∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [IsDomain R] [inst_3 : Algebra R S]
  [IsIntegrallyClosed R] [IsDomain S] [Module.IsTorsionFree R S] {s : S},
  IsIntegral R s → RingHom.ker (Polynomial.aeval s).toRingHom = Ideal.span {minpoly R s}