Fixpoint RoseS_spec (x y z : bs) :=
match z with
| nil => nil
| _ :: z' =>
if leb (length z) (length x - length y)
then false :: RoseS_spec x y z'
else hd false (skipn (length x - length z) x) :: RoseS_spec x y z'
end.

Lemma bs2nat_cons_eq : forall b l1 l2,
bs2nat l1 = bs2nat l2 ->
bs2nat (b :: l1) = bs2nat (b :: l2).