consider v being Vertex of G such that
the_Vertices_of G = {v} and
A4: the_Source_of G = (the_Edges_of G) --> v and
A5: the_Target_of G = (the_Edges_of G) --> v by GLIB_006:21;
now :: thesis: for e1, e2 being object st e1 in the_Edges_of G & e2 in the_Edges_of G holds
e1 = e2
let e1, e2 be object ; :: thesis: ( e1 in the_Edges_of G & e2 in the_Edges_of G implies e1 = e2 )
assume A6: ( e1 in the_Edges_of G & e2 in the_Edges_of G ) ; :: thesis: e1 = e2
then ( (the_Source_of G) . e1 = v & (the_Target_of G) . e1 = v & (the_Source_of G) . e2 = v & (the_Target_of G) . e2 = v ) by A4, A5, FUNCOP_1:7;
then ( e1 DJoins v,v,G & e2 DJoins v,v,G ) by A6, GLIB_000:def 14;
hence e1 = e2 by GLIB_000:def 21; :: thesis: verum
end;
hence the_Edges_of G is trivial by ZFMISC_1:def 10; :: thesis: verum