proposition: Lemma rational_arctan_big_pos_correct : forall a (Ha: 1 < a), (rational_arctan_big_pos Ha == IRasCR (ArcTan (inj_Q IR a)))%CR.
proof: Proof. intros a Ha. unfold rational_arctan_big_pos. rewrite -> rational_arctan_small_correct. apply rational_arctan_big_pos_correct_aux. now apply Qlt_trans with 1. 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