Definition setd {T} (f : M.elt -> T) (g : T -> T -> T) (b : T) (s : M.t) :=
  listd f g b (M.elements s).

Lemma listd_fold_left cls0 l s (H : forall c cls, listd f inter b cls s -> f c s -> listd f inter b (h cls c) s) : listd f inter b l s -> listd f inter b cls0 s -> listd f inter b (fold_left h l cls0) s.