Transparent RoseS'_e.

(* Specifications: *)
Lemma bs2nat_firstn_false : forall n l,
bs2nat (firstn n (false :: l)) = 2 * bs2nat (firstn (n-1) l).
Lemma bs2nat_app : forall l1 l2,
bs2nat (l1 ++ l2) = bs2nat l1 + bs2nat (repeat (length l1) false ++ l2).
Lemma bs2nat_power : forall l n,
bs2nat (repeat n false ++ l) = (power 2 n) * (bs2nat l).