apply this kind of theorem to prove lower bounds for restricted classes of circuits see fancy see ok I won't go into what the definitions of these things are but the the way in which they're proof lays out exactly as you might expect we show that faster circuits at algorithms for this for particular classes can imply circuit lower bounds for that particular class ok so just some generic kind of theorem if see circuits sat on circuits with n inputs can be solved and to the N over in ten steps then this class in X or