reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem
  for f being FinSequence holds len(f/^i) <= len f
proof
  let f be FinSequence;
  per cases;
  suppose
    i <= len f;
    then len(f/^i) = len f - i by RFINSEQ:def 1;
    then len(f/^i)+i = len f;
    hence thesis by NAT_1:11;
  end;
  suppose
    len f < i;
    then f/^i = {} by RFINSEQ:def 1;
    hence thesis;
  end;
end;
