
theorem Th104:
  for G1, G2, G3 being _Graph, F1 being PGraphMapping of G1, G2,
    F2 being PGraphMapping of G2, G3
  st F1 is total & F2 is total holds F2 * F1 is total
proof
  let G1, G2, G3 be _Graph;
  let F1 be PGraphMapping of G1, G2;
  let F2 be PGraphMapping of G2, G3;
  assume A1: F1 is total & F2 is total;
  then rng F1_V c= dom F2_V & rng F1_E c= dom F2_E;
  hence thesis by A1, Th103;
end;
