proposition: Lemma Qinv_one_lt : forall (a:Q), 1 < a -> -1 < /a < 1.
proof: Proof. split. apply (Qlt_le_trans _ 0). reflexivity. apply Qinv_le_0_compat; apply Qle_trans with 1; auto with qarith. change (/a < /1); apply Q.Qdiv_flip_lt; auto with qarith. 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