theorem
  G.vChromaticNum() c= G.tChromaticNum()
proof
  per cases;
  suppose G is non loopless;
    hence thesis;
  end;
  suppose G is loopless;
    then G is G.tChromaticNum()-tcolorable by Th186;
    hence thesis by Th57, Th162;
  end;
end;
