
theorem
  for a be Complex, n be non zero Nat,
      f be n-element complex-valued FinSequence holds <*a*>+f = <*(a+f.1)*>
  proof
    let a be Complex, n be non zero Nat,
        f be n-element complex-valued FinSequence;
    reconsider g = <*a*> as 1-element complex-valued FinSequence;
    A2: len (g+f) = 1 by CARD_1:def 7; then
    1 in dom (g+f) by FINSEQ_3:25; then
    (<*a*>+f).1 = <*a*>.1+f.1 by VALUED_1:def 1;
    hence thesis by A2,FINSEQ_1:40;
  end;
