proposition: Lemma root_biggcd x (ps : seq {poly R}) : root (\big[gcdp/0]_(p <- ps) p) x = all (fun p => root p x) ps.
proof: Proof. elim: ps => [|p ps ihp]; first by rewrite big_nil root0. by rewrite big_cons /= root_gcd ihp. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)