proposition: Lemma le_gtF x y: x <= y -> y < x = false.
proof: Proof. by move=> le_xy; apply/negP => /lt_le_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)