
theorem
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is onto holds F | dom F is onto
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is onto;
  A2: rng(F|dom F)_V = rng F_V by Th86
    .= the_Vertices_of G2 by A1, GLIB_010:def 12;
  rng(F|dom F)_E = rng F_E by Th86
    .= the_Edges_of G2 by A1, GLIB_010:def 12;
  hence thesis by A2, GLIB_010:def 12;
end;
