Theorem. (t62_setlim_2)
∀k3_kurato_0 : setsetset, ∀r2_hidden : setsetprop, ∀esk23_4 : setsetsetsetset, ∀k2_nat_1 : setsetset, ∀k3_funct_2 : setsetsetsetset, ∀k1_funct_1 : setsetset, ∀v1_partfun1 : setsetprop, ∀v4_relat_1 : setsetprop, ∀k1_numbers : set, ∀v3_ordinal1 : setprop, ∀esk12_1 : setset, ∀k4_ordinal1 : set, ∀v1_xxreal_0 : setprop, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk14_0 : set, ∀esk11_2 : setsetset, ∀esk16_1 : setset, ∀esk20_0 : set, ∀esk10_0 : set, ∀esk13_0 : set, ∀esk18_0 : set, ∀esk7_1 : setset, ∀esk15_1 : setset, ∀esk9_2 : setsetset, ∀esk21_0 : set, ∀esk17_1 : setset, ∀v5_ordinal1 : setprop, ∀v2_ordinal1 : setprop, ∀v1_ordinal1 : setprop, ∀esk19_1 : setset, ∀v6_ordinal1 : setprop, ∀v1_xreal_0 : setprop, ∀v1_subset_1 : setsetprop, ∀esk5_2 : setsetset, ∀r1_tarski : setsetprop, ∀k2_xcmplx_0 : setsetset, ∀v1_xcmplx_0 : setprop, ∀v1_relat_1 : setprop, ∀esk8_2 : setsetset, ∀v5_relat_1 : setsetprop, ∀m2_subset_1 : setsetsetprop, ∀v7_ordinal1 : setprop, ∀esk6_3 : setsetsetset, ∀k4_xboole_0 : setsetset, ∀v1_xboole_0 : setprop, ∀esk22_3 : setsetsetset, ∀esk4_4 : setsetsetsetset, ∀k9_setfam_1 : setset, ∀k8_nat_1 : setsetsetset, ∀k7_subset_1 : setsetsetset, ∀v1_funct_2 : setsetsetprop, ∀k5_numbers : set, ∀m1_subset_1 : setsetprop, ∀k2_zfmisc_1 : setsetset, ∀v1_funct_1 : setprop, ∀k3_setlim_2 : setsetsetset, (∀X3 X1 X2 X4, (X2 = (k3_setlim_2 X1 X3 X4)False)(k7_subset_1 X1 (k8_nat_1 (k9_setfam_1 X1) X3 (esk4_4 X1 X3 X4 X2)) (k8_nat_1 (k9_setfam_1 X1) X4 (esk4_4 X1 X3 X4 X2))) = (k8_nat_1 (k9_setfam_1 X1) X2 (esk4_4 X1 X3 X4 X2))v1_funct_1 X4v1_funct_1 X3v1_funct_1 X2v1_funct_2 X4 k5_numbers (k9_setfam_1 X1)v1_funct_2 X3 k5_numbers (k9_setfam_1 X1)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X4 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X4 X2 X3 X1, (r2_hidden X1 (k3_kurato_0 X2 X3)False)v1_funct_1 X3m1_subset_1 X4 k5_numbersv1_funct_2 X3 k5_numbers (k9_setfam_1 X2)m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X2)))r2_hidden X1 (k3_funct_2 k5_numbers (k9_setfam_1 X2) X3 (k2_nat_1 X4 (esk23_4 X2 X3 X1 X4)))False)(∀X1 X2 X3 X4, (r2_hidden X2 (k3_funct_2 k5_numbers (k9_setfam_1 X3) X4 (k2_nat_1 (esk22_3 X3 X4 X2) X1))False)v1_funct_1 X4m1_subset_1 X1 k5_numbersr2_hidden X2 (k3_kurato_0 X3 X4)v1_funct_2 X4 k5_numbers (k9_setfam_1 X3)m1_subset_1 X4 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X3)))False)(∀X3 X1 X2 X4, (X4 = (k3_setlim_2 X1 X2 X3)False)(m1_subset_1 (esk4_4 X1 X2 X3 X4) k5_numbersFalse)v1_funct_1 X4v1_funct_1 X3v1_funct_1 X2v1_funct_2 X4 k5_numbers (k9_setfam_1 X1)v1_funct_2 X3 k5_numbers (k9_setfam_1 X1)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X4 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X5 X4 X3 X2 X1, ((k8_nat_1 (k9_setfam_1 X2) X1 X5) = (k7_subset_1 X2 (k8_nat_1 (k9_setfam_1 X2) X3 X5) (k8_nat_1 (k9_setfam_1 X2) X4 X5))False)X1 = (k3_setlim_2 X2 X3 X4)v1_funct_1 X4v1_funct_1 X3v1_funct_1 X1m1_subset_1 X5 k5_numbersv1_funct_2 X4 k5_numbers (k9_setfam_1 X2)v1_funct_2 X3 k5_numbers (k9_setfam_1 X2)v1_funct_2 X1 k5_numbers (k9_setfam_1 X2)m1_subset_1 X4 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X2)))m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X2)))m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X2)))False)(∀X4 