∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] [IsLocalization M S] (N : Submonoid R), M ≤ N → (∀ n ∈ N, ∃ m ∈ M, n ∣ m) → IsLocalization N S