proposition: Lemma cn_zero_zero : forall N, cn 0 N = 0.
proof: Proof. intros. cut (2 * cn 0 N = 0). intro H. apply Rmult_integral in H. destruct H. lra. assumption. rewrite double. replace (cn 0 N + cn 0 N) with (cn 0 N + cn (- 0) N) by (inject; ring). rewrite cn_odd. ring. Qed.
imports: Reals Lra Rsequence_facts Rseries Rsequence_subsequence Rtactic Lia ZArith