(** 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).

Lemma Rbar_opp_lub_glb (E : Rbar -> Prop) :
Rbar_lub (fun x => E (Rbar_opp x)) = Rbar_opp (Rbar_glb E).