let G1, G2 be _Graph; :: thesis: for F being PGraphMapping of G1,G2 st F is weak_SG-embedding & G2 is finite-tcolorable holds
G1 is finite-tcolorable
let F be PGraphMapping of G1,G2; :: thesis: ( F is weak_SG-embedding & G2 is finite-tcolorable implies G1 is finite-tcolorable )
assume A1: ( F is weak_SG-embedding & G2 is finite-tcolorable ) ; :: thesis: G1 is finite-tcolorable
then consider n being Nat such that
A2: G2 is n -tcolorable ;
G1 is n -tcolorable by A1, A2, Th176;
hence G1 is finite-tcolorable ; :: thesis: verum