Let $\Sigma$ be the set {a,b} of letters. For a language $L\subset\Sigma^{*}$ over $\Sigma$, we define $\Gamma(L)$ as follows; $\Gamma(L)=\{v\in\Sigma^{*}|\exists w\in \Sigma^{*}.(|v|=|w|\wedge vw\in L)\}$. Here, $|x|$ denotes the length of the string $x$.
Then, for every context-free language $L\subset \Sigma^{*}$, $\Gamma(L)$ is also a context-free language?
