(** * The sign function *)
Definition sign (x : R) :=
match total_order_T 0 x with
| inleft (left _) => 1
| inleft (right _) => 0
| inright _ => -1
end.

Lemma sign_min_max (a b : R) :
sign (b - a) * (Rmax a b - Rmin a b) = b - a.