proposition: Lemma rational_arctan_correct : forall (a:Q), (rational_arctan a == IRasCR (ArcTan (inj_Q IR a)))%CR.
proof: Proof. intros a. unfold rational_arctan. destruct (Qle_total a 0); rewrite -> rational_arctan_pos_correct. apply rational_arctan_small_correct_aux. reflexivity. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR CoRN.reals.Q_in_CReals CoRN.model.totalorder.QMinMax CoRN.reals.fast.CRarctan_small CoRN.reals.fast.CRpi CoRN.transc.MoreArcTan CoRN.reals.fast.ModulusDerivative CoRN.reals.fast.ContinuousCorrect CoRN.tactics.CornTac CoRN.stdlib_omissions.Q MathClasses.interfaces.abstract_algebra Coq.micromega.Psatz