proposition: Lemma roots_in p a b x : x \in roots p a b -> x \in `]a, b[.
proof: Proof. by case: rootsP=> //= np0 ron_p *; apply: (roots_on_in ron_p). 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)