Complement of Limit Superior is Limit Inferior of Complements

Theorem
Let $\left\{{E_n : n \in \N}\right\}$ be a sequence of sets.

Then:
 * $\displaystyle \complement \left({\limsup_{n \to \infty} \ E_n}\right) = \liminf_{n \to \infty} \ \complement \left({E_n}\right)$