proposition: Lemma gt_eqF x y : y < x -> x == y = false.
proof: Proof. by apply: contraTF => /eqP ->; 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)