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.