
theorem Th40:
  for G2, G3 being _Graph, G1 being Supergraph of G3
  st G1 == G2 holds G2 is Supergraph of G3
proof
  let G2, G3 be _Graph, G1 be Supergraph of G3;
  assume G1 == G2;
  then A1: the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 = the_Edges_of G2 &
    the_Source_of G1 = the_Source_of G2 &
    the_Target_of G1 = the_Target_of G2 by GLIB_000:def 34;
  the_Vertices_of G3 c= the_Vertices_of G1 &
    the_Edges_of G3 c= the_Edges_of G1 &
    for e being set st e in the_Edges_of G3 holds
      (the_Source_of G3).e = (the_Source_of G1).e &
      (the_Target_of G3).e = (the_Target_of G1).e by GLIB_006:def 9;
  hence thesis by A1, GLIB_006:def 9;
end;
