∀ {κ : Type u_3} {R : Type u_2} {M : Type u_1} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (b : Module.Basis κ R M) (i : κ),
  ((((FreeAlgebra.lift R) (⇑(TensorAlgebra.ι R) ∘ ⇑b)).comp
            ((TensorAlgebra.lift R) (Finsupp.linearCombination R (FreeAlgebra.ι R) ∘ₗ ↑b.repr))).toLinearMap ∘ₗ
        TensorAlgebra.ι R)
      (b i) =
    ((AlgHom.id R (TensorAlgebra R M)).toLinearMap ∘ₗ TensorAlgebra.ι R) (b i)