∀ {R : Type u} {S : Type v} {A : Type w} [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],
  (∀ (x : R), (algebraMap R A) x = (algebraMap S A) ((algebraMap R S) x)) → IsScalarTower R S A