(** 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_glb_unique (E : Rbar -> Prop) (l : Rbar) : Rbar_is_glb E l -> Rbar_glb E = l.