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. *)

Lemma real_leif_mean_square x y :
x \is real -> y \is real -> x * y <= mid (x ^+ 2) (y ^+ 2) ?= iff (x == y).