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 Th14:
  (ex f st f is proper) implies G is loopless
proof
  given f such that
    A1: f is proper;
  now
    given v,e being object such that
      A2: e Joins v,v,G;
    f.v = f.v;
    hence contradiction by A1, A2, Th10;
  end;
  hence thesis by GLIB_000:18;
end;
