proposition: Lemma deriv_poly_example_neq0 : poly_example^`() != 0.
proof: Proof. apply/eqP => /(congr1 (fun p => p.[0])). by rewrite deriv_poly_example !pesimp => /eqP; compute. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field polyrcf) Abel(various classic_ext map_gal algR) Abel(char0 cyclotomic_ext real_closed_ext)