One more note:  I used round parenthesis in the diagrams above to
indicate intervals.  If you think about it a bit, you'll realize I
should be using square brackets in some places, or make some
distinctive graphic.  Open and closed circles, perhaps?

Otherwise, there are tiny pinpoint gaps in the case analysis where
things leak through.  You want the case analysis to be watertight, not
like a sieve.  :P
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