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 lowbit_is_trunc : forall v : BV, v <> nilbv -> consbv (lowbit v) nilbv = truncbv v 1.