reserve FT for non empty RelStr;
reserve A for Subset of FT;
reserve T for non empty TopStruct;
reserve FMT for non empty FMT_Space_Str;
reserve x, y for Element of FMT;
reserve A, B, W, V for Subset of FMT;

theorem
  A` is Fo_closed implies A is Fo_open
proof
  assume A` is Fo_closed;
  then
A1: (A`) = (A`)^Fob;
  (A`)^Fob = (((A`)`)^Foi)` by Th38
    .= (A^Foi)`;
  then A = (A^Foi)`` by A1
    .= A^Foi;
  hence thesis;
end;
