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
  x in A & x <> <%>E implies A* <> {<%>E}
proof
  assume that
A1: x in A and
A2: x <> <%>E;
  A <> {<%>E} by A1,A2,TARSKI:def 1;
  hence thesis by A1,FLANG_1:47;
end;
