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
  |- f^<*p*> implies |- Per(f,P)^<*p*>
proof
  set g = f^<*p*>;
  assume |- f^<*p*>;
  then |- Per(f,P)^f^<*p*> by Th20;
  then
A1: |- Per(f,P)^g by FINSEQ_1:32;
  1 <= len(g) by CALCUL_1:10;
  then |- Per(f,P)^<*Impl(Rev g)*> by A1,Th28;
  hence thesis by Th29;
end;
