reserve FT for non empty RelStr;
reserve A for Subset of FT;

theorem
  A` is open implies A is closed
proof
  assume A` is open;
  then
A1: A` = (A`)^i;
  (A`)^i = (((A`)`)^b)` by FIN_TOPO:17
    .= (A^b)`;
  then A = (A^b)`` by A1
    .= A^b;
  hence thesis;
end;
