Complement of Limit Inferior is Limit Superior of Complements

Theorem
Let $\sequence {E_n}_{n \mathop \in \N}$ be a sequence of sets.

Then:
 * $\ds \map \complement {\liminf_{n \mathop \to \infty} \ E_n} = \limsup_{n \mathop \to \infty} \ \map \complement {E_n}$

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