proposition: Lemma Smorph_morph : ring_morph 0 1 radd rmul rsub ropp req cO cI cadd cmul csub copp ceqb phi.
proof: Proof. 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. Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req. Lemma ARth_SRth : semi_ring_theory 0 1 radd rmul req. Proof. elim ARth; intros. constructor; trivial. Qed.
imports: Setoid Morphisms BinPos BinNat