proposition: Lemma nmulr_rgt0 x y : x < 0 -> (0 < x * y) = (y < 0).
proof: Proof. by move=> x_lt0; rewrite -mulrNN pmulr_rgt0 lterNE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)