∀ {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] {x : P} {I J : FractionalIdeal S P},
  (FractionalIdeal.spanSingleton S x * I ≤ J) = ∀ z ∈ I, x * z ∈ J