When using the pumping lemma for a context free language, if I write any $w \in L$ as $uvxyz$, is my goal to show that a string will not pump for ANY arrangement of $uvxyz$ that I choose, or is my goal to show that THERE EXISTS some arrangement of $uvxyz$ over $w$ that will pump?
Using pumping lemma to prove a language is not context free
formal languages;context free;pumping lemma