proposition: Lemma integral_root_monic u p : p \is monic -> root p u -> {in p : seq K, integralRange RtoK} -> integralOver RtoK u.
proof: Proof. move=> mon_p pu0 intRp; rewrite -[u]hornerX. apply: integral_horner_root mon_p pu0 intRp _. by apply/integral_poly => i; rewrite coefX; apply: integral_nat. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(div fintype tuple finfun bigop fingroup perm) mathcomp(ssralg zmodp matrix mxalgebra poly polydiv)