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

(** * ssreflect.seq *)
(** Finite subdivision *)
Lemma interval_finite_subdiv (a b : R) (eps : posreal) : (a <= b) ->
{l : seq R | head 0 l = a /\ last 0 l = b /\
forall i, (S i < size l)%nat -> nth 0 l i < nth 0 l (S i) <= nth 0 l i + eps}.