Let $($A$,<=)$ be a partially ordered set. Consider the relation $<=$lex on the Cartesian product

A $\backslash$times A :

$($a$,$ b$)<=$lex $($c$,$ d$)($a $<=$ c$)(($a $=$ c$)($b $<=$ d$)).$

This relation is called the lexicographic order in analogy with the order used in dictionaries.