∀ (R : Type u_2) (A : Type u_1) (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] [isIntegral : Algebra.IsIntegral R S]
  (x y : S),
  IsIntegralClosure.mk' A ((algebraMap S B) (x * y)) ⋯ =
    IsIntegralClosure.mk' A ((algebraMap S B) x) ⋯ * IsIntegralClosure.mk' A ((algebraMap S B) y) ⋯