proposition: Lemma eq_leLR x y z t : (x <= y -> z <= t) -> (y < x -> t < z) -> (x <= y) = (z <= t).
proof: Proof. by rewrite !ltNge => ? /contraTT ?; apply/idP/idP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)