
theorem
  for a,b be Complex holds <*a*>-<*b*> = <*(a-b)*>
  proof
    let a,b be Complex;
    reconsider p = <*(-b)*> as 1-element FinSequence;
    reconsider q = -<*b*> as 1-element FinSequence;
    A1: len p = 1 & len q = 1 by CARD_1:def 7;
    (-<*b*>).1 = -(<*b*>.1) by VALUED_1:8
    .= <*(-b)*>.1; then
    A2: q = p by A1,FINSEQ_1:40;
    <*a*>+<*(-b)*> = <*(a+(-b))*> by APB;
    hence thesis by A2,VALUED_1:def 9;
  end;
