proposition: Lemma is_lim_seq_Reals (u : nat -> R) (l : R) : is_lim_seq u l <-> Un_cv u l.
proof: Proof. split => Hl. move => e He. apply (Hl (fun y => R_dist y l < e)). now exists (mkposreal _ He). unfold is_lim_seq. change (Rbar_locally l) with (locally l). apply (filterlim_locally u l). case => e He. case: (Hl e He) => {Hl} /= N Hl. exists N => n Hn. by apply (Hl n Hn). Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy