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

theorem Th71:
  (A |^ (m, n)) |^ (k, l) c= A*
proof
  let x be object;
  assume x in (A |^ (m, n)) |^ (k, l);
  then consider kl such that
  k <= kl and
  kl <= l and
A1: x in (A |^ (m, n)) |^ kl by Th19;
  (A |^ (m, n)) |^ kl c= A* by Th32,FLANG_1:59;
  hence thesis by A1;
end;
