Proof
(mkmorph 0 1 radd rmul rsub ropp req cO cI cadd cmul csub copp ceqb phi
(Smorph0 Smorph) (Smorph1 Smorph)
(Smorph_add Smorph) Smorph_sub (Smorph_mul Smorph) Smorph_opp
(Smorph_eq Smorph)).
End RING.
(** Useful lemmas on almost ring *)
Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req.

(* Specifications: *)
Lemma ARth_SRth : semi_ring_theory 0 1 radd rmul req.
Instance ARsub_ext : Proper (req ==> req ==> req) rsub.