reserve Al for QC-alphabet,
     PHI for Consistent Subset of CQC-WFF(Al),
     PSI for Subset of CQC-WFF(Al),
     p,q,r,s for Element of CQC-WFF(Al),
     A for non empty set,
     J for interpretation of Al,A,
     v for Element of Valuations_in(Al,A),
     m,n,i,j,k for Element of NAT,
     l for CQC-variable_list of k,Al,
     P for QC-pred_symbol of k,Al,
     x,y for bound_QC-variable of Al,
     z for QC-symbol of Al,
     Al2 for Al-expanding QC-alphabet;
reserve J2 for interpretation of Al2,A,
        Jp for interpretation of Al,A,
        v2 for Element of Valuations_in(Al2,A),
        vp for Element of Valuations_in(Al,A);

theorem Th3:
  for k being Nat for S being FCEx-Sequence of Al,k holds
  S.(k+1) is QC-alphabet
proof
  let k be Nat;
  let S be FCEx-Sequence of Al,k;
  0 < 0 + (k + 1);
  then 1 <= k + 1 & k + 1 <= k + 1 by NAT_1:19;
  hence thesis by Def7;
end;
