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This commit is contained in:
Stefan Kebekus 2024-06-19 08:20:36 +02:00
parent 50591a54c2
commit 7a281ff514
2 changed files with 4 additions and 5 deletions

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@ -44,8 +44,10 @@ theorem CauchyRiemann₃ : (DifferentiableAt f z)
simp
theorem CauchyRiemann₄ {F : Type*} [NormedAddCommGroup F] [NormedSpace F] {f : → F} : (Differentiable f)
→ partialDeriv Complex.I f = Complex.I • partialDeriv 1 f := by
theorem CauchyRiemann₄
{F : Type*} [NormedAddCommGroup F] [NormedSpace F]
{f : → F} :
(Differentiable f) → partialDeriv Complex.I f = Complex.I • partialDeriv 1 f := by
intro h
unfold partialDeriv

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@ -4,9 +4,7 @@ import Mathlib.MeasureTheory.Integral.DivergenceTheorem
import Mathlib.MeasureTheory.Integral.IntervalIntegral
import Mathlib.MeasureTheory.Function.LocallyIntegrable
import Nevanlinna.cauchyRiemann
import Nevanlinna.partialDeriv
theorem MeasureTheory.integral2_divergence₃
@ -108,7 +106,6 @@ theorem integral_divergence₅
exact h₁f
let A := integral_divergence₄ (-Complex.I • F) F h₁g h₁f lowerLeft.re upperRight.im upperRight.re lowerLeft.im
have {z : } : fderiv F z Complex.I = partialDeriv _ F z := by rfl
conv at A in (fderiv F _) _ => rw [this]
have {z : } : fderiv (-Complex.I • F) z 1 = partialDeriv _ (-Complex.I • F) z := by rfl