∀ (n : ℕ) (B₁ B₂ : Fin (n + 1) → ℝ) (val : Fin (n + 1) → ℤ)
  (property : val ∈ ↑(Finset.Icc (fun x => ⌈B₁ x⌉) fun x => ⌊B₂ x⌋)),
  ((Polynomial.ofFn (n + 1)) ↑⟨val, property⟩).natDegree ≤ n ∧
    ∀ (i : Fin (n + 1)),
      B₁ i ≤ IntCast.intCast (((Polynomial.ofFn (n + 1)) ↑⟨val, property⟩).coeff ↑i) ∧
        IntCast.intCast (((Polynomial.ofFn (n + 1)) ↑⟨val, property⟩).coeff ↑i) ≤ B₂ i