let G1, G2, G3 be _Graph; :: thesis: for F1 being PGraphMapping of G1,G2
for F2 being PGraphMapping of G2,G3 st F2 * F1 is onto holds
F2 is onto
let F1 be PGraphMapping of G1,G2; :: thesis: for F2 being PGraphMapping of G2,G3 st F2 * F1 is onto holds
F2 is onto
let F2 be PGraphMapping of G2,G3; :: thesis: ( F2 * F1 is onto implies F2 is onto )
assume F2 * F1 is onto ; :: thesis: F2 is onto
then ( the_Vertices_of G3 c= rng (F2 _V) & the_Edges_of G3 c= rng (F2 _E) ) by RELAT_1:26;
hence F2 is onto by XBOOLE_0:def 10; :: thesis: verum