
theorem Th87:
  for G1, G2 being _Graph, F being PGraphMapping of G1, G2
  st F is total holds (rng F) |` F is total
proof
  let G1, G2 be _Graph, F be PGraphMapping of G1, G2;
  assume A1: F is total;
  A2: dom((rng F)|`F)_V = dom F_V by Th86
    .= the_Vertices_of G1 by A1, GLIB_010:def 11;
  dom((rng F)|`F)_E = dom F_E by Th86
    .= the_Edges_of G1 by A1, GLIB_010:def 11;
  hence thesis by A2, GLIB_010:def 11;
end;
