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

theorem
  G.tChromaticNum() c= G.vChromaticNum() +` G.eChromaticNum()
proof
  per cases;
  suppose G is non loopless;
    then G.tChromaticNum() = 0;
    hence thesis by XBOOLE_1:2;
  end;
  suppose G is loopless;
    then G is G.vChromaticNum()-vcolorable G.eChromaticNum()-ecolorable
      by Th54, Th122;
    hence thesis by Th163, Th189;
  end;
end;
