proposition: Lemma atan_opp : forall x, atan (- x) = - atan x.
proof: Proof. intros x; generalize (atan_bound (-x)); rewrite Rdiv_opp_l;intros [a b]. generalize (atan_bound x); rewrite Rdiv_opp_l; intros [c d]. apply tan_inj; try rewrite Rdiv_opp_l; try split; try lra. rewrite tan_neg, !tan_atan; reflexivity. Qed.
imports: Lra Rbase PSeries_reg Rtrigo1 Rtrigo_facts Ranalysis_reg Rfunctions AltSeries Rseries SeqProp Ranalysis5 SeqSeries PartSum Lia