theorem
  for D being non empty set, f1,f2 being FinSequence of D, n st 1
  <= n & n <= len f2 holds (f1^f2)/.(n + len f1) = f2/.n
proof
  let D be non empty set, f1,f2 be FinSequence of D, n such that
A1: 1 <= n and
A2: n <= len f2;
A3: len f1 < n + len f1 by A1,NAT_1:19;
  len(f1^f2) = len f1 + len f2 by FINSEQ_1:22;
  then
A4: n + len f1 <= len(f1^f2) by A2,XREAL_1:6;
  n + len f1 >= n by NAT_1:11;
  then n + len f1 >= 1 by A1,XXREAL_0:2;
  hence (f1^f2)/.(n + len f1) = (f1^f2).(n + len f1) by A4,FINSEQ_4:15
    .= f2.(n + len f1 - len f1) by A3,A4,FINSEQ_1:24
    .= f2/.n by A1,A2,FINSEQ_4:15;
end;
