proposition: Lemma root_bigrgcd (x : R) (ps : seq {poly R}) : root (\big[(@rgcdp _)/0]_(p <- ps) p) x = all (root^~ x) ps.
proof: Proof. elim: ps; first by rewrite big_nil root0. move=> p ps ihp; rewrite big_cons /=. by rewrite (eqp_root (eqp_rgcd_gcd _ _)) root_gcd ihp. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp) mathcomp(polyorder path interval ssrint)