proposition: Lemma ball_clamp : forall (e:Qpos) (a b : Q), @ball Q_as_MetricSpace (proj1_sig e) a b -> ball (proj1_sig e) (clamp a) (clamp b).
proof: Proof. destruct l; destruct r; unfold clamp; intros e a b Hab; try apply uc_prf; apply Hab. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.Q_in_CReals CoRN.reals.fast.CRIR CoRN.ftc.Rolle CoRN.tactics.CornTac CoRN.model.metric2.Qmetric CoRN.model.totalorder.QposMinMax CoRN.model.totalorder.QMinMax