proposition: Lemma Qsqr_lt_one : forall (a:Q), (-(1) < a) -> a < 1 -> (a^2 < 1).
proof: Proof. intros a H0 H1. rewrite -> Qlt_minus_iff in *. replace RHS with ((1 + - a)*(a + - -(1))) by simpl; ring. Qauto_pos. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.iso_CReals CoRN.reals.fast.CRAlternatingSum CoRN.reals.fast.CRGeometricSum CoRN.reals.fast.CRstreams CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR Coq.QArith.Qabs Coq.QArith.Qpower CoRN.model.ordfields.Qordfield CoRN.reals.Q_in_CReals CoRN.model.metric2.Qmetric CoRN.model.totalorder.QMinMax CoRN.transc.ArTanH CoRN.reals.fast.CRarctan_small CoRN.tactics.Qauto CoRN.tactics.CornTac