
theorem Th64:
  for G1 being _Graph, G2 being LGraphComplement of G1, e1,e2,v,w being object
  holds e1 Joins v,w,G1 implies not e2 Joins v,w,G2
proof
  let G1 be _Graph, G2 be LGraphComplement of G1, e1,e2,v,w be object;
  assume A1: e1 Joins v,w,G1;
  then v in the_Vertices_of G1 & w in the_Vertices_of G1 by GLIB_000:13;
  hence thesis by A1, Def7;
end;
