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