Definition arity_RoseS' :
  arity RoseS'_e = ok_arity 3.

(* Specifications: *)
Lemma rec_bounded_RoseS' : rec_bounded RoseS'_e.
Lemma arity_RoseS : arity RoseS_e = ok_arity 3.
Lemma rec_bounded_RoseS : rec_bounded RoseS_e.
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).