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