Definition Mux := If BV.Definition lowbit (l : list bool) :=
  match l with
  | nil => false
  | b :: _ => b
  end.Definition highs (l : list bool) :=
  match l with
  | nil => nil (A:=bool)
  | _ :: v => v
  end.

Lemma length_abit : forall (v : BV) (i : nat), i < lengthbv v -> lengthbv (abit v i) = 1.