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Update holomorphic.primitive.lean

This commit is contained in:
Stefan Kebekus 2024-06-12 13:50:29 +02:00
parent a9f1c3eaa6
commit ce751dff83
1 changed files with 14 additions and 6 deletions
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Nevanlinna/holomorphic.primitive.lean
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@ -161,15 +161,21 @@ theorem integral_divergence₅
(∫ (x : ℝ) in a₁..b₁, Complex.I • F { re := x, im := a₂ }) + (∫ (x : ℝ) in a₁..b₁, Complex.I • F { re := x, im := a₂ }) +
(∫ (y : ℝ) in a₂..b₂, F { re := a₁, im := y }) := by (∫ (y : ℝ) in a₂..b₂, F { re := a₁, im := y }) := by
let f := F let h₁f : ContDiff ℝ 1 F := (hF.contDiff : ContDiff ℂ 1 F).restrict_scalars ℝ
let h₁f : ContDiff ℝ 1 f := by sorry
let g := Complex.I • F let g := Complex.I • F
let h₁g : ContDiff ℝ 1 g := by sorry let h₁g : ContDiff ℝ 1 (Complex.I • F) := by
have : Complex.I • F = fun x ↦ Complex.I • F x := by rfl
rw [this]
apply ContDiff.comp
exact contDiff_const_smul Complex.I
exact h₁f
let A := integral_divergence₄ f g h₁f h₁g a₁ a₂ b₁ b₂
have {z : ℂ} : fderiv ℝ f z 1 = partialDeriv ℝ 1 f z := by rfl let A := integral_divergence₄ F g h₁f h₁g a₁ a₂ b₁ b₂
conv at A in (fderiv ℝ f _) 1 => rw [this]
have {z : ℂ} : fderiv ℝ F z 1 = partialDeriv ℝ 1 F z := by rfl
conv at A in (fderiv ℝ F _) 1 => rw [this]
have {z : ℂ} : fderiv ℝ g z Complex.I = partialDeriv ℝ Complex.I g z := by rfl have {z : ℂ} : fderiv ℝ g z Complex.I = partialDeriv ℝ Complex.I g z := by rfl
conv at A in (fderiv ℝ g _) Complex.I => rw [this] conv at A in (fderiv ℝ g _) Complex.I => rw [this]
@ -186,4 +192,6 @@ theorem integral_divergence₅
simp simp
simp at A simp at A
sorry sorry