proposition: Lemma uniq_rootsE rs : uniq_roots rs = uniq rs.
proof: Proof. elim: rs => //= r rs ->; congr (_ && _); rewrite -has_pred1 -all_predC. by apply: eq_all => t; rewrite /diff_roots mulrC eqxx unitfE subr_eq0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)