End NormedModule2.
(** Rings with absolute values are normed modules *)
Section AbsRing_NormedModule.
Variable (K : AbsRing).
Canonical AbsRing_NormedModuleAux :=
NormedModuleAux.Pack K K (NormedModuleAux.Class _ _ (ModuleSpace.class _ (AbsRing_ModuleSpace K)) (UniformSpace.class (AbsRing_UniformSpace K))) K.

Lemma AbsRing_norm_compat2 :
forall (x y : AbsRing_NormedModuleAux) (eps : posreal),
ball x eps y -> abs (minus y x) < 1 * eps.