(** Continuity of norm *)

Lemma filterlim_norm_zero {U} {K : AbsRing} {V : NormedModule K}
{F : (U -> Prop) -> Prop} {FF : Filter F} (f : U -> V) :
filterlim (fun x => norm (f x)) F (locally 0)
-> filterlim f F (locally (zero (G := V))).