
theorem AMB:
  for a,b be Complex holds <*a*>(#)<*b*> = <*(a*b)*>
  proof
    let a,b be Complex;
    dom <*a*> = Seg 1 & dom <*b*> = Seg 1 & dom <*(a*b)*> = Seg 1
      by FINSEQ_1:def 8; then
    A2: dom (<*a*>(#)<*b*>) = (Seg 1)/\(Seg 1) by VALUED_1:def 4
    .= Seg 1; then
    1 in dom (<*a*>(#)<*b*>); then
    (<*a*>(#)<*b*>).1 = <*a*>.1*<*b*>.1 by VALUED_1:def 4;
    hence thesis by A2,FINSEQ_1:def 8;
  end;
