#[global]
Instance CR_cv_morph
: forall {R : ConstructiveReals} (un : nat -> CRcarrier R), CMorphisms.Proper
(CMorphisms.respectful (CReq R) CRelationClasses.iffT) (CR_cv R un).

Lemma Un_cv_real_nat : forall {R : ConstructiveReals}
(un : nat -> CRcarrier R) (l : CRcarrier R),
(forall eps : CRcarrier R,
0 < eps
-> { p : nat & forall i:nat, le p i -> CRabs R (un i - l) < eps })
-> CR_cv R un l.