let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2 st F is weak_SG-embedding & G2 is finite-vcolorable holds
G1 is finite-vcolorable
let F be PGraphMapping of G1,G2; :: thesis: ( F is weak_SG-embedding & G2 is finite-vcolorable implies G1 is finite-vcolorable )
assume A1: ( F is weak_SG-embedding & G2 is finite-vcolorable ) ; :: thesis: G1 is finite-vcolorable
then consider n being Nat such that
A2: G2 is n -vcolorable ;
G1 is n -vcolorable by A1, A2, Th42;
hence G1 is finite-vcolorable ; :: thesis: verum