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