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

theorem Th4:
  FT is connected implies for A, B being Subset of FT st [#]FT = A
  \/ B & A misses B & A,B are_separated holds A = {}FT or B = {}FT
proof
  assume FT is connected;
  then
A1: [#]FT is connected;
  let A, B be Subset of FT;
  assume that
A2: [#]FT = A \/ B & A misses B and
A3: A,B are_separated;
  A^b misses B by A3,FINTOPO4:def 1;
  hence thesis by A1,A2;
end;
