I was reading up on this wiki article on Shell Sort. The following claim is made in the text in the Description section –
If the list is then k-sorted for some smaller integer k, then the list remains h-sorted. This is, of course, after the array was already h-sorted for some h>k.

Is there a formal proof for the above claim? I have no idea how to start on this. I have tried to think of the 2 kinds of sorting (h and k) as a combination of individual sorted subsequences which are interleaved, and that doesn’t seem to help.