proposition: Lemma uniq_roots_dvdp p rs : all (root p) rs -> uniq_roots rs -> (\prod_(z <- rs) ('X - z%:P)) %| p.
proof: Proof. move=> rrs; case/(uniq_roots_prod_XsubC rrs)=> q ->. by apply: dvdp_mull; rewrite // (eqP (monic_prod_XsubC _)) unitr1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)