nevanlinna/Nevanlinna/realHarmonic.lean

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import Mathlib.Analysis.Calculus.LineDeriv.Basic
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import Mathlib.Analysis.Calculus.ContDiff.Defs
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noncomputable def Real.laplace : ( × ) → ( × ) := by
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intro f
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let f₁ := fun x ↦ lineDeriv f x ⟨1,0⟩
let f₁₁ := fun x ↦ lineDeriv f₁ x ⟨1,0⟩
let f₂ := fun x ↦ lineDeriv f x ⟨0,1⟩
let f₂₂ := fun x ↦ lineDeriv f₂ x ⟨0,1⟩
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exact f₁₁ + f₂₂
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def Harmonic (f : × ) : Prop :=
(ContDiff 2 f) ∧ (∀ x, Real.laplace f x = 0)