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

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