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.