proposition: Lemma annul_from_alg_neq0 p : p != 0 -> annul_from_alg p != 0.
proof: Proof. move=> p_neq0; rewrite /annul_from_alg. case: ifP; first by rewrite lead_coef_eq0 poly_ground_eq0. rewrite /annul_pet_alg; case: eqP p_neq0=> //= p_neq0 _. by case: annul_from_alg_proof. 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)