(** * 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).