Section FinGroup.
Variables (R : numDomainType) (gT : finGroupType).
Implicit Types G : {group gT}.
Definition midf_lte := (midf_le, midf_lt).
(* The AGM, unscaled but without the nth root. *)
Implicit Type p : {poly F}.

Lemma Cauchy_root_bound p : p != 0 -> {b | forall x, root p x -> `|x| <= b}.