proposition: Lemma CompactCompleteCompact_prf : forall x, is_RegularFunction (@ball (Compact X)) (Cmap_raw FinCompact x).
proof: Proof. intros x e1 e2. unfold Cmap_raw. simpl. apply (@FinCompact_uc (e1+e2)%Qpos). unfold ball_ex. apply regFun_prf. Qed.
imports: CoRN.model.totalorder.QposMinMax CoRN.metric2.Limit CoRN.metric2.FinEnum Coq.ZArith.Zpow_facts CoRN.metric2.Complete CoRN.logic.Classic Coq.QArith.Qpower Coq.QArith.Qround CoRN.metric2.Prelength