proposition: Lemma root_annul_alg (x : {alg F}) : root ((annul_alg x) ^ to_alg) x.
proof: Proof. apply/rootP; rewrite -[x]reprK horner_pi /= zeroE -equiv_alg. by rewrite horner_algcrealE root_annul_algcreal. 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)