
theorem Th75:
  for G being _Graph st ex E being RepEdgeSelection of G st E = the_Edges_of G
  holds G is non-multi
proof
  let G be _Graph;
  given E being RepEdgeSelection of G such that
    A1: E = the_Edges_of G;
  now
    let e1,e2,v1,v2 be object;
    assume A2: e1 Joins v1,v2,G & e2 Joins v1,v2,G;
    then consider e3 being object such that
      e3 Joins v1,v2,G & e3 in E and
      A3: for e being object st e Joins v1,v2,G & e in E holds e = e3
      by Def5;
    e1 in the_Edges_of G & e2 in the_Edges_of G &
      E = the_Edges_of G by A1, A2, GLIB_000:def 13;
    then e1 = e3 & e2 = e3 by A2, A3;
    hence e1 = e2;
  end;
  hence thesis by GLIB_000:def 20;
end;
