proposition: Lemma annul_pet_alg_neq0 p : p != 0 -> annul_pet_alg p != 0.
proof: Proof. rewrite /annul_pet_alg; case: eqP=> /=; last by rewrite ?rmorph0 ?root0. by move=> p_neq0; case: annul_from_alg_proof=> ? ? /andP[]. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg ssrnum ssrint rat poly polydiv polyorder) mathcomp(perm matrix mxpoly polyXY binomial generic_quotient) mathcomp(cauchyreals separable zmodp bigenough)