diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean index 1f916e0..536a415 100644 --- a/Nevanlinna/complexHarmonic.lean +++ b/Nevanlinna/complexHarmonic.lean @@ -159,6 +159,7 @@ theorem logabs_of_holomorphic_is_harmonic have : (2 : ℝ)⁻¹ • (Real.log ∘ Complex.normSq ∘ f) = (fun z ↦ (2 : ℝ)⁻¹ • ((Real.log ∘ ⇑Complex.normSq ∘ f) z)) := by simp + exact rfl rw [this] apply contDiff_iff_contDiffAt.2 @@ -229,18 +230,18 @@ theorem logabs_of_holomorphic_is_harmonic exact h₂ z rw [this] rw [laplace_add] - + have : Differentiable ℂ (Complex.log ∘ f) := by intro z - apply DifferentiableAt.comp + apply DifferentiableAt.comp exact Complex.differentiableAt_log (h₃ z) exact h₁ z - have : Complex.laplace (Complex.log ∘ f) = 0 := by + have t₁: Complex.laplace (Complex.log ∘ f) = 0 := by let A := holomorphic_is_harmonic this funext z exact A.2 z - rw [this] + rw [t₁] simp have : Complex.log ∘ ⇑(starRingEnd ℂ) ∘ f = ⇑(starRingEnd ℂ) ∘ Complex.log ∘ f := by @@ -253,13 +254,9 @@ theorem logabs_of_holomorphic_is_harmonic have : ⇑(starRingEnd ℂ) ∘ Complex.log ∘ f = Complex.conjCLE ∘ Complex.log ∘ f := by rfl rw [this] - have : ContDiff ℝ 2 (Complex.log ∘ f) := by sorry - - have : Complex.laplace (⇑Complex.conjCLE ∘ f) = ⇑Complex.conjCLE ∘ Complex.laplace (f) := by - - sorry - - sorry - + rw [laplace_compCLE] + rw [t₁] + simp + sorry sorry sorry