A vector exchange property of submodular systems

Abstract Generalizing the multiple basis exchange property for matroids, the following theorem is proved: If x and y are vectors of a submodular system in R E and x 1 ,x 2 ϵ R E such that x = x1 + x2, then there are y 1 ,y 2 ϵ R E such that y = y1 + y2 and both x1 + y1 and x2 + y2 belong to the submodular system. An integral analogue holds for the integral submodular systems and a non-negative analogue for polymatroids.