Confused about 3rd rule of CFG pumping lemma
Remember that the PL is stated for any partition $s=uvxyz$, so it is not enough to show that for one specific partition pumping $v$ and $y$ will exclude the resulting string from $L$. While it is true that $xyz$ can consist only of 0′s, it could also be the case that $xyz$ is of the form $0^i1^j$ for some $i, j &lt; p$, for instance. You must show that pumping excludes the resulting string from $L$ in this (and all possible other) cases as well.