(** 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_is_lub_unique (E : Rbar -> Prop) (l : Rbar) :
Rbar_is_lub E l -> Rbar_lub E = l.