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

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

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