Add Parametric Relation : C ceq
     reflexivity  proved by (@Equivalence_Reflexive _ _ Csth)
     symmetry     proved by (@Equivalence_Symmetric _ _ Csth)
     transitivity proved by (@Equivalence_Transitive _ _ Csth)
    as C_setoid.Add Morphism cadd with signature (ceq ==> ceq ==> ceq) as cadd_ext.Add Morphism cmul with signature (ceq ==> ceq ==> ceq) as cmul_ext.Add Morphism copp with signature (ceq ==> ceq) as copp_ext.Add Morphism phi with signature (ceq ==> req) as phi_ext1.

Lemma ARth_SRth : semi_ring_theory 0 1 radd rmul req.