(** * 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.