Theorem. (
t9_card_lar)
∀a_3_0_card_lar : set → set → set → set, ∀esk8_4 : set → set → set → set → set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk5_2 : set → set → set, ∀esk6_2 : set → set → set, ∀esk23_2 : set → set → set, ∀r1_tarski : set → set → prop, ∀v4_card_3 : set → prop, ∀v7_ordinal1 : set → prop, ∀esk16_0 : set, ∀esk17_0 : set, ∀esk7_1 : set → set, ∀esk13_0 : set, ∀esk10_0 : set, ∀esk12_0 : set, ∀esk14_0 : set, ∀esk19_0 : set, ∀esk21_0 : set, ∀esk11_0 : set, ∀esk15_0 : set, ∀esk22_0 : set, ∀v5_ordinal1 : set → prop, ∀v5_card_3 : set → prop, ∀v2_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀esk20_1 : set → set, ∀v3_card_1 : set → set → prop, ∀v1_card_1 : set → prop, ∀esk18_1 : set → set, ∀v6_ordinal1 : set → prop, ∀v1_xboole_0 : set → prop, ∀esk4_3 : set → set → set → set, ∀k1_xboole_0 : set, ∀esk24_3 : set → set → set → set, ∀v1_card_lar : set → set → prop, ∀k1_setfam_1 : set → set, ∀k2_ordinal1 : set → set, ∀k1_card_lar : set → set → set → set, ∀esk9_4 : set → set → set → set → set, ∀r2_hidden : set → set → prop, ∀a_3_1_card_lar : set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v4_ordinal1 : set → prop, ∀v3_ordinal1 : set → prop, ∀v1_finset_1 : set → prop, (∀X4 X1 X3 X2, (v1_finset_1 X2 → False) → (r2_hidden (esk9_4 X1 X2 X3 X4) X3 → False) → v3_ordinal1 X4 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_1_card_lar X2 X3 X4) → False) → (∀X3 X1 X4 X2, (v1_finset_1 X2 → False) → (r2_hidden (esk8_4 X1 X2 X3 X4) X4 → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X4 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_card_lar X2 X3 X4) → False) → (∀X4 X1 X3 X2, (v1_finset_1 X2 → False) → (m1_subset_1 (esk9_4 X1 X2 X3 X4) X2 → False) → v3_ordinal1 X4 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_1_card_lar X2 X3 X4) → False) → (∀X3 X1 X4 X2, (v1_finset_1 X2 → False) → (m1_subset_1 (esk8_4 X1 X2 X3 X4) X2 → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X4 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_card_lar X2 X3 X4) → False) → (∀X2 X4 X1 X3, (v1_finset_1 X3 → False) → (r2_hidden X1 (esk9_4 X2 X3 X4 X1) → False) → v3_ordinal1 X3 → v3_ordinal1 X1 → v4_ordinal1 X3 → m1_subset_1 X4 (k1_zfmisc_1 X3) → r2_hidden X2 (a_3_1_card_lar X3 X4 X1) → False) → (∀X2 X4 X1 X3, (v1_finset_1 X3 → False) → (r2_hidden X1 (esk8_4 X2 X3 X1 X4) → False) → v3_ordinal1 X3 → v3_ordinal1 X1 → v4_ordinal1 X3 → m1_subset_1 X4 (k1_zfmisc_1 X3) → r2_hidden X2 (a_3_0_card_lar X3 X1 X4) → False) → (∀X4 X1 X3 X2, ((esk9_4 X1 X2 X3 X4) = X1 → False) → (v1_finset_1 X2 → False) → v3_ordinal1 X4 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_1_card_lar X2 X3 X4) → False) → (∀X3 X1 X4 X2, ((esk8_4 X1 X2 X3 X4) = X1 → False) → (v1_finset_1 X2 → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X4 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_card_lar X2 X3 X4) → False) → (∀X3 X2 X1, ((k1_setfam_1 (k2_ordinal1 (a_3_1_card_lar X1 X2 X3))) = (k1_card_lar X1 X2 X3) → False) → (v1_finset_1 X1 → False) → v3_ordinal1 X3 → v3_ordinal1 X1 → v4_ordinal1 X1 → v1_card_lar X2 X1 → r2_hidden X3 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (r2_hidden esk2_0 (k1_card_lar esk1_0 esk3_0 esk2_0) → r2_hidden (k1_card_lar esk1_0 esk3_0 esk2_0) esk3_0 → False) → (∀X2 X3 X1, (v1_finset_1 X1 → False) → (r2_hidden (esk24_3 X1 X2 X3) (a_3_0_card_lar X1 X2 X3) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → v1_card_lar X3 X1 → r2_hidden X2 X1 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X4 X3, (v1_finset_1 X3 → False) → (r2_hidden X1 X2 → False) → v3_ordinal1 X3 → v3_ordinal1 X1 → v4_ordinal1 X3 → m1_subset_1 X4 (k1_zfmisc_1 X3) → r2_hidden X2 (a_3_0_card_lar X3 X1 X4) → False) → (∀X2 X1 X4 X3, (v1_finset_1 X3 → False) → (r2_hidden X1 X2 → False) → v3_ordinal1 X4 → v3_ordinal1 X3 → v4_ordinal1 X3 → m1_subset_1 X2 (k1_zfmisc_1 X3) → r2_hidden X1 (a_3_0_card_lar X3 X4 X2) → False) → (∀X3 X5 X4 X1 X2, (v1_finset_1 X2 → False) → (r2_hidden X3 (a_3_0_card_lar X2 X5 X4) → False) → X1 = X3 → v3_ordinal1 X5 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X1 X2 → r2_hidden X5 X1 → r2_hidden X1 X4 → m1_subset_1 X4 (k1_zfmisc_1 X2) → False) → (∀X3 X4 X5 X1 X2, (v1_finset_1 X2 → False) → (r2_hidden X3 (a_3_1_card_lar X2 X4 X5) → False) → X1 = X3 → v3_ordinal1 X5 → v3_ordinal1 X2 → v4_ordinal1 X2 → m1_subset_1 X1 X2 → r2_hidden X5 X1 → r2_hidden X1 X4 → m1_subset_1 X4 (k1_zfmisc_1 X2) → False) → (∀X2 X3 