(** * 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_lb_le_ub (E : Rbar -> Prop) (l1 l2 : Rbar) : (exists x, E x) -> Rbar_is_lower_bound E l1 -> Rbar_is_upper_bound E l2 -> Rbar_le l1 l2.