proposition: Lemma LimSup_InfSup_seq (u : nat -> R) : LimSup_seq u = Inf_seq (fun m => Sup_seq (fun n => u (n + m)%nat)).
proof: Proof. apply is_LimSup_seq_unique. apply is_LimSup_infSup_seq. rewrite /Inf_seq. by case: ex_inf_seq. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy