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).

Lemma sgr_nat n : sg n%:R = (n != 0%N)%:R :> R.