A = A
A = B  <=>  B = A
A < B  <=>  B > A
A <= B  <=>  B >= A
(A < B) & (B < C)  =>  A < C
(A <= B) & (B <= C)  =>  A <= C

##</code><code>##

            The comparison function is required to behave. If it returns
            inconsistent results (sometimes saying $x[1] is less than $x[2]
            and sometimes saying the opposite, for example) the results are
            not well-defined.