proposition: Lemma nmulr_rle0 x y : x < 0 -> (x * y <= 0) = (0 <= y).
proof: Proof. by move=> x_lt0; rewrite -mulrNN pmulr_rle0 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)