proposition: Lemma Cmap_slow_raw_strongInf : forall (x:Complete X) (d:QposInf) (e:QposInf), QposInf_le d (QposInf_mult (Qpos2QposInf (exist (Qlt 0) (1#2) eq_refl)) (QposInf_bind (mu f) e)) -> ball_ex e (f (approximate x d)) (Cmap_slow_raw x e).
proof: Proof. intros x [d|] [e|] Hd; try constructor. - apply uc_prf. simpl. case_eq (mu f e); simpl; trivial. intros q Hq. simpl in Hd. rewrite Hq in Hd. eapply ball_weak_le;[|apply regFun_prf]. simpl. simpl in Hd. apply (Qplus_le_l _ _ (-(1#2)*proj1_sig q)). ring_simplify. exact Hd. - unfold Cmap_slow_raw. simpl in *. apply uc_prf. destruct (mu f e) as [q|]. contradiction. constructor. Qed.
imports: CoRN.metric2.UniformContinuity CoRN.model.structures.QposInf CoRN.metric2.Classification CoRN.model.totalorder.QposMinMax CoRN.model.totalorder.QMinMax