proposition: Lemma ltEprod x y : (x < y) = [&& x != y, x.1 <= y.1 & x.2 <= y.2].
proof: Proof. by rewrite lt_neqAle. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)