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_sum : forall {R1 R2 : ConstructiveReals}
(f : @ConstructiveRealsMorphism R1 R2)
(un : nat -> CRcarrier R1) (n : nat),
CRmorph f (CRsum un n) ==
CRsum (fun n0 : nat => CRmorph f (un n0)) n.