reserve E,V for set, G,G1,G2 for _Graph, c,c1,c2 for Cardinal, n for Nat;
reserve f for VColoring of G;

theorem Th9:
  for F being PGraphMapping of G1,G st F is total
  holds f*F_V is VColoring of G1
proof
  let F be PGraphMapping of G1, G;
  assume F is total;
  then dom F_V = the_Vertices_of G1 by GLIB_010:def 11;
  hence thesis by Th8;
end;
