Definition fpm := sig finMap.Instance Join_fpm : Join fpm := 
     Join_prop (A -> option B)  (Join_fun A (option B) Join_Rng) finMap.Definition PAF: (@Perm_alg (A -> Rng)  (Join_fun A Rng Join_Rng))
  := Perm_fun _ _ _ Perm_Rng.Instance Perm_fpm : @Perm_alg fpm Join_fpm :=
    Perm_prop (A -> Rng) _ _ finMap finMap_join.

(* Specifications: *)
Lemma finMap_core x: finMap x -> finMap (@core _ _ (Sep_fun A (option B) Join_Rng _ ) x).