Section POrderTheory.
Context {disp : unit} {T : porderType disp}.
Implicit Types (x y : T) (s : seq T).
Definition lt_gtF x y hxy := le_gtF (@ltW x y hxy).

Lemma lt_sorted_ltn_nth (x0 : T) (s : seq T) : sorted <%O s ->
{in [pred n | (n < size s)%N] &,
{mono nth x0 s : i j / (i < j)%N >-> i < j}}.