(** * 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_strong (r1 r2 : Rbar) (P : Rbar -> Type) :
(Rbar_le r1 r2 -> P r1) -> (Rbar_le r2 r1 -> P r2)
-> P (Rbar_min r1 r2).