1theory Real_Asymp 2 imports Multiseries_Expansion_Bounds 3keywords 4 "real_limit" "real_expansion" :: diag 5begin 6 7ML_file \<open>real_asymp_diag.ML\<close> 8 9(*<*) 10(* Hide constants and lemmas to avoid polluting global namespace *) 11hide_const (open) 12gbinomial_series lcoeff mssnth MSSCons MSLNil MSLCons mslmap convergent_powser convergent_powser' 13powser mssalternate basis_wf eval_monom inverse_monom is_expansion expansion_level eval 14zero_expansion const_expansion powr_expansion power_expansion trimmed dominant_term trimmed_pos 15trimmed_neg ms_aux_hd_exp ms_exp_gt modify_eval is_lifting expands_to asymp_powser flip_cmp_result 16compare_lists compare_expansions compare_list_0 powr_nat rfloor rceil rnatmod 17 18hide_fact (open) 19convergent_powser_stl isCont_powser powser_MSLNil powser_MSLCons 20convergent_powser'_imp_convergent_powser convergent_powser'_eventually 21convergent_powser'_geometric convergent_powser'_exp convergent_powser'_ln gbinomial_series_abort 22convergent_powser'_gbinomial convergent_powser'_gbinomial' convergent_powser_sin_series_stream 23convergent_powser_cos_series_stream convergent_powser_arctan basis_wf_Nil basis_wf_Cons 24basis_wf_snoc basis_wf_singleton basis_wf_many eval_monom_Nil1 eval_monom_Nil2 eval_monom_Cons 25length_snd_inverse_monom eval_monom_pos eval_monom_uminus eval_monom_neg eval_monom_nonzero 26eval_real eval_inverse_monom eval_monom_smallo' eval_monom_smallomega' eval_monom_smallo 27eval_monom_smallomega hd_exp_powser hd_exp_inverse eval_pos_if_dominant_term_pos 28eval_pos_if_dominant_term_pos' eval_neg_if_dominant_term_neg' eval_modify_eval trimmed_pos_real_iff 29trimmed_pos_ms_iff not_trimmed_pos_MSLNil trimmed_pos_MSLCons is_liftingD is_lifting_lift hd_exp_map 30is_expansion_map is_expansion_map_aux is_expansion_map_final trimmed_map_ms is_lifting_map 31is_lifting_id is_lifting_trans is_expansion_X dominant_term_expands_to trimmed_lifting 32trimmed_pos_lifting hd_exp_powser' compare_lists.simps compare_lists_Nil compare_lists_Cons 33flip_compare_lists compare_lists_induct eval_monom_smallo_eval_monom eval_monom_eq 34compare_expansions_real compare_expansions_MSLCons_eval compare_expansions_LT_I 35compare_expansions_GT_I compare_expansions_same_exp compare_expansions_GT_flip compare_expansions_LT 36compare_expansions_GT compare_expansions_EQ compare_expansions_EQ_imp_bigo 37compare_expansions_EQ_same compare_expansions_EQ_imp_bigtheta compare_expansions_LT' 38compare_expansions_GT' compare_expansions_EQ' compare_list_0.simps compare_reals_diff_sgnD 39trimmed_realI trimmed_pos_realI trimmed_neg_realI trimmed_pos_hd_coeff lift_trimmed lift_trimmed_pos 40lift_trimmed_neg lift_trimmed_pos' lift_trimmed_neg' trimmed_eq_cong trimmed_pos_eq_cong 41trimmed_neg_eq_cong trimmed_hd trim_lift_eq basis_wf_manyI trimmed_pos_uminus 42trimmed_pos_imp_trimmed trimmed_neg_imp_trimmed intyness_0 intyness_1 intyness_numeral 43intyness_uminus intyness_of_nat intyness_simps powr_nat_of_nat powr_nat_conv_powr reify_power 44sqrt_conv_root tan_conv_sin_cos landau_meta_eq_cong 45asymp_equiv_meta_eq_cong eventually_lt_imp_eventually_le eventually_conv_filtermap 46filterlim_conv_filtermap eval_simps real_eqI lift_ms_simps nhds_leI 47(*>*) 48 49end