A laminarity property of the polyhedron described by a weakly posi-modular set function

Recently, Nagamochi and Ibaraki have introduced a concept of posi-modular set function and considered the structure of the polyhedron described by an intersecting submodular and posi-modular function. They showed that the facets of the polyhedron form a laminar family. We show that such a laminarity property also holds for a much more general class of set functions, called weakly posi-modular set functions, without submodularity.