proposition: Lemma neighpl_wit p a x : a < x -> p != 0 -> {y | y \in neighpl p a x}.
proof: Proof. move=> xb; exists (mid (prev_root p a x) x). by rewrite mid_in_itv //= prev_root_lt. 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)