
theorem Th33:
  for G2 being _Graph, G1 being Supergraph of G2
  st the_Edges_of G1 = the_Edges_of G2
  holds G1 is addVertices of G2, the_Vertices_of G1 \ the_Vertices_of G2
proof
  let G2 be _Graph, G1 be Supergraph of G2;
  assume A1: the_Edges_of G1 = the_Edges_of G2;
  the_Vertices_of G2 c= the_Vertices_of G1 by GLIB_006:def 9;
  then A2: the_Vertices_of G1 = the_Vertices_of G2 \/
    (the_Vertices_of G1 \ the_Vertices_of G2) by XBOOLE_1:45;
  A3: the_Source_of G2 = (the_Source_of G1)|the_Edges_of G2 by GLIB_006:69
    .= the_Source_of G1 by A1;
  the_Target_of G2 = (the_Target_of G1)|the_Edges_of G2 by GLIB_006:69
    .= the_Target_of G1 by A1;
  hence thesis by A1, A2, A3, GLIB_006:def 10;
end;
