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 Th133:
  for F being PGraphMapping of G1, G2 st F is weak_SG-embedding
  holds G1.eChromaticNum() c= G2.eChromaticNum()
proof
  let F be PGraphMapping of G1, G2;
  assume F is weak_SG-embedding;
  then G1 is G2.eChromaticNum()-ecolorable by Th110, Lm14;
  hence thesis by Lm15;
end;
