proposition: Lemma eq_ltLR x y z t : (x < y -> z < t) -> (y <= x -> t <= z) -> (x < y) = (z < t).
proof: Proof. by rewrite !leNgt => ? /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)