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

theorem
  for C being Subset of FT st FT is filled symmetric & C is connected
holds for S being Subset of FT st S is_a_component_of FT holds C misses S or C
  c= S
proof
  let C be Subset of FT;
  assume
A1: FT is filled symmetric & C is connected;
  let S be Subset of FT;
  assume
A2: S is_a_component_of FT;
A3: S c= C \/ S by XBOOLE_1:7;
  assume
A4: C meets S;
  S is connected by A2;
  then C \/ S is connected by A1,A4,Th33,FINTOPO4:6;
  then S = C \/ S by A2,A3;
  hence thesis by XBOOLE_1:7;
end;
