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.

Lemma lem_sing_not_empty : forall x : E, singleton x <> Vide.