Section ListOfDomDef.
Variable A : Type.
Definition ad_list_of_dom :=
MapFold A (list ad) nil (app (A:=ad)) (fun (a:ad) (_:A) => a :: nil).

Lemma ad_in_list_of_dom_in_dom :
forall (m:Map A) (a:ad), ad_in_list a (ad_list_of_dom m) = in_dom A a m.