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
  G1 == G2 implies G1.eChromaticNum() = G2.eChromaticNum()
proof
  assume A1: G1 == G2;
  then A2: G2 is G1.eChromaticNum()-ecolorable by Lm14, Th103;
  for c st G2 is c-ecolorable holds G1.eChromaticNum() c= c by A1, Th103, Lm15;
  hence thesis by A2, Th122;
end;
