theorem
  for G2 being reverseEdgeDirections of G1, E
  holds G1.tChromaticNum() = G2.tChromaticNum()
proof
  let G2 be reverseEdgeDirections of G1, E;
  per cases;
  suppose G1 is non loopless;
    then G1.tChromaticNum() = 0 & G2.tChromaticNum() = 0;
    hence thesis;
  end;
  suppose G1 is loopless;
    then G2 is G1.tChromaticNum()-tcolorable &
      for c st G2 is c-tcolorable holds G1.tChromaticNum() c= c
      by Th168, Th186, Th189;
    hence thesis by Th190;
  end;
end;
