A Relation satisfies StrictWeakOrder only if it imposes a strict weak ordering on its arguments.
The term strict refers to the requirement of an irreflexive relation (!comp(x, x) for all x), and the term weak to requirements that are not as strong as those for a total ordering, but stronger than those for a partial ordering. If we define equiv(a, b) as !comp(a, b) && !comp(b, a), then the requirements are that comp and equiv both be transitive relations:
comp(a, b) && comp(b, c) implies comp(a, c)
equiv(a, b) && equiv(b, c) implies equiv(a, c) [ Note: Under these conditions, it can be shown that
equiv is an equivalence relation
comp induces a well-defined relation on the equivalence classes determined by equiv
The induced relation is a strict total ordering. — end note ]