theorem Th34:
  for h being FinSequence holds h is CQC-variable_list of k,A iff h
  is FinSequence of bound_QC-variables(A) & len h = k
proof
  let h be FinSequence;
  thus h is CQC-variable_list of k,A implies h is FinSequence of
  bound_QC-variables(A) & len h = k
  proof
    assume
A1: h is CQC-variable_list of k,A;
    then rng h c= bound_QC-variables(A) by RELAT_1:def 19;
    hence h is FinSequence of bound_QC-variables(A) by FINSEQ_1:def 4;
    thus thesis by A1,CARD_1:def 7;
  end;
  thus h is FinSequence of bound_QC-variables(A) & len h = k implies h is
  CQC-variable_list of k,A
  proof
    assume that
A2: h is FinSequence of bound_QC-variables(A) and
A3: len h = k;
    rng h c= bound_QC-variables(A) by A2,FINSEQ_1:def 4;
    then rng h c= QC-variables(A) by XBOOLE_1:1;
    hence thesis by A2,A3,CARD_1:def 7,FINSEQ_1:def 4;
  end;
end;
