(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(* File: axs_fundation.v                                                   *)
(* auteur: alex@sysal.ibp.fr                                               *)
(* date: 19/10/95                                                          *)
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Require Export axs_choice.

(* Specifications: *)
Axiom axs_vide_or_not : forall x : E, x = Vide \/ x <> Vide.
Axiom
axs_fundation :
forall x : E, x <> Vide -> exists y : E, In y x /\ inter y x = Vide.
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(* Un ensemble ne s'appartient pas.                                        *)
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Lemma lem_sing_not_empty : forall x : E, singleton x <> Vide.
unfold not in |- *; intros.