
theorem Th9:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is total onto semi-continuous
  holds G2 is loopfull implies G1 is loopfull
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is total onto semi-continuous;
  G2.loops() c= the_Edges_of G2;
  then dom F_V=the_Vertices_of G1 & G2.loops() c= rng F_E
    by A1, GLIB_010:def 11, GLIB_010:def 12;
  hence thesis by A1, Th8;
end;
