theorem
  for c being Element of fixed_QC-variables(A) for a being Element of
  free_QC-variables(A) holds c <> a
proof
  let c be Element of fixed_QC-variables(A);
  let a be Element of free_QC-variables(A);
  consider a1,a2 being object such that
A1: a1 in {6} and
  a2 in NAT and
A2: a = [a1,a2] by ZFMISC_1:def 2;
  consider c1,c2 being object such that
A3: c1 in {5} and
  c2 in QC-symbols(A) and
A4: c = [c1,c2] by ZFMISC_1:def 2;
A5: c1 = 5 by A3,TARSKI:def 1;
  a1 = 6 by A1,TARSKI:def 1;
  hence thesis by A2,A4,A5,XTUPLE_0:1;
end;