X1 X2 X3, (r2_hidden X3 (k3_kurato_0 X1 X2)False)(m1_subset_1 (esk23_4 X1 X2 X3 X4) k5_numbersFalse)v1_funct_1 X2m1_subset_1 X4 k5_numbersv1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X2 X3 X4 X1, (v1_xboole_0 X1False)(m1_subset_1 (k3_funct_2 X1 X3 X2 X4) X3False)v1_funct_1 X2m1_subset_1 X4 X1v1_funct_2 X2 X1 X3m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X1 X3))False)(∀X2 X1 X3, (m1_subset_1 (k3_setlim_2 X1 X2 X3) (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)v1_funct_1 X3v1_funct_1 X2v1_funct_2 X3 k5_numbers (k9_setfam_1 X1)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X2 X1 X3, (v1_funct_2 (k3_setlim_2 X1 X2 X3) k5_numbers (k9_setfam_1 X1)False)v1_funct_1 X3v1_funct_1 X2v1_funct_2 X3 k5_numbers (k9_setfam_1 X1)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X2 X1 X3, (v1_funct_1 (k3_setlim_2 X1 X2 X3)False)v1_funct_1 X3v1_funct_1 X2v1_funct_2 X3 k5_numbers (k9_setfam_1 X1)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X3 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk6_3 X1 X2 X3) X2False)r2_hidden (esk6_3 X1 X2 X3) X3r2_hidden (esk6_3 X1 X2 X3) X1False)(∀X2 X3 X4 X1, ((k3_funct_2 X1 X3 X2 X4) = (k1_funct_1 X2 X4)False)(v1_xboole_0 X1False)v1_funct_1 X2m1_subset_1 X4 X1v1_funct_2 X2 X1 X3m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X1 X3))False)(∀X1 X3 X2, (m1_subset_1 (esk22_3 X1 X2 X3) k5_numbersFalse)v1_funct_1 X2r2_hidden X3 (k3_kurato_0 X1 X2)v1_funct_2 X2 k5_numbers (k9_setfam_1 X1)m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X1)))False)(∀X2 X3 X1, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk6_3 X1 X2 X3) X3False)r2_hidden (esk6_3 X1 X2 X3) X2False)(∀X3 X2 X1, (m1_subset_1 (k8_nat_1 X2 X1 X3) X2False)v1_funct_1 X1v7_ordinal1 X3v1_funct_2 X1 k5_numbers X2m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 k5_numbers X2))False)(∀X2 X1, (m1_subset_1 (k3_kurato_0 X2 X1) (k9_setfam_1 X2)False)v1_funct_1 X1v1_funct_2 X1 k5_numbers (k9_setfam_1 X2)m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 X2)))False)(∀X3 X2 X1, ((k8_nat_1 X2 X1 X3) = (k1_funct_1 X1 X3)False)v1_funct_1 X1v7_ordinal1 X3v1_funct_2 X1 k5_numbers X2m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 k5_numbers X2))False)(∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk6_3 X1 X2 X3) X3False)(r2_hidden (esk6_3 X1 X2 X3) X1False)False)(∀X2 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)v1_funct_1 X1v1_xboole_0 X1v1_funct_2 X1 X2 X3m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X2 X3))False)(∀X3 X2 X1, (v1_partfun1 X2 X1False)v1_xboole_0 X1v1_funct_2 X2 X1 X3m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X1 X3))False)(∀X3 X2 X1, (v1_xboole_0 X1False)(v1_partfun1 X2 X3False)v1_funct_2 X2 X3 X1m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X3 X1))False)(∀X2 X1, (v1_partfun1 X1 X2False)v1_funct_2 X1 X2 X2m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X2 X2))False)(∀X3 X1 X2, (v1_funct_2 X1 X2 X3False)v1_partfun1 X1 X2m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X2 X3))False)(∀X3 X2 X1, (m1_subset_1 (k7_subset_1 X2 X1 X3) (k9_setfam_1 X2)False)m1_subset_1 X1 (k9_setfam_1 X2)False)(∀X1 X3 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 