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 Th29:
  G is loopless implies G is G.order()-vcolorable
proof
  assume A1: G is loopless;
  reconsider f = id the_Vertices_of G as VColoring of G;
  card rng f = G.order();
  hence G is G.order()-vcolorable by A1;
end;
