
theorem
  for G1 being non-Dmulti _Graph, G2 being DLGraphComplement of G1
  holds G1 is DLGraphComplement of G2
proof
  let G1 be non-Dmulti _Graph, G2 be DLGraphComplement of G1;
  A1: the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 misses the_Edges_of G2 by Def6;
  now
    let v,w be Vertex of G2;
    v is Vertex of G1 & w is Vertex of G1 by Def6;
    hence (ex e2 being object st e2 DJoins v,w,G2) iff
      (not ex e1 being object st e1 DJoins v,w,G1) by Def6;
  end;
  hence thesis by A1, Def6;
end;
