diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean index 0f19833..28da225 100644 --- a/Nevanlinna/complexHarmonic.lean +++ b/Nevanlinna/complexHarmonic.lean @@ -162,9 +162,6 @@ theorem logabs_of_holomorphic_is_harmonic apply ContDiff.comp_contDiffAt z normSq_is_real_C2 exact ContDiff.contDiffAt f_is_real_C2 - - - have t₂ : Complex.log ∘ ⇑(starRingEnd ℂ) ∘ f = Complex.conjCLE ∘ Complex.log ∘ f := by funext z unfold Function.comp @@ -172,9 +169,6 @@ theorem logabs_of_holomorphic_is_harmonic rfl exact Complex.slitPlane_arg_ne_pi (h₃ z) - - - constructor · -- logabs f is real C² have : (fun z ↦ Real.log ‖f z‖) = (2 : ℝ)⁻¹ • (Real.log ∘ Complex.normSq ∘ f) := by @@ -188,14 +182,10 @@ theorem logabs_of_holomorphic_is_harmonic rw [this] 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 - intro z - apply ContDiffAt.const_smul - exact ContDiff.contDiffAt t₄ + apply ContDiff.const_smul + exact t₄ · -- Laplace vanishes have : (fun z ↦ Real.log ‖f z‖) = (2 : ℝ)⁻¹ • (Real.log ∘ Complex.normSq ∘ f) := by