(** * Bounds for sets in [Rbar] *)
(** ** Upper and Lower bounds *)

Definition Rbar_is_upper_bound (E : Rbar -> Prop) (l : Rbar) :=
  forall x, E x -> Rbar_le x l.Definition Rbar_is_lower_bound (E : Rbar -> Prop) (l : Rbar) :=
  forall x, E x -> Rbar_le l x.

Lemma Rbar_ub_dec (E : Rbar -> Prop) (Hp : ~ E p_infty) : {M : R | Rbar_is_upper_bound E M} + {(forall (M : R), ~Rbar_is_upper_bound E M)}.