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;

theorem Th16:
  Seq((g^f)|seq(len g,len f)) = Sgm(seq(len g,len f)) * (g^f)
proof
  reconsider gf = (g^f)|seq(len g,len f) as FinSubsequence;
  Seq(gf) = gf * Sgm(dom(gf)) by FINSEQ_1:def 15
    .= gf * Sgm(seq(len g,len f)) by Th15
    .= (((g^f)|rng Sgm(seq(len g,len f))) qua Function) * (Sgm(seq(len g,len
  f)) qua Function) by Th12
    .= ((g^f) qua Function) * (Sgm(seq(len g,len f))qua Function) by FUNCT_4:2;
  hence thesis;
end;
