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 RoseS_spec2_false : forall x y z, length z <= length x - length y -> bs2nat (RoseS_spec x y z) = 0.