Add Parametric Relation {R : ConstructiveReals} : (CRcarrier R) (CReq R)
    reflexivity proved by (CReq_refl)
    symmetry proved by (CReq_sym)
    transitivity proved by (CReq_trans)
      as CReq_rel.#[global]
Instance CReq_relT : forall {R : ConstructiveReals},
    CRelationClasses.Equivalence (CReq R).#[global]
Instance CRlt_morph
  : forall {R : ConstructiveReals}, CMorphisms.Proper
      (CMorphisms.respectful (CReq R) (CMorphisms.respectful (CReq R) CRelationClasses.iffT)) (CRlt R).Add Parametric Morphism {R : ConstructiveReals} : (CRle R)
    with signature CReq R ==> CReq R ==> iff
      as CRle_morph.

Lemma CRplus_le_lt_compat : forall {R : ConstructiveReals} (r1 r2 r3 r4 : CRcarrier R), r1 <= r2 -> r3 < r4 -> r1 + r3 < r2 + r4.