Definition pmap_finite_c (m: PMap.t A) : positive :=
           p_tree_finite_c (snd m).

(* Specifications: *)
Lemma pmap_finite_sound_c: forall (m: PMap.t A) n, ((pmap_finite_c m) <= n)%positive -> PMap.get n m = fst m.
Lemma pmap_finite_sound_c: forall (m: PMap.t A) n, ((pmap_finite_c m) <= n)%positive -> PMap.get n m = fst m.