proposition: Lemma no_roots_on (p : {poly R}) a b : {in `]a, b[, noroot p} -> roots_on p `]a, b[ [::].
proof: Proof. by move=> hr x; case: (boolP (x \in _)) => //= /hr /negPf. 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)