(** * Rmin and Rmax *)
(** Rewritings *)

(* Specifications: *)
Lemma Rplus_max_distr_l :
forall a b c, a + Rmax b c = Rmax (a + b) (a + c).
Lemma Rplus_max_distr_r :
forall a b c, Rmax b c + a = Rmax (b + a) (c + a).
Lemma Rplus_min_distr_l :
forall a b c, a + Rmin b c = Rmin (a + b) (a + c).
Lemma Rplus_min_distr_r :
forall a b c, Rmin b c + a = Rmin (b + a) (c + a).
Lemma Rmult_max_distr_l :
forall a b c, 0 <= a -> a * Rmax b c = Rmax (a * b) (a * c).
Lemma Rmult_max_distr_r :
forall a b c, 0 <= a -> Rmax b c * a = Rmax (b * a) (c * a).
Lemma Rmult_min_distr_l :
forall a b c, 0 <= a -> a * Rmin b c = Rmin (a * b) (a * c).
Lemma Rmult_min_distr_r :
forall a b c, 0 <= a -> Rmin b c * a = Rmin (b * a) (c * a).
Lemma Rmin_assoc : forall x y z, Rmin x (Rmin y z) =
Rmin (Rmin x y) z.