Instance Disj_fpm {DA_B: Disj_alg B}: Disj_alg fpm.

Lemma insert_fpm_join : forall i v (x y z:fpm),
lookup_fpm y i = None ->
@join _ Join_fpm x y z ->
@join _ Join_fpm (insert_fpm i v x) y (insert_fpm i v z).