End CycleArc.
Prenex Implicits arc.
Section Monotonicity.
Variables (T : eqType) (r : rel T).
Hypothesis r_trans : transitive r.

(* Specifications: *)
Lemma sorted_lt_nth x0 (s : seq T) : sorted r s ->
{in [pred n | n < size s] &, {homo nth x0 s : i j / i < j >-> r i j}}.
Lemma ltn_index (s : seq T) : sorted r s ->
{in s &, forall x y, index x s < index y s -> r x y}.