proposition: Lemma roots_on_nil p i : roots_on p i [::] -> {in i, noroot p}.
proof: Proof. by move=> hp x hx; move: (hp x); rewrite in_nil hx /=; move->. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp) mathcomp(polyorder path interval ssrint)