Complement of Limit Inferior is Limit Superior of Complements

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

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

where $\liminf$ and $\limsup$ denote the limit inferior and limit superior, respectively.