(* End of proof of lem_rfull_prop                                          *)

(***************************************************************************)
(* La relation identite                                                    *)
(***************************************************************************)
Definition rId (a : E) :=
  subset (fun c : E => exists x : E, c = couple x x) (cartesien a a).

(* Specifications: *)
Lemma lem_rId_rel_sig : forall a : E, rel_sig (rId a) a a.
Lemma lem_rId_dom : forall a : E, rdom (rId a) a a (lem_rId_rel_sig a) = a.