
theorem Th5:
  for G2 being loopfull _Graph, G1 being Supergraph of G2
  st the_Vertices_of G1 = the_Vertices_of G2 holds G1 is loopfull
proof
  let G2 be loopfull _Graph, G1 be Supergraph of G2;
  assume A1: the_Vertices_of G1 = the_Vertices_of G2;
  let v be Vertex of G1;
  consider e being object such that
    A2: e Joins v,v,G2 by A1, Def1;
  take e;
  thus e Joins v,v,G1 by A2, GLIB_006:70;
end;
