Basic
import Mathlib.Topology.Algebra.InfiniteSum.Module import Mathlib.Topology.Algebra.InfiniteSum.Module
import Mathlib.Topology.Basic
import Mathlib.Topology.Instances.RealVectorSpace import Mathlib.Topology.Instances.RealVectorSpace
import Nevanlinna.cauchyRiemann import Nevanlinna.cauchyRiemann
import Nevanlinna.partialDeriv import Nevanlinna.partialDeriv
@ -79,7 +80,19 @@ theorem laplace_compContLinAt {f : → F} {l : F →L[] G} {x : } (h :
Complex.laplace (l ∘ f) x = (l ∘ (Complex.laplace f)) x := by Complex.laplace (l ∘ f) x = (l ∘ (Complex.laplace f)) x := by
have A₂ : ∃ v ∈ nhds x, (IsOpen v) ∧ (x ∈ v) ∧ (ContDiffOn 2 f v) := by have A₂ : ∃ v ∈ nhds x, (IsOpen v) ∧ (x ∈ v) ∧ (ContDiffOn 2 f v) := by
sorry have : ∃ u ∈ nhds x, ContDiffOn 2 f u := by
apply ContDiffAt.contDiffOn h
rfl
obtain ⟨u, hu₁, hu₂⟩ := this
obtain ⟨v, hv₁, hv₂, hv₃⟩ := mem_nhds_iff.1 hu₁
use v
constructor
· exact IsOpen.mem_nhds hv₂ hv₃
· constructor
exact hv₂
constructor
· exact hv₃
· exact ContDiffOn.congr_mono hu₂ (fun x => congrFun rfl) hv₁
obtain ⟨v, hv₁, hv₂, hv₃, hv₄⟩ := A₂ obtain ⟨v, hv₁, hv₂, hv₃, hv₄⟩ := A₂
have D : ∀ w : , partialDeriv w (l ∘ f) =ᶠ[nhds x] l ∘ partialDeriv w (f) := by have D : ∀ w : , partialDeriv w (l ∘ f) =ᶠ[nhds x] l ∘ partialDeriv w (f) := by