proposition: Lemma asin_sin : forall x, -(PI/2) <= x <= PI/2 -> asin (sin x) = x.
proof: Proof. intros x HB. apply sin_inj; auto. { apply asin_bound. } apply sin_asin. apply SIN_bound. Qed.
imports: Lra Rbase PSeries_reg Rtrigo1 Rtrigo_facts Ranalysis_reg Rfunctions AltSeries Rseries SeqProp Ranalysis5 SeqSeries PartSum Lia