(* Proof of lem_comprehension_rl                                           *)
intros; elim (axs_comprehension F a v0); intros; exact (H1 H).
Qed.
(* End of proof of lem_comprehension_rl                                    *)
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(* Consequences                                                            *)
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(* Existence de l'ensemble vide                                            *)
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Definition def_F_vide (v0 : E) := v0 <> v0.
Definition vide (a : E) := subset def_F_vide a.

Lemma lem_vide_propertie : forall v0 v1 : E, ~ In v0 (vide v1).
intros; unfold vide in |- *; unfold def_F_vide in |- *; unfold not in |- *;
intros.