set IT = { W where W is directed Walk of G : verum } ;
A1: G .walkOf (choose (the_Vertices_of G)) in { W where W is directed Walk of G : verum } ;

now

let e be set ; :: thesis: ( e in { W where W is directed Walk of G : verum } implies e in G .allWalks() )
assume e in { W where W is directed Walk of G : verum } ; :: thesis: e in G .allWalks()
then consider W being directed Walk of G such that
A2: e = W ;
thus e in G .allWalks() by A2; :: thesis: verum

end;

hence { W where W is DWalk of G : verum } is non empty Subset of (G .allWalks() ) by A1, TARSKI:def 3; :: thesis: verum