∀ {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},
  (I ≤ FractionalIdeal.spanSingleton S x * J) = ∀ zI ∈ I, ∃ zJ ∈ J, x * zJ = zI