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

Lemma ad_list_Elems :
forall l l':list ad,
MapCard _ (Elems l) = MapCard _ (Elems l') ->
length l = length l' -> ad_list_stutters l = ad_list_stutters l'.