reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;
reserve f for Function of A,B;

theorem
  for D being non empty set, f being FinSequence of D,
      p being Element of D holds (f^<*p*>)/.(len f + 1) = p
proof
  let D be non empty set, f be FinSequence of D, p be Element of D;
  len(f^<*p*>) = len f + len<*p*> by FINSEQ_1:22;
  then 1 <= len f + 1 & len f + 1 <= len(f^<*p*>) by FINSEQ_1:39,NAT_1:11;
  then len f + 1 in dom(f^<*p*>) by FINSEQ_3:25;
  hence (f^<*p*>)/.(len f + 1) = (f^<*p*>).(len f + 1) by PARTFUN1:def 6
    .= p by FINSEQ_1:42;
end;
