theorem
  for G being _trivial loopless _Graph holds the_Edges_of G = {}
proof
  let G be _trivial loopless _Graph;
  consider v being Vertex of G such that
A1: the_Vertices_of G = {v} by Th22;
  now
    assume the_Edges_of G <> {};
    then consider e being object such that
A2: e in the_Edges_of G by XBOOLE_0:def 1;
    (the_Target_of G).e in {v} by A1,A2,FUNCT_2:5;
    then
A3: (the_Target_of G).e = v by TARSKI:def 1;
    (the_Source_of G).e in {v} by A1,A2,FUNCT_2:5;
    then (the_Source_of G).e = v by TARSKI:def 1;
    hence contradiction by A2,A3,Def18;
  end;
  hence thesis;
end;
