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Datei: deriv_domain_def.pvs Sprache: Lisp
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rahmenlose Ansicht.summary DruckansichtMT940 {MT940[537] Hlasm[1257] Haskell[1657]}zum Wurzelverzeichnis wechseln *** *** top (16:28:29 11/7/2014) *** Generated by proveit - ProofLite-6.0.9 (3/14/14) *** Proof summary for theory top Theory totals: 0 formulas, 0 attempted, 0 succeeded (0.00 s) Proof summary for theory fundamental_theorem deriv_domain..........................proved - complete [shostak](0.02 s) IMP_derivative_props_TCC1.............proved - complete [shostak](0.00 s) IMP_derivative_props_TCC2.............proved - complete [shostak](0.01 s) fundamental_TCC1......................proved - complete [shostak](0.04 s) fundamental_TCC2......................proved - complete [shostak](0.00 s) fundamental2_TCC1.....................proved - complete [shostak](0.00 s) fundamental2..........................proved - complete [shostak](0.07 s) fundamental3_TCC1.....................proved - complete [shostak](0.00 s) derivable_Integrable?.................proved - complete [shostak](0.17 s) fundamental3b.........................proved - complete [shostak](0.01 s) Theory totals: 10 formulas, 10 attempted, 10 succeeded (0.32 s) Proof summary for theory deriv_domain_def connected_deriv_domain................proved - complete [shostak](0.16 s) del_neigh_all_lem.....................proved - complete [shostak](0.17 s) Theory totals: 2 formulas, 2 attempted, 2 succeeded (0.32 s) Proof summary for theory integral IMP_integral_def_TCC1.................proved - complete [shostak](0.00 s) IMP_integral_def_TCC2.................proved - complete [shostak](0.01 s) Integral_a_to_a_TCC1..................proved - complete [shostak](0.00 s) cont_Integrable?......................proved - complete [shostak](0.02 s) cont_fun_Integrable?..................proved - complete [shostak](0.01 s) Integral_diff.........................proved - complete [shostak](0.14 s) Integral_neg..........................proved - complete [shostak](0.05 s) Theory totals: 7 formulas, 7 attempted, 7 succeeded (0.22 s) Proof summary for theory integral_def integral_TCC1.........................proved - complete [shostak](0.03 s) Integral_rew_TCC1.....................proved - complete [shostak](0.01 s) Theory totals: 2 formulas, 2 attempted, 2 succeeded (0.04 s) Proof summary for theory derivatives IMP_derivatives_def_TCC1..............proved - complete [shostak](0.00 s) IMP_derivatives_def_TCC2..............proved - complete [shostak](0.00 s) deriv_TCC1............................proved - complete [shostak](0.01 s) derivable_cont_fun....................proved - complete [shostak](0.03 s) sum_derivable_fun.....................proved - complete [shostak](0.04 s) neg_derivable_fun.....................proved - complete [shostak](0.03 s) diff_derivable_fun....................proved - complete [shostak](0.04 s) prod_derivable_fun....................proved - complete [shostak](0.05 s) scal_derivable_fun....................proved - complete [shostak](0.03 s) const_derivable_fun...................proved - complete [shostak](0.00 s) inv_derivable_fun.....................proved - complete [shostak](0.02 s) div_derivable_fun.....................proved - complete [shostak](0.05 s) identity_derivable_fun................proved - complete [shostak](0.00 s) id_derivable_fun......................proved - complete [shostak](0.00 s) derivable_cont........................proved - complete [shostak](0.01 s) nz_derivable_cont.....................proved - complete [shostak](0.00 s) derivable_sum.........................proved - complete [shostak](0.01 s) derivable_diff........................proved - complete [shostak](0.00 s) derivable_prod........................proved - complete [shostak](0.01 s) derivable_scal........................proved - complete [shostak](0.00 s) derivable_neg.........................proved - complete [shostak](0.00 s) derivable_div.........................proved - complete [shostak](0.00 s) derivable_inv.........................proved - complete [shostak](0.06 s) derivable_const.......................proved - complete [shostak](0.01 s) derivable_id..........................proved - complete [shostak](0.00 s) deriv_sum_fun.........................proved - complete [shostak](0.04 s) deriv_neg_fun.........................proved - complete [shostak](0.02 s) deriv_diff_fun........................proved - complete [shostak](0.03 s) deriv_prod_fun........................proved - complete [shostak](0.06 s) deriv_scal_fun........................proved - complete [shostak](0.03 s) deriv_inv_fun_TCC1....................proved - complete [shostak](0.01 s) deriv_inv_fun.........................proved - complete [shostak](0.05 s) deriv_scaldiv_fun.....................proved - complete [shostak](0.11 s) deriv_div_fun.........................proved - complete [shostak](0.08 s) deriv_const_fun_TCC1..................proved - complete [shostak](-.00 s) deriv_const_fun.......................proved - complete [shostak](0.02 s) deriv_const_func......................proved - complete [shostak](0.01 s) deriv_id_fun_TCC1.....................proved - complete [shostak](0.00 s) deriv_id_fun..........................proved - complete [shostak](0.04 s) deriv_I_fun...........................proved - complete [shostak](0.00 s) deriv_linear_fun......................proved - complete [shostak](0.20 s) deriv_exp_fun_TCC1....................proved - complete [shostak](0.01 s) deriv_x_n_TCC1........................proved - complete [shostak](0.01 s) deriv_x_n_TCC2........................proved - complete [shostak](0.03 s) deriv_x_n.............................proved - complete [shostak](0.13 s) deriv_x_to_n_TCC1.....................proved - complete [shostak](0.00 s) deriv_x_to_n_TCC2.....................proved - complete [shostak](0.02 s) deriv_x_to_n..........................proved - complete [shostak](0.18 s) Theory totals: 48 formulas, 48 attempted, 48 succeeded (1.48 s) Proof summary for theory derivatives_def div_derivable.........................proved - complete [shostak](0.02 s) deriv_sum_TCC1........................proved - complete [shostak](0.00 s) deriv_neg_TCC1........................proved - complete [shostak](0.00 s) deriv_diff_TCC1.......................proved - complete [shostak](0.01 s) deriv_prod_TCC1.......................proved - complete [shostak](0.00 s) deriv_const_TCC1......................proved - complete [shostak](0.00 s) deriv_scal_TCC1.......................proved - complete [shostak](0.00 s) deriv_inv_TCC1........................proved - complete [shostak](0.01 s) deriv_div_TCC1........................proved - complete [shostak](0.00 s) deriv_div.............................proved - complete [shostak](0.15 s) deriv_identity_TCC1...................proved - complete [shostak](0.00 s) Theory totals: 11 formulas, 11 attempted, 11 succeeded (0.19 s) Proof summary for theory continuous_functions expt_continuous.......................proved - complete [shostak](0.07 s) const_set_continuous..................proved - complete [shostak](0.02 s) identity_set_continuous...............proved - complete [shostak](0.05 s) continuous_def2.......................proved - complete [shostak](0.16 s) continuity_subset2....................proved - complete [shostak](0.08 s) continuous_fun_TCC1...................proved - complete [shostak](0.01 s) sum_fun_continuous....................proved - complete [shostak](0.01 s) diff_fun_continuous...................proved - complete [shostak](0.02 s) prod_fun_continuous...................proved - complete [shostak](0.01 s) const_fun_continuous..................proved - complete [shostak](0.01 s) scal_fun_continuous...................proved - complete [shostak](0.01 s) neg_fun_continuous....................proved - complete [shostak](0.01 s) div_fun_continuous....................proved - complete [shostak](0.01 s) id_fun_continuous.....................proved - complete [shostak](0.01 s) inv_fun_continuous....................proved - complete [shostak](0.01 s) linear_fun_cont.......................proved - complete [shostak](0.08 s) one_over_x_cont_TCC1..................proved - complete [shostak](0.00 s) one_over_x_cont.......................proved - complete [shostak](0.03 s) x_to_n_continuous_TCC1................proved - complete [shostak](0.00 s) x_to_n_continuous.....................proved - complete [shostak](0.14 s) expt_fun_continuous...................proved - complete [shostak](0.01 s) sum_cont_fun..........................proved - complete [shostak](0.02 s) diff_cont_fun.........................proved - complete [shostak](0.03 s) prod_cont_fun.........................proved - complete [shostak](0.02 s) const_cont_fun........................proved - complete [shostak](0.00 s) scal_cont_fun.........................proved - complete [shostak](0.01 s) neg_cont_fun..........................proved - complete [shostak](0.01 s) div_cont_fun..........................proved - complete [shostak](0.03 s) inv_cont_fun..........................proved - complete [shostak](0.01 s) identity_cont_fun.....................proved - complete [shostak](0.00 s) expt_cont_fun.........................proved - complete [shostak](0.00 s) Theory totals: 31 formulas, 31 attempted, 31 succeeded (0.88 s) Proof summary for theory derivative_props deriv_domain..........................proved - complete [shostak](0.00 s) deriv_maximum_TCC1....................proved - complete [shostak](0.01 s) deriv_maximum_TCC2....................proved - complete [shostak](0.00 s) deriv_minimum.........................proved - complete [shostak](0.08 s) mean_value_aux_TCC1...................proved - complete [shostak](0.00 s) mean_value_aux_TCC2...................proved - complete [shostak](0.00 s) mean_value_aux_TCC3...................proved - complete [shostak](0.01 s) mean_value_TCC1.......................proved - complete [shostak](0.00 s) mean_value............................proved - complete [shostak](0.31 s) mean_value_abs_TCC1...................proved - complete [shostak](0.00 s) nonneg_derivative_TCC1................proved - complete [shostak](0.01 s) positive_derivative...................proved - complete [shostak](0.11 s) negative_derivative...................proved - complete [shostak](0.11 s) null_derivative.......................proved - complete [shostak](0.13 s) minimum_derivative....................proved - complete [shostak](0.29 s) maximum_derivative....................proved - complete [shostak](0.16 s) strict_minimum_derivative.............proved - complete [shostak](0.08 s) strict_maximum_derivative.............proved - complete [shostak](0.12 s) monotonic_antideriv...................proved - complete [shostak](0.07 s) epsi_lt_le............................proved - complete [shostak](0.03 s) Theory totals: 20 formulas, 20 attempted, 20 succeeded (1.52 s) Proof summary for theory continuous_functions_props inj_continuous........................proved - complete [shostak](0.07 s) inj_monotone..........................proved - complete [shostak](0.11 s) Theory totals: 2 formulas, 2 attempted, 2 succeeded (0.19 s) Proof summary for theory table_of_integrals IMP_fundamental_theorem_TCC1..........proved - complete [shostak](0.00 s) IMP_fundamental_theorem_TCC2..........proved - complete [shostak](0.00 s) antideriv_x_to_n_TCC1.................proved - complete [shostak](0.01 s) antideriv_x_to_n_TCC2.................proved - complete [shostak](0.01 s) antideriv_x_to_n......................proved - complete [shostak](0.29 s) integral_x_to_n.......................proved - complete [shostak](0.41 s) integral_linear_TCC1..................proved - complete [shostak](0.02 s) integral_linear.......................proved - complete [shostak](0.38 s) integral_quadratic_TCC1...............proved - complete [shostak](0.01 s) integral_quadratic_TCC2...............proved - complete [shostak](0.04 s) integral_quadratic_TCC3...............proved - complete [shostak](0.03 s) integral_quadratic....................proved - complete [shostak](0.55 s) Theory totals: 12 formulas, 12 attempted, 12 succeeded (1.75 s) Proof summary for theory indefinite_integral deriv_domain..........................proved - complete [shostak](0.01 s) IMP_integral_TCC1.....................proved - complete [shostak](0.00 s) IMP_integral_TCC2.....................proved - complete [shostak](0.00 s) antiderivative?_TCC1..................proved - complete [shostak](0.00 s) antiderivative_lem....................proved - complete [shostak](0.16 s) derivs_eq.............................proved - complete [shostak](0.01 s) cont_fun_integrable?..................proved - complete [shostak](0.14 s) integral_TCC1.........................proved - complete [shostak](0.03 s) integral_lem..........................proved - complete [shostak](0.01 s) deriv_integ...........................proved - complete [shostak](0.00 s) indef_integral_thm_TCC1...............proved - complete [shostak](0.19 s) indef_integral_thm....................proved - complete [shostak](0.02 s) fundamental_indef_TCC1................proved - complete [shostak](0.01 