reserve A for QC-alphabet;
reserve i,j,k,l,m,n for Nat;
reserve a,b,e for set;
reserve t,u,v,w,z for QC-symbol of A;
reserve p,q,r,s for Element of CQC-WFF(A);
reserve x for Element of bound_QC-variables(A);
reserve ll for CQC-variable_list of k,A;
reserve P for QC-pred_symbol of k,A;

theorem Th13:
  for l being CQC-variable_list of k,A, i st 1<=i & i<=len l holds l
  .i in bound_QC-variables(A)
proof
  let l be CQC-variable_list of k,A, i;
  assume that
A1: 1<=i and
A2: i<=len l;
  i in dom l by A1,A2,FINSEQ_3:25;
  then
A3: l.i in rng l by FUNCT_1:def 3;
  rng l c= bound_QC-variables(A) by RELAT_1:def 19;
  hence thesis by A3;
end;
