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