So I'm trying to understand the pumping lemma for CFL ( context free languages ).I've already used it to show that a language is not contextfree and I have considered the proof of this lemma (see the PDF below ) Now I've read that there is a variant of the pumping lemma for context free languages. You replace the condition " $ vy \neq \varepsilon $ " with " $v$ and $y$ are not $\varepsilon$". Like I've said. Here is the proof of the"normal" pumping lemma for CFL.
What do I have to change for the variant of the pumping lemma?