Definition build_map (l:list (A * B)) : map :=
fold_right
(fun (ab:A * B) m =>
insert_fpm EqDec_A
(fst ab)
(mk_lifted fullshare top_share_nonunit,snd ab) m)
empty_map l.

Lemma build_map_join : forall (l1 l2:list (A * B)),
NoDup (List.map (@fst _ _) (l1++l2)) ->
join  (build_map l1)
(build_map l2)
(build_map (l1++l2)).