
theorem
  for G1, G2, G3 being _Graph, F1 being PGraphMapping of G1, G2,
    F2 being PGraphMapping of G2, G3
  st F2 * F1 is total holds F1 is total
proof
  let G1, G2, G3 be _Graph, F1 be PGraphMapping of G1, G2,
    F2 be PGraphMapping of G2, G3;
  assume F2 * F1 is total;
  then the_Vertices_of G1 c= dom F1_V & the_Edges_of G1 c= dom F1_E
    by RELAT_1:25;
  hence thesis by XBOOLE_0:def 10;
end;
