algorithms – How to prove the optimal substructure for the assignment problem of the conference room?


In CLRS, an approach was given to prove the optimal substructure and the accuracy of the greedy algorithm for the activity selection problem. In the amphitheater assignment problem, we sort the classes according to their start times and allocate them amphitheatres accordingly, choosing a new amphitheater if the class schedules conflict with all existing amphitheatres. Is there a way to prove the optimal substructure in this problem? Why do we sort the courses only by their start times and not by their end times?
How to prove that there is always an optimal solution that makes the greedy choice?