Are supersets of non-regular languages also non-regular?
Since this holds for all $x\in L_1$, we can construct a finite automata which language is $L_1$.


And how would you do this? You have an infinite amount of paths in hands which you have to mold into a finite set of states and edges.

In fact, the statement does not hold.


   Remember that $\Sigma^*$ is regular but there are non-regular languages.