Notation bs := (list bool).
Definition unary (v : bs) := forallb id v.
(** * Boolean interpretation of bitstrings *)
Definition bs2bool (v:bs) : bool := hd false v.
Definition bool2bs (b:bool) : bs :=
if b then true::nil else nil.

Lemma bs_nat2bool_false v :
unary v = true ->
bs2bool v = false -> length v = 0.