∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K],
  Fintype.card
      (Module.Free.ChooseBasisIndex ℤ (Additive ((NumberField.RingOfIntegers K)ˣ ⧸ NumberField.Units.torsion K))) =
    Fintype.card (Fin (NumberField.Units.rank K))