proposition: Lemma CompactIntervalQ_nat : forall (e:Qpos), (0 <= Qceiling ((r-l)/(inject_Z 2*proj1_sig e)))%Z.
proof: Proof. intros e. change (0%Z) with (Qceiling 0). apply Qceiling_resp_le. apply Qle_shift_div_l. auto with *. rewrite Qmult_0_l. unfold Qminus. rewrite <- Qle_minus_iff. exact Hlr. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.totalorder.QposMinMax CoRN.metric2.Compact CoRN.metric2.LocatedSubset CoRN.reals.fast.CRArith CoRN.reals.fast.CRabs CoRN.model.metric2.Qmetric Coq.QArith.Qround Coq.QArith.Qabs CoRN.model.totalorder.QMinMax CoRN.logic.Classic