
theorem
  for S being Graph-membered set holds S is vertex-disjoint edge-disjoint iff
    for G1, G2 being _Graph st G1 in S & G2 in S & G1 <> G2
    holds the_Vertices_of G1 misses the_Vertices_of G2 &
      the_Edges_of G1 misses the_Edges_of G2;
