fact: Definition bench := ANd (Iff be1_cout be2_cout) (ANd (Iff be1_som1 be2_som1) (ANd (Iff be1_som2 be2_som2) (ANd (Iff be1_som3 be2_som3) (ANd (Iff be1_som4 be2_som4) (ANd (Iff be1_som5 be2_som5) (ANd (Iff be1_som6 be2_som6) (ANd (Iff be1_som7 be2_som7) (Iff be1_som8 be2_som8)))))))).