
theorem A8B8:
  for a1,a2,a3,a4,a5,a6,a7,a8,b1,b2,b3,b4,b5,b6,b7,b8 be Complex holds
  <*a1,a2,a3,a4,a5,a6,a7,a8*> + <*b1,b2,b3,b4,b5,b6,b7,b8*> =
    <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5,a6+b6,a7+b7,a8+b8*>
  proof
    let a1,a2,a3,a4,a5,a6,a7,a8,b1,b2,b3,b4,b5,b6,b7,b8 be Complex;
    A1: <*a1,a2,a3,a4,a5*> + <*b1,b2,b3,b4,
      b5*> = <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5*> by A5B5;
    <*a1,a2,a3,a4,a5,a6,a7,a8*> = <*a1,a2,a3,a4,a5*>^<*a6,a7,a8*> &
    <*b1,b2,b3,b4,b5,b6,b7,b8*> = <*b1,b2,b3,b4,b5*>^<*b6,b7,b8*>
      by AOFA_A00:def 6; then
    <*a1,a2,a3,a4,a5,a6,a7,a8*> + <*b1,b2,b3,b4,b5,b6,b7,b8*> =
      <*a1+b1,a2+b2,a3+b3,a4+b4,a5+b5*>^<*a6+b6,a7+b7,a8+b8*> by A1,FINSEQ940B;
    hence thesis by AOFA_A00:def 6;
  end;
