Definition from_elements A (l : list (key * A))
: t A (List.fold_left (fun acc xv => Dom.add (fst xv) acc) l Dom.empty) :=
exist (OK (List.fold_left (fun acc xv => Dom.add (fst xv) acc) l Dom.empty))
(List.fold_left (fun acc xv => S.add (fst xv) (snd xv) acc) l (@S.empty A))
(from_elements_OK l).
(** ***  Specifications  **)

Lemma fold_spec : forall A B (f : key -> A -> B -> B) dom (m : t A dom) (i : B),
fold f m i = List.fold_left (fun acc xv => f (fst xv) (snd xv) acc) (elements m) i.