s) fundamental_indef.....................proved - complete [shostak](0.02 s) Theory totals: 14 formulas, 14 attempted, 14 succeeded (0.60 s) Proof summary for theory taylors deriv_domain..........................proved - complete [shostak](0.00 s) sigma_derivable_TCC1..................proved - complete [shostak](0.01 s) sigma_derivable_TCC2..................proved - complete [shostak](0.00 s) sigma_derivable_TCC3..................proved - complete [shostak](0.01 s) sigma_derivable.......................proved - complete [shostak](0.19 s) tay1_TCC1.............................proved - complete [shostak](0.01 s) tay1..................................proved - complete [shostak](0.13 s) tay2..................................proved - complete [shostak](0.04 s) tay3_TCC1.............................proved - complete [shostak](0.02 s) tay3..................................proved - complete [shostak](0.40 s) deriv_sigma_TCC1......................proved - complete [shostak](0.01 s) deriv_sigma_TCC2......................proved - complete [shostak](0.01 s) deriv_sigma...........................proved - complete [shostak](0.34 s) nderiv_term_derivable_TCC1............proved - complete [shostak](0.03 s) nderiv_term_derivable.................proved - complete [shostak](0.14 s) taylor_derivable_TCC1.................proved - complete [shostak](0.02 s) taylor_derivable_TCC2.................proved - complete [shostak](0.03 s) taylor_derivable_TCC3.................proved - complete [shostak](0.04 s) taylor_derivable......................proved - complete [shostak](0.31 s) deriv_nderiv_TCC1.....................proved - complete [shostak](0.02 s) deriv_nderiv_TCC2.....................proved - complete [shostak](0.05 s) deriv_nderiv_TCC3.....................proved - complete [shostak](0.04 s) deriv_nderiv..........................proved - complete [shostak](0.04 s) term_by_term_deriv_TCC1...............proved - complete [shostak](0.03 s) term_by_term_deriv_TCC2...............proved - complete [shostak](0.04 s) term_by_term_deriv_TCC3...............proved - complete [shostak](0.04 s) term_by_term_deriv_TCC4...............proved - complete [shostak](0.11 s) term_by_term_deriv....................proved - complete [shostak](1.50 s) taylor_lemma_TCC1.....................proved - complete [shostak](0.06 s) taylor_lemma..........................proved - complete [shostak](0.65 s) Taylors...............................proved - complete [shostak](2.60 s) Taylor_term_TCC1......................proved - complete [shostak](0.02 s) Taylors_inf_TCC1......................proved - complete [shostak](0.01 s) Taylors_inf_TCC2......................proved - complete [shostak](0.06 s) Taylors_inf...........................proved - complete [shostak](0.35 s) Theory totals: 35 formulas, 35 attempted, 35 succeeded (7.35 s) Proof summary for theory nth_derivatives derivable_n_times?_TCC1...............proved - complete [shostak](0.01 s) derivable_n_times?_TCC2...............proved - complete [shostak](0.00 s) derivable_n_times?_TCC3...............proved - complete [shostak](0.02 s) derivable_n_times?_TCC4...............proved - complete [shostak](0.00 s) derivable_n_times_lem.................proved - complete [shostak](0.08 s) derivable_n_times_def_TCC1............proved - complete [shostak](0.01 s) derivable_n_times_def_TCC2............proved - complete [shostak](0.01 s) derivable_n_times_def_TCC3............proved - complete [shostak](0.00 s) derivable_n_times_def.................proved - complete [shostak](0.00 s) nderiv_TCC1...........................proved - complete [shostak](0.01 s) nderiv_TCC2...........................proved - complete [shostak](0.01 s) nderiv_TCC3...........................proved - complete [shostak](0.00 s) nderiv_TCC4...........................proved - complete [shostak](0.01 s) nderiv_derivable_TCC1.................proved - complete [shostak](0.02 s) nderiv_derivable_TCC2.................proved - complete [shostak](0.00 s) nderiv_derivable_TCC3.................proved - complete [shostak](0.00 s) nderiv_derivable......................proved - complete [shostak](0.10 s) nderiv_derivable_aux_TCC1.............proved - complete [shostak](0.02 s) nderiv_derivable_aux_TCC2.............proved - complete [shostak](0.02 s) nderiv_derivable_aux_TCC3.............proved - complete [shostak](0.03 s) nderiv_derivable_aux..................proved - complete [shostak](0.09 