10. Dijkstra ascending. Referring to Dijkstra's algorithm as presented in class: (a) Show that at any point in time, we have for all ER and y eV\R Hint: this can be done with an induction argument very similar to what was done in the proof of correctness of Dijkstra's algorithm. (b) Show that if u is removed from Q, then the next node v removed from Q satisfies d(s, u)