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
  <%>E in A |^ n iff n = 0 or <%>E in A
proof
  thus <%>E in A |^ n implies n = 0 or <%>E in A by FLANG_1:31;
  assume
A1: n = 0 or <%>E in A;
  per cases by A1;
  suppose
    n = 0;
    then A |^ n = {<%>E} by FLANG_1:29;
    hence thesis by ZFMISC_1:31;
  end;
  suppose
    <%>E in A;
    hence thesis by FLANG_1:30;
  end;
end;
