proposition: Lemma IR_zring_as_CR : forall z, (IRasCR (zring z) == @zring CRasCRing z)%CR.
proof: Proof. intros [|p|p]. apply IR_Zero_as_CR. apply IR_pring_as_CR. change ((IRasCR [--](pring IR p) == - ((pring CRasCRing p):CR))%CR). rewrite -> IR_opp_as_CR. apply CRopp_wd. apply IR_pring_as_CR. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.CauchySeq CoRN.reals.iso_CReals CoRN.reals.R_morphism CoRN.reals.fast.CRArith CoRN.model.reals.CRreal CoRN.tactics.CornTac