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 natf_indexg (gT : finGroupType) (G H : {group gT}) :
H \subset G -> #|G : H|%:R = (#|G|%:R / #|H|%:R)%R :> F.