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

theorem Th6:
  for A being Subset of FT st FT is symmetric & for A2, B2 being
Subset of FT st A = A2 \/ B2 & A2 misses B2 & A2,B2 are_separated holds A2 = {}
  FT or B2 = {}FT holds A is connected
proof
  let A be Subset of FT;
  assume
A1: FT is symmetric;
  assume
A2: for A2, B2 being Subset of FT st A = A2 \/ B2 & A2 misses B2 & A2,B2
  are_separated holds A2 = {}FT or B2 = {}FT;
  for B,C being Subset of FT st A = B \/ C & B <> {} & C <> {} & B misses
  C holds B^b meets C & B meets C^b
  proof
    let B,C be Subset of FT;
    assume A = B \/ C & B <> {} & C <> {} & B misses C;
    then not B,C are_separated by A2;
    then not(B^b misses C & B misses (C^b)) by FINTOPO4:def 1;
    hence thesis by A1,Th5;
  end;
  hence thesis;
end;
