Kleeneliness is next to Gödeliness
Lemma
Given L a CF language then ∃ n∈N,
n constant so that ∀ z∈L, |z|≥n so that we can decompose z=uvwxy so that
1 |vwx|≤n
2 |vx|>0
3 ∀ i≥0 we have that uvⁱwxⁱy∈L
Usage
One uses the lemma to prove that a language is not CF, to do so one must show, that fixed an arbitrary n
arbitrary, ∃ zⁱwxⁱy∉L \ |z\≥n but so that for every possible decomposition such as uvwxy, with 1. and 2. constraints uvⁱwxⁱy∉L for some i≥0