proposition: Lemma neighpr_wit p x b : x < b -> p != 0 -> {y | y \in neighpr p x b}.
proof: Proof. move=> xb; exists (mid x (next_root p x b)). by rewrite mid_in_itv //= next_root_gt. 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)