reserve Al for QC-alphabet;
reserve a,a1,a2,b,c,d for set,
  X,Y,Z for Subset of CQC-WFF(Al),
  i,k,m,n for Nat,
  p,q for Element of CQC-WFF(Al),
  P for QC-pred_symbol of k,Al,
  ll for CQC-variable_list of k,Al,
  f,f1,f2,g for FinSequence of CQC-WFF(Al);
reserve A for non empty finite Subset of NAT;
reserve C for non empty set;
reserve A for non empty set,
  v for Element of Valuations_in(Al,A),
  J for interpretation of Al,A;

theorem Th13:
  {VERUM(Al)} is Consistent
proof

set A =the  non empty set,J =the  interpretation of Al,A ,v =the  Element of
Valuations_in(Al,A);
  J,v |= VERUM(Al) by VALUAT_1:32;
  then for p st p in {VERUM(Al)} holds J,v |= p by TARSKI:def 1;
  then J,v |= {VERUM(Al)} by CALCUL_1:def 11;
  hence thesis by Th12;
end;
