reserve X for set;

theorem Th21:
  for g being SimpleGraph of X holds
  (the carrier of g) is finite Subset of X &
  (the SEdges of g) is finite Subset of 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 thesis;
end;
