proposition: Lemma filterlim_closely_norm {F : (T -> Prop) -> Prop} {FF : Filter F} (f : T -> V) : filterlim (fun x => (f (fst x), f (snd x))) (filter_prod F F) closely_norm <-> (forall eps : posreal, exists P, F P /\ forall u v : T, P u -> P v -> ball_norm (f u) eps (f v)).
proof: Proof. apply filterlim_prod. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Markov Iter Lub