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# Pumping lemma

If $$A$$ is a regular language, then there is a number $$p$$ (the pumping length) where is $$s$$ is any string in $$A$$ that is at least length $$p$$, then $$s$$ may be divided into three pieces, $$s=xyz$$, satisfying the following conditions: 1. for each $$i \geq 0$$, $$xy^iz \in A$$ 2. $$|y| \gt 0$$ 3. $$|xy| \leq p$$