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 Th134:
  for F being PGraphMapping of G1, G2 st F is isomorphism
  holds G1.eChromaticNum() = G2.eChromaticNum()
proof
  let F be PGraphMapping of G1, G2;
  assume A1: F is isomorphism;
  then reconsider F0 = F as one-to-one PGraphMapping of G1, G2;
  F0" is isomorphism by A1, GLIB_010:75;
  then A2: G2.eChromaticNum() c= G1.eChromaticNum() by Th133;
  G1.eChromaticNum() c= G2.eChromaticNum() by A1, Th133;
  hence thesis by A2, XBOOLE_0:def 10;
end;
