∀ {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] (x y : B) (hx : IsIntegral R x)
  (hy : IsIntegral R y), IsIntegralClosure.mk' A x hx + IsIntegralClosure.mk' A y hy = IsIntegralClosure.mk' A (x + y) ⋯