Check whether the following language is context-free. If yes, a suitable grammar should be given; if no, the pumping lemma should be used as a tool.
$$L=\{a^ib^jc^k \mid i, j, k \in N \text{ and } i <k<j\} $$
Can I choose (since N includes 0)
$$ L=\{b^jc^k \mid j,k >= 1 \text{ and } j > k\} $$
and provide a grammar for that language, and thus say L is indeed context-free? If L is not context-free, how could I prove it using the Pumping Lemma?