X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk24_3 X1 X2 X3) X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → v1_card_lar X3 X1 → r2_hidden X2 X1 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X3 X1 X2, (X2 = k1_xboole_0 → False) → (r2_hidden X1 X3 → False) → X3 = (k1_setfam_1 X2) → r2_hidden X1 (esk4_3 X2 X3 X1) → False) → (∀X2 X3 X1, (v1_finset_1 X1 → False) → (m1_subset_1 (a_3_0_card_lar X1 X2 X3) (k1_zfmisc_1 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X3 X2 X1, (v1_finset_1 X1 → False) → (m1_subset_1 (k1_card_lar X1 X2 X3) X2 → False) → v3_ordinal1 X3 → v3_ordinal1 X1 → v4_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → r2_hidden (esk5_2 X1 X2) X2 → r2_hidden (esk5_2 X1 X2) (esk6_2 X1 X2) → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (r2_hidden X3 X2 → False) → (r2_hidden (esk4_3 X1 X2 X3) X1 → False) → X2 = (k1_setfam_1 X1) → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → (r2_hidden (esk6_2 X1 X2) X1 → False) → r2_hidden (esk5_2 X1 X2) X2 → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → (r2_hidden (esk5_2 X1 X2) X3 → False) → (r2_hidden (esk5_2 X1 X2) X2 → False) → r2_hidden X3 X1 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk23_2 X3 X2) → False) → (∀X2 X1, (v1_finset_1 X1 → False) → v3_ordinal1 X1 → v4_ordinal1 X1 → v1_xboole_0 X2 → v1_card_lar X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X3 X1 X2 X4, (X4 = k1_xboole_0 → False) → (r2_hidden X1 X3 → False) → X2 = (k1_setfam_1 X4) → r2_hidden X3 X4 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (r2_hidden (esk23_2 X1 X2) X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (v4_card_3 X2 → False) → v4_card_3 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, ((k2_ordinal1 X2) = X2 → False) → v3_ordinal1 X1 → r1_tarski X2 X1 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v3_card_1 (esk20_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v3_ordinal1 X1 → v4_ordinal1 X1 → v1_finset_1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v3_card_1 X1 k1_xboole_0 → False) → (∀X1, (v4_ordinal1 X1 → False) → (v1_finset_1 X1 → False) → v3_ordinal1 X1 → v1_card_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (esk18_1 X1) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (k1_zfmisc_1 X1) → False) → (∀X1, (v3_card_1 X1 k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v3_ordinal1 X1 → v1_finset_1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (v5_card_3 X1 → False) → v4_card_3 X1 → False) → (∀X1, (v4_ordinal1 X1 → False) → (v1_finset_1 X1 → False) → v1_card_1 X1 → False) → (∀X1, v1_finset_1 X1 → v5_card_3 X1 → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → X2 = k1_xboole_0 → X1 = (k1_setfam_1 X2) → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v4_card_3 X1 → False) → v5_card_3 X1 → False) → (∀X1, (v4_card_3 X1 → False) → v1_finset_1 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_card_1 X1 → False) → (∀X2 X1, (X1 = (k1_setfam_1 X2) → False) → X2 = k1_xboole_0 → X1 = k1_xboole_0 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (v1_xboole_0 esk22_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_finset_1 esk17_0 → False) → (v1_finset_1 esk11_0 → False) → (v1_finset_1 esk1_0 → False) → (∀X1, (v3_ordinal1 (k1_setfam_1 (k2_ordinal1 X1)) → False) → False) → (∀X1, (m1_subset_1 (esk7_1 X1) X1 → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 esk1_0) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((r2_hidden esk2_0 esk1_0 → False) → False) → ((v1_card_lar esk3_0 esk1_0 → False) → False) → ((v5_card_3 esk21_0 → False) → False) → ((v7_ordinal1 esk22_0 → False) → False) → ((v7_ordinal1 esk19_0 → False) → False) → ((v2_ordinal1 esk15_0 → False) → False) → ((v2_ordinal1 esk14_0 → False) → False) → ((v2_ordinal1 esk11_0 → False) → False) → ((v1_ordinal1 esk15_0 → False) → False) → ((v1_ordinal1 esk14_0 → False) → False) → ((v1_ordinal1 esk11_0 → False) → False) → ((v1_xboole_0 esk13_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_card_1 esk14_0 → False) → False) → ((v1_card_1 esk11_0 → False) → False) → ((v1_card_1 esk10_0 → False) → False) → ((v1_finset_1 esk14_0 → False) → False) → ((v4_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 esk15_0 → False) → False) → ((v3_ordinal1 esk14_0 → False) → False) → ((v3_ordinal1 esk12_0 → False) → False) → ((v3_ordinal1 esk11_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v3_ordinal1 esk1_0 → False) → False) → False