Fixpoint eqbList (l1 l2 : list positive) :=
    match l1, l2 with
      | nil         , nil          => true
      | (hd1 :: tl1), (hd2 :: tl2) => (Pos.eqb hd1 hd2) && (eqbList tl1 tl2)
      | _           , _            => false
    end.

(* Specifications: *)
Lemma eqbListEqList : forall l1 l2, eqbList l1 l2 = true <-> eqList l1 l2.