cpp/concepts/strict weak order

The concept specifies that the   imposes a strict weak ordering on its arguments.

Semantic requirements
A relation is a strict weak ordering if
 * it is irreflexive: for all, is false;
 * it is transitive: for all, and , if  and  are both true then  is true;
 * let be, then  is transitive:  implies.

Under these conditions, it can be shown that is an equivalence relation, and  induces a strict total ordering on the equivalence classes determined by.