In computational theory, we have a lemma called Pumping Lemma and it says: $$If $$ is a regular language, then

there is a positive integer $$ where if $$ is any string in $$ of length at least $,$ then $$ can be divided into three

pieces, $=,$ satisfying the following three conditions: $1)$ for each $>=0,$

$$

$$ in $2)||>0$ and $3)||<=$

$.$

This is a long lemma, and we can use notations and predicate functions to analyze it$.$ Let$$s use $$ to represent

the set of all regular languages, use $()$ to represent the length of string $,$ and let $(,)$ can be

divided into three pieces, $=,$ satisfying the following conditions: $1)$ for each $>=0,$

$$

$$ in $2)||>0$

and $3)||<=.$ Then the above lemma becomes:

$$ in $>0.$ in $.()>=->(,)$