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).

Lemma real_ltr_normlP x y :
x \is real -> reflect ((-x < y) * (x < y)) (`|x| < y).