let G be _Graph; :: thesis: ( ex E being RepDEdgeSelection of G st E = the_Edges_of G implies G is non-Dmulti )
given E being RepDEdgeSelection of G such that A1: E = the_Edges_of G ; :: thesis: G is non-Dmulti
now :: thesis: for e1, e2, v1, v2 being object st e1 DJoins v1,v2,G & e2 DJoins v1,v2,G holds
e1 = e2
let e1, e2, v1, v2 be object ; :: thesis: ( e1 DJoins v1,v2,G & e2 DJoins v1,v2,G implies e1 = e2 )
assume A2: ( e1 DJoins v1,v2,G & e2 DJoins v1,v2,G ) ; :: thesis: e1 = e2
then consider e3 being object such that
( e3 DJoins v1,v2,G & e3 in E ) and
A3: for e being object st e DJoins v1,v2,G & e in E holds
e = e3 by Def6;
( e1 = e3 & e2 = e3 ) by A1, A2, A3, GLIB_000:def 14;
hence e1 = e2 ; :: thesis: verum
end;
hence G is non-Dmulti by GLIB_000:def 21; :: thesis: verum