reserve X for set;

theorem Th18:
  for g being SimpleGraph of X holds the carrier of g c= X &
  the SEdges of g c= TWOELEMENTSETS (the carrier of g)
proof
  let g be SimpleGraph of X;
  g is Element of SIMPLEGRAPHS(X) by Def4;
  then
  ex v being finite Subset of X, e being finite Subset of TWOELEMENTSETS(v)
  st g = SimpleGraphStruct (#v,e#) by Th17;
  hence (the carrier of g) c= X;
  thus thesis;
end;
