reserve E, x, y, X for set;
reserve A, B, C, D for Subset of E^omega;
reserve a, a1, a2, b, c, c1, c2, d, ab, bc for Element of E^omega;
reserve e for Element of E;
reserve i, j, k, l, n, n1, n2, m for Nat;

theorem Th28:
  {<%>E} |^ n = {<%>E}
proof
  defpred P[Nat] means {<%>E} |^ $1 = {<%>E};
A1: now
    let n;
    assume
A2: P[n];
    {<%>E} |^ (n + 1) = ({<%>E} |^ n) ^^ {<%>E} by Th23
      .= {<%>E} by A2,Th13;
    hence P[n + 1];
  end;
A3: P[0] by Th24;
  for n holds P[n] from NAT_1:sch 2(A3, A1);
  hence thesis;
end;
