∀ {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),
  Algebra.TensorProduct.basisAux A b =
    (TensorProduct.congr (Finsupp.LinearEquiv.finsuppUnique R A PUnit.{uι + 1}).symm b.repr).trans
      ((finsuppTensorFinsupp R R A R PUnit.{uι + 1} ι).trans
        (Finsupp.lcongr (Equiv.uniqueProd ι PUnit.{uι + 1}) (TensorProduct.rid R A)))