∀ {R : Type u_2} [inst : CommRing R] {K : Type u_1} [inst_1 : Field K] [inst_2 : Algebra R K]
  [inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] (I I' J' : FractionalIdeal (nonZeroDivisors R) K),
  ¬I'.divMod I J' = 0 → FractionalIdeal.spanSingleton (nonZeroDivisors R) (I'.divMod I J') ≠ 0