(** Functions *)
Definition Rbar_lub (E : Rbar -> Prop)
:= proj1_sig (Rbar_ex_lub E).
Definition Rbar_glb (E : Rbar -> Prop)
:= proj1_sig (Rbar_ex_glb E).

(* Specifications: *)
Lemma Rbar_opp_glb_lub (E : Rbar -> Prop) :
Rbar_glb (fun x => E (Rbar_opp x)) = Rbar_opp (Rbar_lub E).
Lemma Rbar_opp_lub_glb (E : Rbar -> Prop) :
Rbar_lub (fun x => E (Rbar_opp x)) = Rbar_opp (Rbar_glb E).
Lemma Rbar_is_lub_unique (E : Rbar -> Prop) (l : Rbar) :
Rbar_is_lub E l -> Rbar_lub E = l.
Lemma Rbar_is_glb_unique (E : Rbar -> Prop) (l : Rbar) :
Rbar_is_glb E l -> Rbar_glb E = l.