let G2 be addVertices of G,V; :: thesis: G2 is non-Dmulti
for e1, e2, v1, v2 being object st e1 DJoins v1,v2,G2 & e2 DJoins v1,v2,G2 holds
e1 = e2

proof

let e1, e2, v1, v2 be object ; :: thesis: ( e1 DJoins v1,v2,G2 & e2 DJoins v1,v2,G2 implies e1 = e2 )
assume ( e1 DJoins v1,v2,G2 & e2 DJoins v1,v2,G2 ) ; :: thesis: e1 = e2
then ( e1 DJoins v1,v2,G & e2 DJoins v1,v2,G ) by Th89;
hence e1 = e2 by GLIB_000:def 21; :: thesis: verum

end;

hence G2 is non-Dmulti by GLIB_000:def 21; :: thesis: verum