(** * Emptiness is decidable *)

Definition Empty (E : R -> Prop) :=
  Lub_Rbar (fun x => x = 0 \/ E x) = Glb_Rbar (fun x => x = 0 \/ E x)
  /\ Lub_Rbar (fun x => x = 1 \/ E x) = Glb_Rbar (fun x => x = 1 \/ E x).

Lemma Empty_dec (E : R -> Prop) : {~Empty E}+{Empty E}.