reserve E, x, y, X for set;
reserve A, B, C for Subset of E^omega;
reserve a, a1, a2, b for Element of E^omega;
reserve i, k, l, m, n for Nat;

theorem Th9:
  A |^.. n c= A*
proof
    let x be object;
    assume x in A |^.. n;
    then ex k st n <= k & x in A |^ k by Th2;
    hence x in A* by FLANG_1:41;
end;
