Can you provide a detailed explanation of the proof of correctness for the Merge Sort algorithm?

The proof of correctness for the Merge Sort algorithm involves showing that it correctly sorts a list of numbers. This is typically done by induction, where we prove that the algorithm works for a base case (such as a list with one element) and then show that if it works for smaller lists, it will work for larger lists as well. The key idea is that Merge Sort divides the list into smaller sublists, sorts them, and then merges them back together in the correct order. This process is repeated until the entire list is sorted. By ensuring that the merging step is done correctly and that the algorithm handles all possible cases, we can prove that Merge Sort will always produce a sorted list.