s) nderiv_derivable_eqv_TCC1.............proved - complete [shostak](0.01 s) nderiv_derivable_eqv_TCC2.............proved - complete [shostak](0.00 s) nderiv_derivable_eqv..................proved - complete [shostak](0.09 s) Theory totals: 24 formulas, 24 attempted, 24 succeeded (0.54 s) Proof summary for theory chain_rule composition_derivable_TCC1............proved - complete [shostak](0.00 s) composition_derivable_TCC2............proved - complete [shostak](0.01 s) composition_derivable_TCC3............proved - complete [shostak](0.00 s) composition_derivable_TCC4............proved - complete [shostak](0.00 s) composition_derivable_fun_TCC1........proved - complete [shostak](0.01 s) composition_derivable_fun_TCC2........proved - complete [shostak](0.00 s) composition_derivable_fun.............proved - complete [shostak](0.02 s) deriv_composition_TCC1................proved - complete [shostak](0.01 s) gg_TCC1...............................proved - complete [shostak](0.00 s) gg_TCC2...............................proved - complete [shostak](0.00 s) deriv_comp_fun_TCC1...................proved - complete [shostak](0.01 s) deriv_comp_fun........................proved - complete [shostak](0.06 s) comp_derivable_fun....................proved - complete [shostak](0.00 s) chain_rule_TCC1.......................proved - complete [shostak](0.00 s) chain_rule............................proved - complete [shostak](0.01 s) Theory totals: 15 formulas, 15 attempted, 15 succeeded (0.13 s) Proof summary for theory composition_continuous composition_cont......................proved - complete [shostak](0.15 s) composition_cont_fun..................proved - complete [shostak](0.04 s) Theory totals: 2 formulas, 2 attempted, 2 succeeded (0.19 s) Proof summary for theory continuous_lambda id_cont...............................proved - complete [shostak](0.01 s) const_cont............................proved - complete [shostak](0.00 s) add_cont..............................proved - complete [shostak](0.03 s) sub_cont..............................proved - complete [shostak](0.01 s) neg_cont..............................proved - complete [shostak](0.01 s) mult_cont.............................proved - complete [shostak](0.02 s) div_cont..............................proved - complete [shostak](0.02 s) scal_mult_cont........................proved - complete [shostak](0.02 s) scal_div1_cont........................proved - complete [shostak](0.02 s) scal_div2_cont........................proved - complete [shostak](0.02 s) pow_cont_TCC1.........................proved - complete [shostak](0.01 s) pow_cont..............................proved - complete [shostak](0.02 s) sq_cont...............................proved - complete [shostak](0.02 s) sqrt_cont_TCC1........................proved - complete [shostak](0.03 s) sqrt_cont.............................proved - complete [shostak](0.04 s) abs_cont..............................proved - complete [shostak](0.31 s) max_cont..............................proved - complete [shostak](0.37 s) min_cont..............................proved - complete [shostak](0.17 s) Theory totals: 18 formulas, 18 attempted, 18 succeeded (1.12 s) Proof summary for theory sqrt_derivative sqrt_derivable_fun_TCC1...............proved - complete [shostak](0.08 s) sqrt_derivable_fun_TCC2...............proved - complete [shostak](0.02 s) deriv_sqrt_fun_TCC1...................proved - complete [shostak](0.00 s) sqrt_continuous.......................proved - complete [shostak](0.01 s) Theory totals: 4 formulas, 4 attempted, 4 succeeded (0.11 s) Proof summary for theory deriv_domains Theory totals: 0 formulas, 0 attempted, 0 succeeded (0.00 s) Proof summary for theory deriv_domain deriv_domain_real.....................proved - complete [shostak](0.05 s) deriv_domain_nzreal...................proved - complete [shostak](0.08 s) deriv_domain_posreal..................proved - complete [shostak](0.07 s) deriv_domain_nnreal...................proved - complete [shostak](0.07 s) deriv_domain_negreal..................proved - complete [shostak](0.06 s) deriv_domain_open.....................proved - complete [shostak](0.16 s) deriv_domain_closed...................proved - complete [shostak](0.27 s) deriv_domain_oc.......................proved - complete [shostak](0.14 s) deriv_domain_co.......................proved - complete [shostak](0.16 