proposition: Lemma Cjoin_ball : forall (X : MetricSpace) (x : Complete (Complete X)) (e : Qpos), ball (proj1_sig e) (Cjoin_fun x) (approximate x e).
proof: Proof. intros X x e d1 d2. simpl. unfold Cjoin_raw. simpl. destruct x as [x xreg]; simpl. specialize (xreg ((1#2)*d1)%Qpos e ((1#2)*d1)%Qpos d2). simpl in xreg. setoid_replace (proj1_sig d1 + proj1_sig e + proj1_sig d2) with ((1 # 2) * proj1_sig d1 + ((1 # 2) * proj1_sig d1 + proj1_sig e) + proj1_sig d2) by ring. exact xreg. Qed.
imports: CoRN.metric2.UniformContinuity CoRN.model.structures.QposInf CoRN.metric2.Classification CoRN.model.totalorder.QposMinMax CoRN.model.totalorder.QMinMax