∀ {R : Type u_1} [inst : CommRing R] [NoZeroDivisors R] [inst_2 : NormalizationMonoid R] (u : (Polynomial R)ˣ),
  { val := Polynomial.C ↑(normUnit (↑u).leadingCoeff), inv := Polynomial.C ↑(normUnit (↑u).leadingCoeff)⁻¹,
      val_inv := ⋯, inv_val := ⋯ } =
    u⁻¹