
theorem
  for F being non empty Graph-yielding Function
  holds F is vertex-disjoint edge-disjoint iff
    for x1,x2 being Element of dom F st x1 <> x2
    holds the_Vertices_of(F.x1) misses the_Vertices_of(F.x2) &
      the_Edges_of(F.x1) misses the_Edges_of(F.x2);
