I am refereeing an academic paper where the authors constantly use the construct "it is shown that (blah)" immediately followed by a demonstration of (blah). I don't recall seeing this construct used in this way; the demonstration is usually anywhere other than immediately after (another paper, another book, a previous paragraph, whatnot). Is this usage correct? If not, why?
I can't quote the paper, but here is a more concrete made-up example of their construct:
First, it is shown that there is at most one foo in this list. Consider any bar from the first sequence, they all fall into one of the three cases above. Since these three cases lead to the same foo, there is at most one foo in this list.
Next, it is shown that there is at least one foo in this list. Note that odd bars are guaranteed to lead to a foo. Since there is an odd bar in the first sequence, there must be a foo in this list.