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
  (A*) |^ (m, n) c= A*
proof
  let x be object;
  assume x in (A*) |^ (m, n);
  then consider mn such that
  m <= mn and
  mn <= n and
A1: x in (A*) |^ mn by Th19;
  (A*) |^ mn c= A* by FLANG_1:65;
  hence thesis by A1;
end;
