proposition: Lemma Lim_seq_ext_loc (u v : nat -> R) : eventually (fun n => u n = v n) -> Lim_seq u = Lim_seq v.
proof: Proof. intros. rewrite /Lim_seq. apply (f_equal (fun x => Rbar_div_pos x _)). apply f_equal2 ; apply sym_eq. apply is_LimSup_seq_unique. apply is_LimSup_seq_ext_loc with u. by []. rewrite /LimSup_seq ; by case: ex_LimSup_seq. apply is_LimInf_seq_unique. apply is_LimInf_seq_ext_loc with u. by []. rewrite /LimInf_seq ; by case: ex_LimInf_seq. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy