reserve Al for QC-alphabet;
reserve p,q,p1,p2,q1 for Element of CQC-WFF(Al),
  k for Element of NAT,
  f,f1,f2,g for FinSequence of CQC-WFF(Al),
  a,b,b1,b2,c,i,n for Nat;
reserve P for Permutation of dom f;

theorem Th20:
  |- f^<*p*> implies |- g^f^<*p*>
proof
  Suc(f^<*p*>) = p by CALCUL_1:5;
  then
A1: Suc(f^<*p*>) = Suc(g^f^<*p*>) by CALCUL_1:5;
  Ant(f^<*p*>) = f by CALCUL_1:5;
  then Ant(f^<*p*>) is_Subsequence_of g^f by Th18;
  then
A2: Ant(f^<*p*>) is_Subsequence_of Ant(g^f^<*p*>) by CALCUL_1:5;
  assume |- f^<*p*>;
  hence thesis by A2,A1,CALCUL_1:36;
end;
