
theorem AP3:
  for a,b,c,x,y,z be Complex holds <*a,b,c*>+<*x,y,z*> = <*a+x,b+y,c+z*>
  proof
    let a,b,c,x,y,z be Complex;
    <*a,b,c*>+<*x,y,z*> = (<*a,b*>+<*x,y*>)^<*(c+z)*> by FPA
    .= <*(a+x),(b+y)*>^<*(c+z)*> by AP2;
    hence thesis;
  end;
