(** 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_glb_le_lub (E : Rbar -> Prop) : (exists x, E x) -> Rbar_le (Rbar_glb E) (Rbar_lub E).