
theorem
  for G being _Graph holds G is addLoops of G, {}
proof
  let G be _Graph;
  A1: G is Supergraph of G & {}c= the_Vertices_of G by GLIB_006:61, XBOOLE_1:2;
  now
    thus the_Vertices_of G = the_Vertices_of G;
    reconsider E = {} as set;
    reconsider f = the empty Function as one-to-one Function;
    take E, f;
    thus E misses the_Edges_of G by XBOOLE_1:65;
    thus the_Edges_of G = the_Edges_of G \/ E;
    thus dom f = E & rng f = {};
    thus the_Source_of G = the_Source_of G +* f by FUNCT_4:21;
    thus the_Target_of G = the_Target_of G +* f by FUNCT_4:21;
  end;
  hence thesis by A1, Def5;
end;
