proposition: Lemma neighpl_mul a b p q : (neighpl (p * q) a b) =i [predI (neighpl p a b) & (neighpl q a b)].
proof: Proof. move=> x; rewrite !inE /<=%O /= /<=%O /= prev_rootM. by case: (x < b); rewrite // lt_maxl !(andbT, andbF). 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)