Section NormedModule1.
Context {K : AbsRing} {V : NormedModule K}.
Definition norm : V -> R := NormedModule.norm K _ (NormedModule.class K V).
Definition norm_factor : R := NormedModule.norm_factor K _ (NormedModule.class K V).

Lemma norm_compat2 :
forall (x y : V) (eps : posreal), ball x eps y -> norm (minus y x) < norm_factor * eps.