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

Lemma ad_list_stutters_permute :
forall l l':list ad,
ad_list_stutters (l ++ l') = ad_list_stutters (l' ++ l).