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@ -44,8 +44,10 @@ theorem CauchyRiemann₃ : (DifferentiableAt ℂ f z)
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simp
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theorem CauchyRiemann₄ {F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F] {f : ℂ → F} : (Differentiable ℂ f)
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→ partialDeriv ℝ Complex.I f = Complex.I • partialDeriv ℝ 1 f := by
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theorem CauchyRiemann₄
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{F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F]
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{f : ℂ → F} :
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(Differentiable ℂ f) → partialDeriv ℝ Complex.I f = Complex.I • partialDeriv ℝ 1 f := by
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intro h
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unfold partialDeriv
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@ -4,9 +4,7 @@ import Mathlib.MeasureTheory.Integral.DivergenceTheorem
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import Mathlib.MeasureTheory.Integral.IntervalIntegral
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import Mathlib.MeasureTheory.Function.LocallyIntegrable
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import Nevanlinna.cauchyRiemann
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import Nevanlinna.partialDeriv
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theorem MeasureTheory.integral2_divergence₃
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@ -108,7 +106,6 @@ theorem integral_divergence₅
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exact h₁f
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let A := integral_divergence₄ (-Complex.I • F) F h₁g h₁f lowerLeft.re upperRight.im upperRight.re lowerLeft.im
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have {z : ℂ} : fderiv ℝ F z Complex.I = partialDeriv ℝ _ F z := by rfl
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conv at A in (fderiv ℝ F _) _ => rw [this]
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have {z : ℂ} : fderiv ℝ (-Complex.I • F) z 1 = partialDeriv ℝ _ (-Complex.I • F) z := by rfl
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