proposition: Lemma SRth_ARth : almost_ring_theory 0 1 radd rmul SRsub SRopp req.
proof: Proof. Proof (mk_art 0 1 radd rmul SRsub SRopp req (SRadd_0_l SRth) (SRadd_comm SRth) (SRadd_assoc SRth) (SRmul_1_l SRth) (SRmul_0_l SRth) (SRmul_comm SRth) (SRmul_assoc SRth) (SRdistr_l SRth) SRopp_mul_l SRopp_add SRsub_def). Variable reqb : R->R->bool. Hypothesis morph_req : forall x y, (reqb x y) = true -> x == y. Definition SRIDmorph : ring_morph 0 1 radd rmul SRsub SRopp req 0 1 radd rmul SRsub SRopp reqb (@IDphi R). Proof. now apply mkmorph. Qed.
imports: Setoid Morphisms BinPos BinNat