(** Absolute value *)

(* Specifications: *)
Lemma filterlim_Rabs :
forall l : Rbar,
filterlim Rabs (Rbar_locally l) (Rbar_locally (Rbar_abs l)).
Lemma is_lim_seq_abs (u : nat -> R) (l : Rbar) :
is_lim_seq u l -> is_lim_seq (fun n => Rabs (u n)) (Rbar_abs l).
Lemma ex_lim_seq_abs (u : nat -> R) :
ex_lim_seq u -> ex_lim_seq (fun n => Rabs (u n)).
Lemma Lim_seq_abs (u : nat -> R) :
ex_lim_seq u ->
Lim_seq (fun n => Rabs (u n)) = Rbar_abs (Lim_seq u).
Lemma is_lim_seq_abs_0 (u : nat -> R) :
is_lim_seq u 0 <-> is_lim_seq (fun n => Rabs (u n)) 0.