Section NormedZmoduleTheory.
Variable V : normedZmodType R.
Implicit Types (u v w : V).
Hint Resolve normr_real : core.
Arguments real_ler_normlP {x y}.
Definition real_lter_norml := (real_ler_norml, real_ltr_norml).
Arguments real_ltr_normlP {x y}.
Definition real_lter_normr := (real_ler_normr, real_ltr_normr).
(* lteif *)

Lemma leif_AGM_scaled (I : finType) (A : {pred I}) (E : I -> R) (n := #|A|) :
{in A, forall i, 0 <= E i *+ n} ->
\prod_(i in A) (E i *+ n) <= (\sum_(i in A) E i) ^+ n
?= iff [forall i in A, forall j in A, E i == E j].