Prove rigorously $($by induction on an appropriate quantity$)$ that the grammars with a single non$-$terminal

$E$ and production rules $E0E1E|1E0E|$ generates the language $\{\begin{array}{ccc}\text{x}\text{i}\text{n}& \{0,& 1{\}}^{**}|\text{\#}0\end{array}\text{'}$s in $x=$

#$1\text{'}$s in $x.$