(* Proof of lem_refl_dom_inc_img_recip                                     *)
intros.
unfold not in |- *; intros.
generalize (lem_refl_dom_inc_img r a rRel H0); intros.
absurd (inc (rdom r a a rRel) (rImg r a a rRel)); auto with zfc.
Qed.
(* End of proof of lem_refl_dom_inc_img_recip                              *)
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(* Une relation non vide reflexive n'est pas irreflexive                   *)
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Lemma lem_refl_not_irrefl :
forall (r a : E) (rNe : r <> Vide) (rRel : rel_sig r a a),
reflexivity r a rRel -> ~ irreflexivity r a rRel.