proposition: Lemma asin_0 : asin 0 = 0.
proof: Proof. unfold asin; repeat case Rle_dec; intros; try lra. replace (0/_) with 0. - apply atan_0. - field. rewrite Rsqr_pow2; field_simplify (1 - 0^2). rewrite sqrt_1; lra. Qed.
imports: Lra Rbase PSeries_reg Rtrigo1 Rtrigo_facts Ranalysis_reg Rfunctions AltSeries Rseries SeqProp Ranalysis5 SeqSeries PartSum Lia