reserve X for set;

theorem
  for g being SimpleGraph of X holds
  (g=SimpleGraphStruct (#{},{}TWOELEMENTSETS{}#) or
  ex v being set, e being Subset of TWOELEMENTSETS(v) st
  v is non empty & g=SimpleGraphStruct (#v,e#) )
proof
  let g be SimpleGraph of X;
  assume
A1: not g=SimpleGraphStruct (#{},{}TWOELEMENTSETS{}#);
  take (the carrier of g), (the SEdges of g);
  thus (the carrier of g) is non empty by A1;
  thus thesis;
end;
