∀ {R : Type u_1} {A : Type u_2} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : Semiring A]
  [inst_2 : Algebra R A] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] (b : Module.Basis ι R M) (a : A)
  (x : TensorProduct R A M), (Algebra.TensorProduct.basisAux A b) (a • x) = a • (Algebra.TensorProduct.basisAux A b) x