
theorem Th18:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is total holds F_V is PVertexMapping of G1, G2
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume F is total;
  then dom F_E = the_Edges_of G1 by GLIB_010:def 11;
  hence thesis by Th17;
end;
