proposition: Lemma pmulr_rgt0 x y : 0 < x -> (0 < x * y) = (0 < y).
proof: Proof. rewrite !lt_def !ger0_def normrM mulf_eq0 negb_or => /andP[x_neq0 /eqP->]. by rewrite x_neq0 (inj_eq (mulfI x_neq0)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)