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;

theorem Th5:
  |- f^<*p*> implies |- f^g^<*p*>
proof
A1: Ant(f^<*p*>) = f & Ant(f^g^<*p*>) = f^g by CALCUL_1:5;
  Suc(f^g^<*p*>) = p by CALCUL_1:5;
  then
A2: Suc(f^<*p*>) = Suc(f^g^<*p*>) by CALCUL_1:5;
  assume |- f^<*p*>;
  hence thesis by A1,A2,CALCUL_1:8,36;
end;
