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 Th17:
  <%>E in A implies (A |^ n)* = (A*) |^ n
proof
  assume
A1: <%>E in A;
  per cases;
  suppose
A2: n = 0;
    hence (A |^ n)* = {<%>E}* by FLANG_1:24
      .= {<%>E} by FLANG_1:47
      .= (A*) |^ n by A2,FLANG_1:24;
  end;
  suppose
A3: n > 0;
    then (A*) |^ n = A* by FLANG_1:66;
    hence thesis by A1,A3,Th16;
  end;
end;
