∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) (P : Type u_2) [inst_1 : CommRing P] [inst_2 : Algebra R P]
  [inst_3 : IsLocalization S P] (I : FractionalIdeal S P),
  FractionalIdeal.spanSingleton S ((algebraMap R P) ↑I.den) * I = ↑I.num