proposition: Lemma neighpr_mul a b p q : (neighpr (p * q) a b) =i [predI (neighpr p a b) & (neighpr q a b)].
proof: Proof. move=> x; rewrite !inE /<=%O /= /<=%O /= next_rootM. by case: (a < x); rewrite // lt_minr. 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)