∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {x : S} {I : Ideal R}
  [inst_3 : IsDomain R] [inst_4 : IsIntegrallyClosed R] [inst_5 : IsDedekindDomain S]
  [inst_6 : Module.IsTorsionFree R S] (hx' : IsIntegral R x),
  (Ideal.span {Polynomial.map (Ideal.Quotient.mk I) (minpoly R (Algebra.adjoin.powerBasis' hx').gen)}).IsTwoSided