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

Lemma ad_in_list_l :
forall (l l':list ad) (a:ad),
ad_in_list a l = true -> ad_in_list a (l ++ l') = true.