∀ {R : Type u_1} {A : Type u_4} {M : Type u_7} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
  [inst_3 : Monoid M] (F : MonoidAlgebra R M →ₐ[R] A) (m : M),
  ((MonoidAlgebra.lift R A M).symm F) m = F (MonoidAlgebra.single m 1)