X3 X1False)m2_subset_1 X3 X1 X2m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X2 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(m1_subset_1 X1 X3False)m2_subset_1 X1 X2 X3m1_subset_1 X3 (k9_setfam_1 X2)False)(∀X3 X1 X2, (v5_relat_1 X1 X2False)m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X3 X2))False)(∀X3 X1 X2, (v4_relat_1 X1 X2False)m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X2 X3))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X1 X3))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k9_setfam_1 (k2_zfmisc_1 X3 X1))False)(∀X1 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m2_subset_1 (esk8_2 X1 X2) X1 X2False)m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X2 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(m2_subset_1 X1 X3 X2False)m1_subset_1 X1 X2m1_subset_1 X2 (k9_setfam_1 X3)False)(∀X3 X2 X1, (v1_relat_1 X1False)m1_subset_1 X1 (k9_setfam_1 (k2_zfmisc_1 X2 X3))False)(∀X2 X1, (m2_subset_1 (k2_nat_1 X1 X2) k1_numbers k5_numbersFalse)v7_ordinal1 X2m1_subset_1 X1 k5_numbersFalse)(∀X1 X2 X3, ((k2_xcmplx_0 (k2_xcmplx_0 X1 X2) X3) = (k2_xcmplx_0 X1 (k2_xcmplx_0 X2 X3))False)v1_xcmplx_0 X3v1_xcmplx_0 X2v1_xcmplx_0 X1False)(∀X3 X2 X1, ((k7_subset_1 X2 X1 X3) = (k4_xboole_0 X1 X3)False)m1_subset_1 X1 (k9_setfam_1 X2)False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk5_2 X1 X2) X2False)(∀X1 X2 X3, (v5_relat_1 (k4_xboole_0 X1 X3) X2False)v1_relat_1 X3v1_relat_1 X1v5_relat_1 X1 X2False)(∀X1 X2 X3, (v4_relat_1 (k4_xboole_0 X1 X3) X2False)v1_relat_1 X3v1_relat_1 X1v4_relat_1 X1 X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)(r2_hidden X1 X3False)X4 = (k4_xboole_0 X2 X3)r2_hidden X1 X2False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k9_setfam_1 X3)False)(∀X4 X3 X2 X1, X3 = (k4_xboole_0 X4 X2)r2_hidden X1 X3r2_hidden X1 X2False)(∀X2 X1, v1_xboole_0 X1v1_subset_1 X2 X1m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k9_setfam_1 X3)False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k4_xboole_0 X2 X4)r2_hidden X1 X3False)(∀X1 X3 X2, (r2_hidden X3 X2False)r1_tarski X1 X2r2_hidden X3 X1False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X1 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_xboole_0 (k2_zfmisc_1 X1 X2)False)(∀X2 X1, ((k2_nat_1 X1 X2) = (k2_xcmplx_0 X1 X2)False)v7_ordinal1 X2m1_subset_1 X1 k5_numbersFalse)(∀X2 X1, ((k2_nat_1 X1 X2) = (k2_nat_1 X2 X1)False)v7_ordinal1 X2m1_subset_1 X1 k5_numbersFalse)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk5_2 X1 X2) X1False)False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k9_setfam_1 X2)False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X2 X1, (v1_xreal_0 (k2_xcmplx_0 X1 X2)False)v1_xreal_0 X2v1_xreal_0 X1False)(∀X1 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X1 X2, (v6_ordinal1 X2False)v6_ordinal1 X1m1_subset_1 X2 (k9_setfam_1 X1)False)(∀X2 X1, (m1_subset_1 X1 (k9_setfam_1 X2)False)r1_tarski X1 X2False)(∀X2 X1, ((k2_xcmplx_0 X1 X2) = (k2_xcmplx_0 X2 X1)False)v1_xcmplx_0 X2v1_xcmplx_0 X1False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1 X2, (v3_ordinal1 X2False)v3_ordinal1 X1m1_subset_1 X2 X1False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk19_1 