∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsIntegrallyClosed R]
  [IsDomain R], ∀ M ≤ nonZeroDivisors R, ∀ [IsLocalization M S], IsIntegrallyClosed S