
theorem Th74:
  for G being non-multi _Graph, E being RepEdgeSelection of G
  holds E = the_Edges_of G
proof
  let G be non-multi _Graph, E be RepEdgeSelection of G;
  for e being object holds e in the_Edges_of G implies e in E
  proof
    let e be object;
    set v = (the_Source_of G).e, w = (the_Target_of G).e;
    assume e in the_Edges_of G;
    then A1: e Joins v,w,G by GLIB_000:def 13;
    then consider e2 being object such that
      A2: e2 Joins v,w,G & e2 in E and
      for e9 being object st e9 Joins v,w,G & e9 in E holds e9 = e2
      by Def5;
    thus thesis by A1, A2, GLIB_000:def 20;
  end;
  then the_Edges_of G c= E by TARSKI:def 3;
  hence E = the_Edges_of G by XBOOLE_0:def 10;
end;
