Add Parametric Morphism {R : ConstructiveReals} : (CRplus R)
    with signature CReq R ==> CReq R ==> CReq R
      as CRplus_morph.Add Parametric Morphism {R : ConstructiveReals} : (CRopp R)
    with signature CReq R ==> CReq R
      as CRopp_morph.Add Parametric Morphism {R : ConstructiveReals} : (CRmult R)
    with signature CReq R ==> CReq R ==> CReq R
      as CRmult_morph.#[global]
Instance CRplus_morph_T
  : forall {R : ConstructiveReals}, CMorphisms.Proper
      (CMorphisms.respectful (CReq R) (CMorphisms.respectful (CReq R) (CReq R))) (CRplus R).#[global]
Instance CRmult_morph_T
  : forall {R : ConstructiveReals}, CMorphisms.Proper
      (CMorphisms.respectful (CReq R) (CMorphisms.respectful (CReq R) (CReq R))) (CRmult R).#[global]
Instance CRopp_morph_T
  : forall {R : ConstructiveReals}, CMorphisms.Proper
      (CMorphisms.respectful (CReq R) (CReq R)) (CRopp R).Add Parametric Morphism {R : ConstructiveReals} : (CRminus R)
    with signature (CReq R) ==> (CReq R) ==> (CReq R)
      as CRminus_morph.#[global]
Instance CRminus_morph_T
  : forall {R : ConstructiveReals}, CMorphisms.Proper
      (CMorphisms.respectful (CReq R) (CMorphisms.respectful (CReq R) (CReq R))) (CRminus R).

Lemma CRinv_mult_distr : forall {R : ConstructiveReals} (r1 r2 : CRcarrier R) (r1nz : r1 ≶ 0) (r2nz : r2 ≶ 0) (rmnz : (r1*r2) ≶ 0), (/ (r1 * r2)) rmnz == (/ r1) r1nz * (/ r2) r2nz.