Complement of Limit Superior is Limit Inferior of Complements

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

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

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