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

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(* {a,b} = {b,a}                                                           *)
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Lemma lem_paire_sym : forall a b : E, paire a b = paire b a.
intros.