reserve D for non empty set,
  f for FinSequence of D,
  p, p1, p2, p3, q for Element of D,
  i, j, k, l, n for Nat;

theorem
  for f,g being FinSequence st 1 <= i & i <= len f holds
    f.i = (g^f).(len g + i)
proof
  let f,g be FinSequence;
  assume 1 <= i & i <= len f;
  then i in dom f by FINSEQ_3:25;
  hence thesis by FINSEQ_1:def 7;
end;
