∀ {R : Type u} [inst : CommSemiring R] {S : Type u_1} {T : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Semiring T]
  [inst_3 : Module R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [inst_6 : IsScalarTower R S T] (a : Set S),
  Submodule.span R (⇑(algebraMap S T) '' a) = Submodule.map (↑R (Algebra.linearMap S T)) (Submodule.span R a)