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 sorted_filter_lt x s :
sorted <=%O s -> [seq y <- s | y < x] = take (count (< x) s) s.