proposition: Lemma derivable_pt_tan : forall x, -PI/2 < x < PI/2 -> derivable_pt tan x.
proof: Proof. intros x xint. unfold derivable_pt, tan. apply derivable_pt_div ; [reg | reg | ]. apply Rgt_not_eq. unfold Rgt ; apply cos_gt_0; [unfold Rdiv; rewrite <- Ropp_mult_distr_l_reverse; fold (-PI/2) |];tauto. Qed.
imports: Lra Rbase PSeries_reg Rtrigo1 Rtrigo_facts Ranalysis_reg Rfunctions AltSeries Rseries SeqProp Ranalysis5 SeqSeries PartSum Lia