Notice that it was not necessary to check for
a>b. The trichotomy principle
tells us that numbers are related in one of three ways (a
equals b, or a is less
than b, or a is greater
than b). In
order for the computer to get to the "else" condition in the
problem above, it must have answered NO to the first two decisions.
Consequently, there is only ONE possibility left and we do not waste the
computer's time checking it.