proposition: Lemma R_div_as_IR : forall x y Hy, (RasIR (x/y) [=] (RasIR x [/] RasIR y [//] Hy)).
proof: Proof. intros x y Hy. unfold Rdiv. rewrite -> R_mult_as_IR. rstepr ((RasIR x) [*] ([1] [/]RasIR y[//]Hy)). replace (/ y) with (1 / y). rewrite <- R_recip_as_IR; reflexivity. unfold Rdiv. ring. Qed.
imports: Coq.QArith.QArith Coq.QArith.Qreals Coq.QArith.QArith_base CoRN.tactics.CornTac Coq.Reals.RIneq Coq.Reals.Rcomplete Coq.Reals.Rlimit Coq.Reals.Rbasic_fun CoRN.coq_reals.Rreals CoRN.reals.iso_CReals CoRN.reals.CauchySeq Coq.Reals.Rtrigo_def CoRN.transc.PowerSeries Coq.Logic.ConstructiveEpsilon Coq.Reals.Rlogic Coq.Reals.Reals CoRN.transc.Pi CoRN.transc.MoreArcTan CoRN.logic.PropDecid CoRN.transc.Exponential Coq(Lia Lra)