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
  n > 0 implies A |^.. n c= A+
proof
  assume
A1: n > 0;
  let x be object;
  assume x in A |^.. n;
  then ex k st k >= n & x in A |^ k by Th2;
  hence thesis by A1,Th48;
end;