s) deriv_domain_posreal_le...............proved - complete [shostak](0.28 s) deriv_domain_posreal_lt...............proved - complete [shostak](0.18 s) deriv_domain_nnreal_lt................proved - complete [shostak](0.16 s) not_one_element_real..................proved - complete [shostak](0.01 s) not_one_element_nzreal................proved - complete [shostak](0.01 s) not_one_element_posreal...............proved - complete [shostak](0.02 s) not_one_element_nnreal................proved - complete [shostak](0.01 s) not_one_element_negreal...............proved - complete [shostak](0.02 s) connected_real........................proved - complete [shostak](0.00 s) connected_posreal.....................proved - complete [shostak](0.01 s) connected_nnreal......................proved - complete [shostak](0.00 s) connected_negreal.....................proved - complete [shostak](0.01 s) Theory totals: 21 formulas, 21 attempted, 21 succeeded (1.75 s) Proof summary for theory derivatives_lam IMP_derivatives_TCC1..................proved - complete [shostak](0.00 s) IMP_derivatives_TCC2..................proved - complete [shostak](0.00 s) derivable_id_lam......................proved - complete [shostak](0.01 s) derivable_const_lam...................proved - complete [shostak](0.00 s) derivable_add_lam.....................proved - complete [shostak](0.02 s) derivable_mult_lam....................proved - complete [shostak](0.02 s) derivable_pow_lam_TCC1................proved - complete [shostak](0.01 s) derivable_pow_lam.....................proved - complete [shostak](0.11 s) derivable_scal1_lam...................proved - complete [shostak](0.02 s) derivable_scal2_lam...................proved - complete [shostak](0.05 s) derivable_neg_lam.....................proved - complete [shostak](0.01 s) derivable_sub_lam.....................proved - complete [shostak](0.01 s) derivable_sq_lam......................proved - complete [shostak](0.02 s) derivable_div_lam.....................proved - complete [shostak](0.02 s) derivable_scald1_lam..................proved - complete [shostak](0.01 s) derivable_scald2_lam..................proved - complete [shostak](-.72 s) deriv_id_lam_TCC1.....................proved - complete [shostak](0.01 s) deriv_id_lam..........................proved - complete [shostak](0.00 s) deriv_const_lam_TCC1..................proved - complete [shostak](0.00 s) deriv_const_lam.......................proved - complete [shostak](0.01 s) deriv_add_lam_TCC1....................proved - complete [shostak](0.00 s) deriv_add_lam.........................proved - complete [shostak](0.01 s) deriv_mult_lam_TCC1...................proved - complete [shostak](0.00 s) deriv_mult_lam........................proved - complete [shostak](0.01 s) deriv_pow_lam_TCC1....................proved - complete [shostak](0.01 s) deriv_pow_lam_TCC2....................proved - complete [shostak](0.00 s) deriv_pow_lam_TCC3....................proved - complete [shostak](0.00 s) deriv_pow_lam.........................proved - complete [shostak](0.08 s) deriv_scal1_lam_TCC1..................proved - complete [shostak](0.01 s) deriv_scal1_lam.......................proved - complete [shostak](0.01 s) deriv_scal2_lam_TCC1..................proved - complete [shostak](0.00 s) deriv_scal2_lam.......................proved - complete [shostak](0.04 s) deriv_neg_lam_TCC1....................proved - complete [shostak](0.00 s) deriv_neg_lam.........................proved - complete [shostak](0.01 s) deriv_sub_lam_TCC1....................proved - complete [shostak](0.00 s) deriv_sub_lam.........................proved - complete [shostak](0.01 s) deriv_sq_lam_TCC1.....................proved - complete [shostak](0.01 s) deriv_sq_lam..........................proved - complete [shostak](0.07 s) deriv_div_lam_TCC1....................proved - complete [shostak](0.00 s) deriv_div_lam.........................proved - complete [shostak](0.11 s) deriv_scald1_lam_TCC1.................proved - complete [shostak](0.01 s) deriv_scald1_lam......................proved - complete [shostak](0.08 s) deriv_scald2_lam_TCC1.................proved - complete [shostak](0.00 s) deriv_scald2_lam......................proved - complete [shostak](0.05 s) Theory totals: 44 formulas, 44 attempted, 44 succeeded (0.15 s) Grand Totals: 322 proofs, 322 attempted, 322 succeeded (18.83 s) [ Verzeichnis aufwärts0.227unsichere Verbindung ] |