∀ (R : Type u_1) (A : Type u_2) (B : Type u_3) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
  [inst_3 : Algebra R B] [inst_4 : Algebra A B] [inst_5 : IsIntegralClosure A R B] {S : Type u_4} [inst_6 : CommRing S]
  [inst_7 : Algebra R S] [inst_8 : Algebra S B] [inst_9 : IsScalarTower R S B] [inst_10 : Algebra R A]
  [inst_11 : IsScalarTower R A B] [isIntegral : Algebra.IsIntegral R S],
  IsIntegralClosure.lift R A B = IsIntegralClosure.lift R A B