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 Th21:
  |- f^<*p*>^<*p*>
proof
  len(f^<*p*>) in dom(f^<*p*>) by CALCUL_1:10;
  then len f + len <*p*> in dom(f^<*p*>) by FINSEQ_1:22;
  then
A1: len f+1 in dom(f^<*p*>) by FINSEQ_1:39;
  (f^<*p*>).(len f+1) = p by FINSEQ_1:42;
  then p is_tail_of f^<*p*> by A1,CALCUL_1:def 16;
  then Suc(f^<*p*>^<*p*>) is_tail_of f^<*p*> by CALCUL_1:5;
  then Suc(f^<*p*>^<*p*>) is_tail_of Ant(f^<*p*>^<*p*>) by CALCUL_1:5;
  hence thesis by CALCUL_1:33;
end;
