proposition: Lemma deg2_poly_le0m x : 0 <= delta -> r1 <= x <= r2 -> p.[x] <= 0.
proof: Proof. move=> dge0; rewrite le_eqVlt andb_orl => /orP[/andP[/eqP<- _]|]. by rewrite le_eqVlt (rootP (deg2_poly_root1 dge0)) eqxx. rewrite le_eqVlt andb_orr => /orP[/andP[_ /eqP->]|]. by rewrite le_eqVlt (rootP (deg2_poly_root2 dge0)) eqxx. by move=> ?; apply/ltW/deg2_poly_lt0m. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)