proposition: Lemma AQarctan_big_pos_prf (a : AQ) : 1 < a → 0 < a.
proof: Proof. intros. apply (orders.le_lt_trans _ 1). 2: exact H5. apply semirings.le_0_1. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.metric2.MetricMorphisms CoRN.reals.fast.CRarctan_small CoRN.reals.fast.CRarctan CoRN.reals.fast.CRpi_fast CoRN.reals.faster.ARpi CoRN.reals.faster.ARarctan_small CoRN.reals.faster.ARArith