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.