(** * Rbar_min *)

Definition Rbar_min (x y : Rbar) : Rbar :=
  match x, y with
  | z, p_infty | p_infty, z => z
  | _ , m_infty | m_infty, _ => m_infty
  | Finite x, Finite y => Rmin x y
  end.

Lemma Rbar_lt_locally (a b : Rbar) (x : R) : Rbar_lt a x -> Rbar_lt x b -> exists delta : posreal, forall y, Rabs (y - x) < delta -> Rbar_lt a y /\ Rbar_lt y b.