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pierce_birkhoff_conjecture_dim_two

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The Pierce-Birkhoff conjecture holds for `n = 2`. This was proved by Louis Mahé.

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Lean 4 Statement 
theorem pierce_birkhoff_conjecture_dim_two
    (f : (Fin 2 → ℝ) → ℝ) (hf : IsPiecewiseMvPolynomial f) :
    ∃ (ι κ : Type) (g : ι → κ → MvPolynomial (Fin 2) ℝ), Finite ι ∧ Finite κ ∧
      ∀ x, f x = ⨆ i, ⨅ j, MvPolynomial.eval x (g i j)
ID: Wikipedia__PierceBirkhoff__pierce_birkhoff_conjecture_dim_two
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