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.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;
