Definition pos_div_2 (eps : posreal) := mkposreal _ (is_pos_div_2 eps).(** * The sign function *)

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

Lemma zip_rcons {S T : Type} (s : seq S) (t : seq T) hs ht : size s = size t -> zip (rcons s hs) (rcons t ht) = rcons (zip s t) (hs,ht).