Definition AbsRing_NormedModule_mixin :=
NormedModule.Mixin K _ abs 1 abs_triangle abs_mult (fun x y e H => H) AbsRing_norm_compat2 abs_eq_zero.
Canonical AbsRing_NormedModule :=
NormedModule.Pack K _ (NormedModule.Class _ _ _ AbsRing_NormedModule_mixin) K.
End AbsRing_NormedModule.
(** Normed vector spaces have some continuous functions *)
Section NVS_continuity.
Context {K : AbsRing} {V : NormedModule K}.

Lemma filterlim_plus :
forall x y : V,
filterlim (fun z : V * V => plus (fst z) (snd z)) (filter_prod (locally x) (locally y)) (locally (plus x y)).