X1) (k9_setfam_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk12_1 X1) (k9_setfam_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk19_1 X1) X1False)False)(∀X1, (v7_ordinal1 X1False)m1_subset_1 X1 k4_ordinal1False)(∀X1, (v1_xreal_0 X1False)m1_subset_1 X1 k1_numbersFalse)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk12_1 X1)False)(∀X1, (v3_ordinal1 X1False)v1_ordinal1 X1v2_ordinal1 X1False)(∀X1, (v1_xxreal_0 X1False)v1_xreal_0 X1False)(∀X1, (v5_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v1_xcmplx_0 X1False)v1_xreal_0 X1False)(∀X1, (v7_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v1_xreal_0 X1False)v7_ordinal1 X1False)(∀X1, (v2_ordinal1 X1False)v3_ordinal1 X1False)(∀X1, (v1_ordinal1 X1False)v3_ordinal1 X1False)(∀X1, (v3_ordinal1 X1False)v7_ordinal1 X1False)(∀X1, (v3_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v6_ordinal1 X1False)v1_xboole_0 X1False)(r1_tarski (k3_kurato_0 esk1_0 (k3_setlim_2 esk1_0 esk2_0 esk3_0)) (k7_subset_1 esk1_0 (k3_kurato_0 esk1_0 esk2_0) (k3_kurato_0 esk1_0 esk3_0))False)(∀X1, v1_subset_1 (esk17_1 X1) X1False)(∀X1, v1_xboole_0 (k9_setfam_1 X1)False)(v1_xboole_0 esk21_0False)(v1_xboole_0 esk14_0False)(v1_xboole_0 k4_ordinal1False)(∀X2 X1, (m1_subset_1 (esk11_2 X1 X2) (k9_setfam_1 (k2_zfmisc_1 X1 X2))False)False)(∀X2 X1, (m1_subset_1 (esk9_2 X1 X2) (k9_setfam_1 (k2_zfmisc_1 X1 X2))False)False)(∀X2 X1, (v1_funct_2 (esk9_2 X1 X2) X1 X2False)False)((m1_subset_1 esk3_0 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 esk1_0)))False)False)((m1_subset_1 esk2_0 (k9_setfam_1 (k2_zfmisc_1 k5_numbers (k9_setfam_1 esk1_0)))False)False)((v1_funct_2 esk3_0 k5_numbers (k9_setfam_1 esk1_0)False)False)((v1_funct_2 esk2_0 k5_numbers (k9_setfam_1 esk1_0)False)False)(∀X2 X1, (v5_relat_1 (esk11_2 X1 X2) X2False)False)(∀X2 X1, (v5_relat_1 (esk9_2 X1 X2) X2False)False)(∀X1 X2, (v4_relat_1 (esk11_2 X1 X2) X1False)False)(∀X1 X2, (v4_relat_1 (esk9_2 X1 X2) X1False)False)(∀X1, (m1_subset_1 (k9_setfam_1 X1) (k9_setfam_1 (k9_setfam_1 X1))False)False)(∀X1 X2, (v1_xboole_0 (esk11_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk11_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk9_2 X1 X2)False)False)(∀X1 X2, (v1_funct_1 (esk9_2 X1 X2)False)False)(∀X1, (m1_subset_1 (esk17_1 X1) (k9_setfam_1 X1)False)False)(∀X1, (m1_subset_1 (esk15_1 X1) (k9_setfam_1 X1)False)False)(∀X1, (v5_relat_1 (esk16_1 X1) X1False)False)(∀X1, (m1_subset_1 (esk7_1 X1) X1False)False)((m1_subset_1 k5_numbers (k9_setfam_1 k1_numbers)False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, (v5_ordinal1 (esk16_1 X1)False)False)(∀X1, (v1_xboole_0 (esk15_1 X1)False)False)(∀X1, (v1_relat_1 (esk16_1 X1)False)False)(∀X1, (v1_funct_1 (esk16_1 X1)False)False)((v1_xxreal_0 esk20_0False)False)((v1_xcmplx_0 esk20_0False)False)((v7_ordinal1 esk21_0False)False)((v7_ordinal1 esk18_0False)False)((v1_xreal_0 esk20_0False)False)((v1_xreal_0 esk13_0False)False)((v1_xboole_0 esk20_0False)False)((v2_ordinal1 esk14_0False)False)((v1_ordinal1 esk14_0False)False)((v3_ordinal1 esk14_0False)False)((v3_ordinal1 esk10_0False)False)((v3_ordinal1 k4_ordinal1False)False)((v1_funct_1 esk3_0False)False)((v1_funct_1 esk2_0False)False)((k4_ordinal1 = k5_numbersFalse)False)False
Proof:
The rest of the proof is missing.