proposition: Lemma roots_on_in p i s : roots_on p i s -> forall x, x \in s -> x \in i.
proof: Proof. by move=> hp x; rewrite -hp; case/andP. 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)