proposition: Lemma roots_on_cons p a b r s : sorted <%R (r :: s) -> roots_on p `]a, b[ (r :: s) -> roots_on p `]r, b[ s.
proof: Proof. move=> /= hrs hr. have allrs := order_path_min lt_trans hrs. by case: (min_roots_on allrs hr). 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)