(** * 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_min_case (x y : Rbar) (P : Rbar -> Type) :
P x -> P y -> P (Rbar_min x y).