
theorem
  for G1, G2 being _Graph, F being semi-continuous PGraphMapping of G1, G2
  st F is total onto holds F_V is continuous PVertexMapping of G1, G2
proof
  let G1, G2 be _Graph, F be semi-continuous PGraphMapping of G1, G2;
  assume F is total onto;
  then dom F_E = the_Edges_of G1 & rng F_E = the_Edges_of G2
    by GLIB_010:def 11, GLIB_010:def 12;
  hence thesis by Th23;
end;
