Add Parametric Relation : CReal CRealEq
    reflexivity proved by CRealEq_refl
    symmetry proved by CRealEq_sym
    transitivity proved by CRealEq_trans
      as CRealEq_rel.#[global]
Instance CRealEq_relT : CRelationClasses.Equivalence CRealEq.#[global]
Instance CRealLt_morph
  : CMorphisms.Proper
      (CMorphisms.respectful CRealEq (CMorphisms.respectful CRealEq CRelationClasses.iffT)) CRealLt.#[global]
Instance CRealGt_morph
  : CMorphisms.Proper
      (CMorphisms.respectful CRealEq (CMorphisms.respectful CRealEq CRelationClasses.iffT)) CRealGt.#[global]
Instance CReal_appart_morph
  : CMorphisms.Proper
      (CMorphisms.respectful CRealEq (CMorphisms.respectful CRealEq CRelationClasses.iffT)) CReal_appart.Add Parametric Morphism : CRealLtProp
    with signature CRealEq ==> CRealEq ==> iff
      as CRealLtProp_morph.Add Parametric Morphism : CRealLe
    with signature CRealEq ==> CRealEq ==> iff
      as CRealLe_morph.Add Parametric Morphism : CRealGe
    with signature CRealEq ==> CRealEq ==> iff
      as CRealGe_morph.

(* Specifications: *)
Lemma CRealLt_proper_l : forall x y z : CReal, CRealEq x y -> CRealLt x z -> CRealLt y z.
Lemma CRealLt_proper_r : forall x y z : CReal, CRealEq x y -> CRealLt z x -> CRealLt z y.
Lemma CRealLe_proper_l : forall x y z : CReal, CRealEq x y -> CRealLe x z -> CRealLe y z.
Lemma CRealLe_proper_r : forall x y z : CReal, CRealEq x y -> CRealLe z x -> CRealLe z y.
Lemma inject_Q_cauchy : forall q : Q, QCauchySeq (fun _ => q).