proposition: Lemma lt_leAnge x y : (x < y) = (x <= y) && ~~ (y <= x).
proof: Proof. apply/idP/idP => [ltxy|/andP[lexy Nleyx]]; first by rewrite ltW // lt_geF. by rewrite lt_neqAle lexy andbT; apply: contraNneq Nleyx => ->. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)