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

theorem Th5:
  for A,B being Subset of FT st FT is symmetric & A^b misses B
  holds A misses B^b
proof
  let A,B be Subset of FT;
  assume that
A1: FT is symmetric and
A2: A^b misses B;
  assume A meets B^b;
  then consider x being object such that
A3: x in A and
A4: x in B^b by XBOOLE_0:3;
  consider y being Element of FT such that
A5: x=y and
A6: U_FT y meets B by A4;
  consider z being object such that
A7: z in U_FT y and
A8: z in B by A6,XBOOLE_0:3;
  reconsider z2=z as Element of FT by A7;
  y in U_FT z2 by A1,A7;
  then U_FT z2 meets A by A3,A5,XBOOLE_0:3;
  then
A9: z in A^b;
  A^b /\ B={} by A2;
  hence contradiction by A8,A9,XBOOLE_0:def 4;
end;
