proposition: Lemma CR_cv_shift : forall {R : ConstructiveReals} f k l, CR_cv R (fun n => f (n + k)%nat) l -> CR_cv R f l.
proof: Proof. intros. intros eps. specialize (H eps) as [N Nmaj]. exists (N+k)%nat. intros n H. destruct (Nat.le_exists_sub k n). - apply (Nat.le_trans _ (N + k)). 2: exact H. apply (Nat.le_trans _ (0 + k)). + apply Nat.le_refl. + rewrite <- Nat.add_le_mono_r. apply Nat.le_0_l. - destruct H0. subst n. apply Nmaj. unfold ge in H. rewrite <- Nat.add_le_mono_r in H. exact H. Qed.
imports: QArith Qabs ConstructiveReals ConstructiveAbs