(* Proof of lem_paire_sym                                                  *)
apply axs_extensionnalite; intros; unfold iff in |- *; intros.
elim (axs_paire b a v2); intros.
elim (axs_paire a b v2); intros.
split; intros.
clear H; clear H2; apply H0; clear H0; apply lem_or_sym; auto.
clear H0; clear H1; apply H2; clear H2; apply lem_or_sym; auto.
Qed.
(* End of proof of lem_paire_sym                                           *)

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(* Propriete de la paire                                                   *)
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Lemma lem_paire_propertie :
forall a0 b0 a1 b1 : E,
paire a0 b0 = paire a1 b1 <-> a0 = a1 /\ b0 = b1 \/ a0 = b1 /\ b0 = a1.