  The separation theorem of Kirchberger can be proven using a combination of
Farkas' Lemma and Caratheodory's Theorem. Since those theorems are at the heart
of oriented matroids, we are interested in a generalization of Kirchberger's
Theorem to them. This has already been done for rank 3 oriented matroids. Here
we prove it for complexes of oriented matroids, which are a generalization of
oriented matroids.
