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 lteif_anti C1 C2 x y :
(x < y ?<= if C1) && (y < x ?<= if C2) = C1 && C2 && (x == y).