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_le0 x : (sgr x <= 0) = (x <= 0).