proposition: Lemma lead_coef_prod_XsubC {R : idomainType} (cs : seq R) : lead_coef (\prod_(c <- cs) ('X - c%:P)) = 1.
proof: Proof. rewrite -(big_map (fun c : R => 'X - c%:P) xpredT idfun) /=. rewrite lead_coef_prod big_seq (eq_bigr (fun=> 1)) ?big1 //=. by move=> i /mapP[c _ ->]; apply: lead_coef_XsubC. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra all_solvable) mathcomp(all_field)