#[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.