reserve FT for non empty RelStr,
  A,B,C for Subset of FT;

theorem
  for A, B being Subset of FT st A,B are_separated holds A^deltao misses B
proof
  let A,B be Subset of FT;
  assume A,B are_separated;
  then
A1: A^b misses B by FINTOPO4:def 1;
  thus (A^deltao)/\ B = A` /\ ((A^delta) /\ B) by XBOOLE_1:16
    .= A` /\ ((A^b) /\ ((A`)^b)/\ B) by FIN_TOPO:18
    .= A` /\ (((A`)^b) /\ ((A^b)/\ B)) by XBOOLE_1:16
    .= A` /\ (((A`)^b) /\ ({})) by A1
    .= {};
end;
