theorem Th8:
  L1 c= L2 implies L1 WHEREgt(O,n) c= L2 WHERE O
  proof assume
A1: L1 c= L2;
    let z be object; assume z in L1 WHEREgt(O,n); then
    consider x such that
A2: z = x & n in card(x.O) & x in L1;
    x.O <> {} by A2;
    hence thesis by A1,A2,Th3;
  end;
