proposition: Lemma root_is_roots (p : {poly R}) (a b : R) : p != 0 -> forall x, x \in `]a, b[ -> root p x = (x \in roots p a b).
proof: Proof. by case: rootsP=> // p0 hs ps _ y hy /=; rewrite -hs hy. 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)