∀ {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], MonoidAlgebra.mapDomainAlgHom R A (MonoidHom.id M) = AlgHom.id R (MonoidAlgebra A M)