∀ (R : Type u_1) {S : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Semiring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra S A] [inst_5 : Algebra R A] [inst_6 : IsScalarTower R S A]
  (U : Subalgebra S A), IsScalarTower R S ↥U