proposition: Lemma is_lim_seq_incr_n (u : nat -> R) (N : nat) (l : Rbar) : is_lim_seq u l <-> is_lim_seq (fun n => u (n + N)%nat) l.
proof: Proof. split. elim: N u => [ | N IH] u Hu. move: Hu ; apply is_lim_seq_ext => n ; by rewrite Nat.add_0_r. apply is_lim_seq_incr_1, IH in Hu. move: Hu ; by apply is_lim_seq_ext => n ; by rewrite plus_n_Sm. elim: N u => [ | N IH] u Hu. move: Hu ; apply is_lim_seq_ext => n ; by rewrite Nat.add_0_r. apply is_lim_seq_incr_1, IH. move: Hu ; by apply is_lim_seq_ext => n ; by rewrite plus_n_Sm. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Lub Markov Hierarchy