A simple proof of the generalized farkas lemma for oriented matroids

In this note we consider the feasibility problem of oriented matroids. An alternative theorem, which is a generalization of Farkas’ famous result, is stated and proved. Our proof is constructive and new. In the proof of the generalized Farkas lemma, the finiteness of a criss-cross type algorithm is used. The algorithm’s pivot rule, for criss-cross type methods, first was used by S. Zhang for linear programming problems.