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;

theorem Th125:
  for G2 being reverseEdgeDirections of G1, E
  holds G1.eChromaticNum() = G2.eChromaticNum()
proof
  let G2 be reverseEdgeDirections of G1, E;
  A1: G1 is G1.eChromaticNum()-ecolorable by Lm14;
  for c st G2 is c-ecolorable holds G1.eChromaticNum() c= c by Th104, Lm15;
  hence thesis by A1, Th122;
end;
