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.

(* Specifications: *)
Lemma Smorph_opp x : [-!x] == -[x].
Lemma Smorph_sub x y : [x -! y] == [x] - [y].
Lemma Smorph_morph : ring_morph 0 1 radd rmul rsub ropp req cO cI cadd cmul csub copp ceqb phi.
Lemma ARth_SRth : semi_ring_theory 0 1 radd rmul req.