∀ (R : Type u_1) {M : Type u_2} {N : Type u_3} [inst : CommSemiring R] [inst_1 : AddMonoid M] [inst_2 : AddMonoid N]
  (f : M →+ N),
  (Algebra.TensorProduct.map (AddMonoidAlgebra.mapDomainAlgHom R R f) (AddMonoidAlgebra.mapDomainAlgHom R R f)).comp
      (Bialgebra.comulAlgHom R (AddMonoidAlgebra R M)) =
    (Bialgebra.comulAlgHom R (AddMonoidAlgebra R N)).comp (AddMonoidAlgebra.mapDomainAlgHom R R f)