
theorem
  for f be complex-valued FinSequence holds f-f = 0(#)f & f-f = ((len f)|-> 0)
  proof
    let f be complex-valued FinSequence;
    f - f = f + (-f) by VALUED_1:def 9
    .= 1(#)f + (-1)(#)f by VALUED_1:def 6
    .= (1 + (-1))(#)f by TOPREALC:2
    .= 0(#)f;
    hence thesis by EMP;
  end;
