Definition series_cv_abs {R : ConstructiveReals} (u : nat -> CRcarrier R)
  : CR_cauchy R (CRsum (fun n => CRabs R (u n)))
    -> { l : CRcarrier R & series_cv u l }.

Lemma CRmorph_series_cv : forall {R1 R2 : ConstructiveReals} (f : @ConstructiveRealsMorphism R1 R2) (un : nat -> CRcarrier R1) (l : CRcarrier R1), series_cv un l -> series_cv (fun n => CRmorph f (un n)) (CRmorph f l).