proposition: Lemma uniq_roots_rdvdp p rs : all (root p) rs -> uniq_roots rs -> rdvdp (\prod_(z <- rs) ('X - z%:P)) p.
proof: Proof. move=> rrs /(uniq_roots_prod_XsubC rrs) [q ->]. exact/RingMonic.rdvdp_mull/monic_prod_XsubC. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)