proposition: Lemma lt_geF x y : (x < y) -> y <= x = false.
proof: Proof. by move=> le_xy; apply/negP => /le_lt_trans /(_ le_xy); rewrite ltxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)