proposition: Lemma regFunBall_ball : forall (x y:Complete) (e0 : Q) (e1 e2:Qpos), ball e0 (approximate x e1) (approximate y e2) -> ball (proj1_sig e1 + e0 + proj1_sig e2) x y.
proof: Proof. intros x y e0 e1 e2 H d1 d2. setoid_replace (proj1_sig d1+(proj1_sig e1+e0+proj1_sig e2)+proj1_sig d2)%Q with ((proj1_sig d1+proj1_sig e1)+e0+(proj1_sig e2+proj1_sig d2)) by (simpl; ring). eapply ball_triangle. eapply ball_triangle. apply regFun_prf. apply H. apply regFun_prf. Qed.
imports: CoRN.metric2.UniformContinuity CoRN.model.structures.QposInf CoRN.metric2.Classification CoRN.model.totalorder.QposMinMax CoRN.model.totalorder.QMinMax