theorem Th7:
  Collapse (E,A) c= E
proof
  let x be object;
  assume x in Collapse (E,A);
  then
  x in { d : for d1 st d1 in d ex B st B in A & d1 in Collapse (E,B) } by Th1;
  then
  ex d st x = d & for d1 st d1 in d ex B st B in A & d1 in Collapse (E,B);
  hence thesis;
end;
