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

Definition is_ub_Rbar (E : R -> Prop) (l : Rbar) :=
  forall (x : R), E x -> Rbar_le x l.Definition is_lb_Rbar (E : R -> Prop) (l : Rbar) :=
  forall (x : R), E x -> Rbar_le l x.

Lemma is_ub_Rbar_dec (E : R -> Prop) : {l : R | is_ub_Rbar E l} + {(forall l : R, ~is_ub_Rbar E l)}.