#[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 CR_cv_bound_down : forall {R : ConstructiveReals} (u : nat -> CRcarrier R) (A l : CRcarrier R) (N : nat), (forall n:nat, le N n -> A <= u n) -> CR_cv R u l -> A <= l.