
theorem Th20:
  for G1, G2 being _Graph, F being directed PGraphMapping of G1, G2
  st dom F_E = the_Edges_of G1 holds F_V is directed PVertexMapping of G1, G2
proof
  let G1, G2 be _Graph, F be directed PGraphMapping of G1, G2;
  assume A1: dom F_E = the_Edges_of G1;
  for v,w being object st v in dom F_V & w in dom F_V holds
    (ex e being object st e DJoins v,w,G1) implies
    (ex e being object st e in dom F_E & e DJoins v,w,G1)
    by A1, GLIB_000:def 14;
  hence thesis by Th19;
end;
