
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 4;
    hence thesis by A2,FINSEQ_1:40;
  end;
