Prove that the order of the sum of two distributions is less than or equal to the maximum of the orders of the summands. Prove that, for $\varphi$ a distribution and $h$ in $T$, the order of $h \varphi$ is less than or equal to that of $\varphi$. Prove that the order of $\varphi^{\prime}$ is one greater than that of $\varphi$.