Prove that the foilowing assertion is an invariant of the Chandy-Musra algorithm for computing paths towards $v_0$ (Algorithm 4.7).
$$
\begin{gathered}
\forall u, w:\left\langle\text { mydist, } v_0, d\right\rangle \in M_{\mathrm{tw} u} \Rightarrow d\left(w, v_0\right) \leq d \\
\wedge \forall u: d\left(u, v_0\right) \leq D_u\left[v_0\right]
\end{gathered}
$$
Give an example of an execution for which the number of messages is exponential in the number of channels of the network.