(* End of proof of lem_Vide_Img                                            *)

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

(* Specifications: *)
Lemma lem_rfull_rel_sig : forall a : E, rel_sig (rfull a) a a.
Lemma lem_rfull_dom : forall a : E, rdom (rfull a) a a (lem_rfull_rel_sig a) = a.
Lemma lem_rfull_Img : forall a : E, rImg (rfull a) a a (lem_rfull_rel_sig a) = a.
Lemma lem_rfull_eq_cart : forall a : E, rfull a = cartesien a a.
Lemma lem_rfull_prop : forall a x y : E, In x a -> In y a -> In (couple x y) (rfull a).