
theorem Th7:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is total onto holds G1 is loopfull implies G2 is loopfull
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is total onto;
  G1.loops() c= the_Edges_of G1;
  then G1.loops() c= dom F_E & rng F_V = the_Vertices_of G2
    by A1, GLIB_010:def 11, GLIB_010:def 12;
  hence thesis by Th6;
end;
