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(** We need the decidability of the belonging relation on sets              *)
(** This is equivalent to classical logic                                   *)

Definition in_or_not_in (U : Type) (x : U) (A : Ensemble U) :=
  classic (In U A x).

(* Specifications: *)
Lemma F_growing : forall C C' : SU, Included U C C' -> Included U (F C) (F C').
Lemma J_is_in_FJ : Included U J (F J).
Lemma FJ_is_in_J : Included U (F J) J.