I mostly need help on the proof. Thank you very much!

Problem 1. (25 points) Consider the Activity Selection problem we discussed in class. Suppose that instead of always selecting the first activity to finish, we instead select the last activity to start (as long as it is compatible with all the previously selected activities). In other words, instead of considering the activities by "earliest finish", we consider them by latest start". Explain why this approach is a greedy algorithm, analyze its time complexity, and prove that it yields an optimal solution (greedy choice and optimal substructure)