∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K] {x ζ : (NumberField.RingOfIntegers K)ˣ}
  {f : Fin (NumberField.Units.rank K) → ℤ},
  ζ ∈ NumberField.Units.torsion K →
    x = ζ * ∏ i, NumberField.Units.fundSystem K i ^ f i →
      f = ⇑((NumberField.Units.basisModTorsion K).repr (Additive.ofMul ↑x))