import Mathlib

namespace OAI

namespace SymmetricMahler

variable {I : Type*} [Fintype I]

def coordinatePolar (K : Set (I → ℝ)) : Set (I → ℝ) :=
  {p | ∀ v ∈ K, (∑ i, p i*v i) ≤ 1}

noncomputable section
open Set MeasureTheory

theorem symmetric_mahler {n : ℕ} (hn : 1 ≤ n)
    {K : Set (Fin n → ℝ)} (hK : IsCompact K) (hconv : Convex ℝ K)
    (hsym : ∀ x ∈ K, -x ∈ K) (hint : (interior K).Nonempty) :
    (4:ℝ)^n/(Nat.factorial n:ℝ) ≤
      (volume K).toReal*(volume (coordinatePolar K)).toReal := by
  sorry

end

end SymmetricMahler

end OAI