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The lexicographic order on N x N is a total order:
x <= y : <=> x0 < y0 \/ (x0 = y0 /\ x1 <= y1)
<0, 0> < <0, 1> < <0, 2> < ...< <1, 0> < <1, 1> < <1, 2> < ...
Comparison first by first component, then by second component.