proposition: Lemma separable_example : separable_poly poly_example.
proof: Proof. rewrite separable_poly.unlock. apply/coprimepP => q /(irredp_XsubCP irreducible_example) [//| eqq]. have size_deriv_example : size poly_example^`() = 5%N. rewrite !derivCE addr0 alg_polyC -scaler_nat addr0. by rewrite size_addl ?size_scale ?size_opp ?size_polyXn ?size_polyC. rewrite gtNdvdp -?size_poly_eq0 ?size_deriv_example//. by rewrite (eqp_size eqq) ?size_poly_example. 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)