proposition: Lemma AQsin_bound_pos : forall a, 0 < 1 * 3 ^ AQsin_bound a.
proof: Proof. intro a. destruct H4, aq_ring, ring_monoid. destruct commonoid_mon. rewrite monoid_left_id. apply (strictly_order_reflecting (cast AQ Q)). rewrite preserves_nat_pow. rewrite rings.preserves_3. rewrite <- (int_pow_nat_pow (f:=cast nat Z)). rewrite rings.preserves_0. apply (Qpower_0_lt 3 (Z.of_nat (AQsin_bound a))). reflexivity. Qed.
imports: Coq.QArith.Qround Coq.QArith.Qpower MathClasses.interfaces.abstract_algebra MathClasses.theory.nat_pow MathClasses.theory.int_pow CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.MetricMorphisms CoRN.metric2.UniformContinuity CoRN.model.totalorder.QMinMax CoRN.util.Qdlog CoRN.stdlib_omissions.Q CoRN.reals.fast.CRsin CoRN.reals.fast.CRstreams CoRN.reals.fast.CRAlternatingSum CoRN.reals.fast.Compress CoRN.reals.faster.ARAlternatingSum CoRN.reals.faster.ARArith