proposition: Lemma pmulr_rle0 x y : 0 < x -> (x * y <= 0) = (y <= 0).
proof: Proof. by move=> x_gt0; rewrite -oppr_ge0 -mulrN pmulr_rge0 // oppr_ge0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)