(* LL: TODO: Add proof obligation that the result paths be prefix free? *)
Class CoArbitrary (A : Type) : Type :=
  {
    coarbitrary : A -> positive;
    coarbReverse : positive -> option A;
    coarbCorrect : forall a, coarbReverse (coarbitrary a) = Some a
  }.(* LL: TODO: Add proof obligation that the result paths be prefix free? *)
Class CoArbitrary (A : Type) : Type :=
  {
    coarbitrary : A -> positive;
    coarbReverse : positive -> option A;
    coarbCorrect : forall a, coarbReverse (coarbitrary a) = Some a
  }.(* LL: TODO: Add proof obligation that the result paths be prefix free? *)
Class CoArbitrary (A : Type) : Type :=
  {
    coarbitrary : A -> positive;
    coarbReverse : positive -> option A;
    coarbCorrect : forall a, coarbReverse (coarbitrary a) = Some a
  }.(* LL: TODO: Add proof obligation that the result paths be prefix free? *)
Class CoArbitrary (A : Type) : Type :=
  {
    coarbitrary : A -> positive;
    coarbReverse : positive -> option A;
    coarbCorrect : forall a, coarbReverse (coarbitrary a) = Some a
  }.Instance coArbPos : CoArbitrary positive.

Lemma nat_lemma : forall a : nat, Some (Init.Nat.pred (Pos.to_nat (Pos.of_nat (S a)))) = Some a.