Lemma inv_ind_true : forall t n : nat, (n <= size -> BV_to_nat (appbv (stripbv (R1 n) (size - n)) (R2 n)) = BV_to_nat V2 * BV_to_nat (truncbv V1 n)) -> S n <= size -> n <= size -> BV_to_nat (appbv (stripbv (appbv (highs (R1 n)) (Mux true (abit (BV_full_adder_sum (R2 n) V2 false) 0) (consbv (lowbit (R2 n)) nilbv))) (size - S n)) (appbv (highs (Mux true (BV_full_adder_sum (R2 n) V2 false) (R2 n))) (Mux true (consbv (BV_full_adder_carry (R2 n) V2 false) nilbv) (consbv false nilbv)))) = BV_to_nat V2 * BV_to_nat (appbv (truncbv V1 n) (consbv true nilbv)).