Fixpoint Elems (l:list ad) : FSet :=
    match l with
    | nil => M0 unit
    | a :: l' => MapPut _ (Elems l') a tt
    end.

Lemma ad_in_elems_in_list : forall (l:list ad) (a:ad), in_FSet a (Elems l) = ad_in_list a l.