proposition: Lemma Cmap_fun_prf (x:Complete X) : is_RegularFunction (@ball Y) (fun e => f (approximate x (QposInf_bind (mu f) e))).
proof: Proof. intros e1 e2. simpl. apply (@mu_sum X plX Y e2 (e1::nil)). simpl. destruct (mu f e1) as [d1|]. destruct (mu f e2) as [d2|]. apply (@regFun_prf _ (@ball X)). constructor. constructor. Qed.
imports: CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.metric2.Complete CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax CoRN.stdlib_omissions.List CoRN.stdlib_omissions.Q