reserve FT for non empty RelStr;
reserve x, y, z for Element of FT;
reserve A for Subset of FT;
reserve F for Subset of FT;

theorem
  (A`)^delta = A^delta
proof
  for x being object holds x in (A`)^delta iff x in A^delta
  proof
    let x be object;
    thus x in (A`)^delta implies x in A^delta
    proof
      assume
A1:   x in (A`)^delta;
      then reconsider y=x as Element of FT;
      U_FT y meets (A`) & U_FT y meets (A`)` by A1,Th5;
      hence thesis;
    end;
    assume
A2: x in A^delta;
    then reconsider y=x as Element of FT;
    U_FT y meets (A`)` & U_FT y meets A` by A2,Th5;
    hence thesis;
  end;
  hence thesis by TARSKI:2;
end;
