proposition: Lemma abs_power_neg_one : forall n:nat, Qabs ((-1)^n) == 1.
proof: Proof. induction n. reflexivity. change (S n) with (1+n)%nat. rewrite Nat2Z.inj_add, Qpower_plus. rewrite Qabs_Qmult, IHn. reflexivity. intro abs. discriminate. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.iso_CReals CoRN.reals.Q_in_CReals Coq.setoid_ring.ArithRing CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR CoRN.reals.fast.CRabs Coq.Bool.Bool CoRN.algebra.COrdAbs CoRN.model.ordfields.Qordfield CoRN.model.metric2.Qmetric CoRN.reals.fast.LazyNat CoRN.metric2.Limit CoRN.model.totalorder.QposMinMax Coq.QArith.Qpower Coq.QArith.Qabs MathClasses.theory.CoqStreams CoRN.transc.PowerSeries CoRN.tactics.CornTac CoRN.classes.Qclasses MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.series MathClasses.theory.streams CoRN.reals.fast.CRAlternatingSum