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

theorem Th3:
  for A being Subset of FT holds A is connected implies for A2, B2
  being Subset of FT st A = A2 \/ B2 & A2 misses B2 & A2,B2 are_separated holds
  A2 = {}FT or B2 = {}FT
proof
  let A be Subset of FT;
  assume
A1: A is connected;
  let A2, B2 be Subset of FT;
  assume that
A2: A = A2 \/ B2 & A2 misses B2 and
A3: A2,B2 are_separated;
  A2^b misses B2 by A3,FINTOPO4:def 1;
  hence thesis by A1,A2;
end;
