proposition: Lemma sqrt_id : forall n : nat, (INR n <> 0)%R -> sqrt (2 * n) / (2 * n) = /sqrt (2 * n).
proof: Proof. intros n H1. rewrite <- (sqrt_sqrt (2 * n)) at 2. field. intro H. apply H1. apply Rmult_eq_reg_l with 2. rewrite Rmult_0_r. apply sqrt_eq_0 ; intuition. apply Rmult_le_pos ; intuition. intro ; lra. apply Rmult_le_pos ; intuition. Qed.
imports: PeanoNat Reals Rintegral Rintegral_usual Rintegral_tactic Lia Lra Rsequence_facts Rsequence_subsequence Rpser RTaylor MyRfunctions Rsequence_tactics