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 nth_count_lt x x0 s i : sorted <=%O s ->
(i < count (< x) s)%N -> nth x0 s i < x.