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

theorem Th7:
  for X being non empty SubSpace of FT st FT is filled holds X is filled
proof
  let X be non empty SubSpace of FT;
  assume
A1: FT is filled;
  let x be Element of X;
  the carrier of X c= the carrier of FT by Def2;
  then reconsider x2=x as Element of FT;
A2: U_FT x= (U_FT x2) /\ ([#]X) by Def2;
  x2 in U_FT x2 by A1;
  hence thesis by A2,XBOOLE_0:def 4;
end;
