proposition: Lemma sgr_neighpl_same p a x : {in neighpl p a x &, forall y z, (sgr p.[y] = sgr p.[z])}.
proof: Proof. by rewrite /neighpl=> y z *; apply: (polyrN0_itv (@prev_noroot p a x)). 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)