Define the behead operation on a string $$ as follows: If $=,$ then $()=.$ Otherwise, $=,$ for $$ in $$ and $$ in $$ ; then $()=.($That is$,$ the behead operation removes the first character if there is one, and then returns the remaining string.$)$ Now define behead$($L$)$ as the set of strings resulting from applying behead to every string in L$.$ Prove that, if L is regular, then so is behead$($L$).$