
theorem Th11:
  for X being set, f being Function holds X-indexing (X-indexing f
  ) = X-indexing f
proof
  let X be set, f be Function;
  dom (X-indexing f) = X by PARTFUN1:def 2;
  then for x being object st x in X holds (X-indexing (X-indexing f)).x = (X
  -indexing f).x by Th9;
  hence thesis by PBOOLE:3;
end;
