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.