proposition: Lemma R_ln_as_IR : forall x prf, RasIR (ln x) [=] Log (RasIR x) prf.
proof: Proof. intros x prf. apply Exp_cancel. rewrite -> Exp_Log. rewrite <- R_exp_as_IR. apply R_as_IR_wd. apply exp_ln. apply R_lt_as_IR. stepl ([0]:IR); [| now symmetry; apply R_Zero_as_IR]. assumption. 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)