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;
reserve CX for Consistent Subset of CQC-WFF(Al),
  P9 for Element of QC-pred_symbols(Al);
reserve JH for Henkin_interpretation of CX;

theorem
  JH,valH(Al) |= VERUM(Al) iff CX |- VERUM(Al)
proof
  set f = <*>CQC-WFF(Al);
  rng f c= CX & |- f^<*VERUM(Al)*> by Th15;
  hence thesis by VALUAT_1:32;
end;
