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
  A+ = {x} implies x = <%>E
proof
  assume that
A1: A+ = {x} and
A2: x <> <%>E;
  A |^.. 1 = {x} by A1,Th50;
  hence thesis by A2,Th38;
end;
