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.

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