let G2 be _Graph; :: thesis: for v, e, w being object
for G1 being addEdge of G2,v,e,w holds
( G1 is finite-ecolorable iff G2 is finite-ecolorable )
let v, e, w be object ; :: thesis: for G1 being addEdge of G2,v,e,w holds
( G1 is finite-ecolorable iff G2 is finite-ecolorable )
let G1 be addEdge of G2,v,e,w; :: thesis: ( G1 is finite-ecolorable iff G2 is finite-ecolorable )

hereby :: thesis: ( G2 is finite-ecolorable implies G1 is finite-ecolorable )

assume A1: G1 is finite-ecolorable ; :: thesis: G2 is finite-ecolorable
G2 is Subgraph of G1 by GLIB_006:57;
hence G2 is finite-ecolorable by A1; :: thesis: verum

end;

assume G2 is finite-ecolorable ; :: thesis: G1 is finite-ecolorable
then consider n being Nat such that
A2: G2 is n -ecolorable ;
G1 is n +` 1 -ecolorable by A2, Th107;
hence G1 is finite-ecolorable ; :: thesis: verum