reserve X,Y,Z for set,
  x,y,z for object,
  E for non empty set,
  A,B,C for Ordinal ,
  L,L1 for Sequence,
  f,f1,f2,h for Function,
  d,d1,d2,d9 for Element of E;

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;
