(** - Fully general intersections of (a set of) sets is introduced as follows: *)

Definition intersection :
  forall A : Setoid, part_set (part_set A) -> part_set A.

(* Specifications: *)
Lemma intersection_to_indexed_intersection : forall (A I : Setoid) (f : MAP I (part_set A)), Equal (intersection (range f)) (indexed_intersection f).