Showing that u#v with u a substring of v is not context-free
Okay I got confused when developing my ideas, and a simple example using Pumping Lemma would be: $a^nb^n\#a^nb^n$. Consider this: clearly $v$ and $x$ cannot contain $\#$, otherwise when pumping more or less $\#$ appear and the new string is not in the language. Now suppose $vwx$ are in the left $a^nb^n$, then $v^2$ and $x^2$ will make it longer than the R.H.S.; then if $vwx$ are in the right $a^nb^n$, then $v^0x^0$ will make the R.H.S. shorter than the left. This gives us the only possibility that $v$ in the first $b^n$ and $x$ in the second $a^n$, and clearly no matter how you pump it the new string cannot be in the same language, and this solves the problem.