proposition: Lemma root_in_roots (p : {poly R}) a b : p != 0 -> forall x, x \in `]a, b[ -> root p x -> x \in (roots p a b).
proof: Proof. by move=> p0 x axb rpx; rewrite -root_is_roots. 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)