% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Arrow_Order/prob_210__5188072_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:38.806

% Could-be-implicit typings (21)
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Ar1108837783le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_se1538189555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar182050865le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Pr1911398973le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Ar3481041le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_se370278869le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr720748555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1094320767le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr269449961le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc518943027le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__List__Olist_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    list_l1515872562le_alt : $tType).
thf(ty_n_t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    list_A2130511660le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (62)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Pro1164444725le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Pro1847889543le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Pro1122205927le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_set1343364587le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_set365323601le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_set1240805297le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_alt).
thf(sy_c_List_Oappend_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    append714424641le_alt : list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Odistinct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    distin2037765919le_alt : list_A2130511660le_alt > $o).
thf(sy_c_List_Oinsert_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    insert1859930562le_alt : arrow_1857593510le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Olexord_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lexord1313992857le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olist_OCons_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    cons_A1864255580le_alt : arrow_1857593510le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    cons_l157309922le_alt : list_A2130511660le_alt > list_l1515872562le_alt > list_l1515872562le_alt).
thf(sy_c_List_Olist_ONil_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    nil_Ar277507244le_alt : list_A2130511660le_alt).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    nil_li2110134322le_alt : list_l1515872562le_alt).
thf(sy_c_List_Olist_Olist__all_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    list_a501266778le_alt : (arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o).
thf(sy_c_List_Olist__ex1_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    list_e746053615le_alt : (arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o).
thf(sy_c_List_Olistrel1_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    listre1329599109le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olistrel_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    listre1681044285le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olistrelp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    listre1372300399le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > list_A2130511660le_alt > $o).
thf(sy_c_List_Oproduct__lists_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc608939669le_alt : list_l1515872562le_alt > list_l1515872562le_alt).
thf(sy_c_List_Osubseqs_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    subseq1380156923le_alt : list_A2130511660le_alt > list_l1515872562le_alt).
thf(sy_c_List_Ounion_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    union_420169888le_alt : list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2047839287le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > produc1094320767le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc961395117le_alt : list_A2130511660le_alt > list_A2130511660le_alt > produc518943027le_alt).
thf(sy_c_Set_OCollect_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1382217680le_alt : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o) > set_Ar182050865le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member896258016le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1108837783le_alt > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member361641010le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt) > set_Ar3481041le_alt > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member183760530le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member167063198le_alt : (produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr1911398973le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1154116596le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr665675179le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1038100052le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr720748555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member1117110356le_alt : (set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se1538189555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member594528958le_alt : (set_Pr367596371le_alt > produc16571293le_alt) > set_se791007093le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1775590686le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se370278869le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member681312074le_alt : produc518943027le_alt > set_Pr269449961le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_P_H____, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_P____, type,
    p2 : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_c____, type,
    c : arrow_1857593510le_alt).

% Relevant facts (185)
thf(fact_0__092_060open_062P_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p2 @ arrow_1951607831e_Prof))). % \<open>P \<in> Prof\<close>
thf(fact_1__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_2_dist, axiom,
    ((distin2037765919le_alt @ (cons_A1864255580le_alt @ a @ (cons_A1864255580le_alt @ b @ (cons_A1864255580le_alt @ c @ nil_Ar277507244le_alt)))))). % dist
thf(fact_3_iff, axiom,
    ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ (p @ I)))))). % iff
thf(fact_4__092_060open_062_092_060forall_062i_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_092_060close_062, axiom,
    ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ c) @ (arrow_887341619_below @ (p2 @ I) @ c @ b)))))). % \<open>\<forall>i. (a <\<^bsub>P i\<^esub> b) = (a <\<^bsub>below (P i) c b\<^esub> c)\<close>
thf(fact_5_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_6_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![C : arrow_1857593510le_alt]: (~ ((distin2037765919le_alt @ (cons_A1864255580le_alt @ a @ (cons_A1864255580le_alt @ b @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))))))). % \<open>\<And>thesis. (\<And>c. distinct [a, b, c] \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_8_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_9_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_10__092_060open_062_I_092_060lambda_062p_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ (^[P : arrow_1429744205e_indi]: (arrow_887341619_below @ (arrow_887341619_below @ (p2 @ P) @ c @ b) @ b @ a)) @ arrow_1951607831e_Prof))). % \<open>(\<lambda>p. below (below (P p) c b) b a) \<in> Prof\<close>
thf(fact_11__092_060open_062_I_092_060lambda_062p_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ (^[P : arrow_1429744205e_indi]: (arrow_887341619_below @ (arrow_887341619_below @ (arrow_887341619_below @ (p2 @ P) @ c @ b) @ b @ a) @ a @ c)) @ arrow_1951607831e_Prof))). % \<open>(\<lambda>p. below (below (below (P p) c b) b a) a c) \<in> Prof\<close>
thf(fact_12_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mkbot
thf(fact_13_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mktop
thf(fact_14_ab, axiom,
    (((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ p2)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ c) @ (f @ (^[P : arrow_1429744205e_indi]: (arrow_887341619_below @ (p2 @ P) @ c @ b))))))). % ab
thf(fact_15__092_060open_062_I_092_060lambda_062p_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ (^[P : arrow_1429744205e_indi]: (arrow_887341619_below @ (p2 @ P) @ c @ b)) @ arrow_1951607831e_Prof))). % \<open>(\<lambda>p. below (P p) c b) \<in> Prof\<close>
thf(fact_16_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_below
thf(fact_17__092_060open_062P_H_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % \<open>P' \<in> Prof\<close>
thf(fact_18__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "2"
thf(fact_19__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "1"
thf(fact_20_assms_I1_J, axiom,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))). % assms(1)
thf(fact_21_alt3, axiom,
    ((?[A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A3 @ (cons_A1864255580le_alt @ B3 @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))). % alt3
thf(fact_22_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_23_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_24_third__alt, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))))). % third_alt
thf(fact_25_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_26_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_27_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_28_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X3))))))). % complete_Lin
thf(fact_29_Lin__irrefl, axiom,
    ((![L : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L)))))))). % Lin_irrefl
thf(fact_30_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_31_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4))))))))))))). % unanimity_def
thf(fact_32_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y3 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (Y3 @ I3))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ Y3))))))))))))))))). % IIA_def
thf(fact_33_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_34_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_35_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_36_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_37_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_38_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_39_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_40_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_41_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_42_Collect__mem__eq, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_43_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_44_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P4))))). % prod_cases
thf(fact_45_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X3 @ Y4)))))). % surj_pair
thf(fact_46_distinct__singleton, axiom,
    ((![X : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % distinct_singleton
thf(fact_47_list_Oinject, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt, Y21 : arrow_1857593510le_alt, Y22 : list_A2130511660le_alt]: (((cons_A1864255580le_alt @ X21 @ X22) = (cons_A1864255580le_alt @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_48_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_above
thf(fact_49_distinct_Osimps_I1_J, axiom,
    ((distin2037765919le_alt @ nil_Ar277507244le_alt))). % distinct.simps(1)
thf(fact_50_distinct__length__2__or__more, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ Xs))) = (((~ ((A = B)))) & ((((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ Xs))) & ((distin2037765919le_alt @ (cons_A1864255580le_alt @ B @ Xs)))))))))). % distinct_length_2_or_more
thf(fact_51_list_Odistinct_I1_J, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: (~ ((nil_Ar277507244le_alt = (cons_A1864255580le_alt @ X21 @ X22))))))). % list.distinct(1)
thf(fact_52_list_OdiscI, axiom,
    ((![List : list_A2130511660le_alt, X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: ((List = (cons_A1864255580le_alt @ X21 @ X22)) => (~ ((List = nil_Ar277507244le_alt))))))). % list.discI
thf(fact_53_list_Oexhaust, axiom,
    ((![Y : list_A2130511660le_alt]: ((~ ((Y = nil_Ar277507244le_alt))) => (~ ((![X212 : arrow_1857593510le_alt, X222 : list_A2130511660le_alt]: (~ ((Y = (cons_A1864255580le_alt @ X212 @ X222))))))))))). % list.exhaust
thf(fact_54_not__Cons__self2, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (~ (((cons_A1864255580le_alt @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_55_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_56_map__tailrec__rev_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt) > list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt, A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt]: ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, X_1 : list_A2130511660le_alt]: (P2 @ F2 @ nil_Ar277507244le_alt @ X_1)) => ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, As : list_A2130511660le_alt, Bs : list_A2130511660le_alt]: ((P2 @ F2 @ As @ (cons_A1864255580le_alt @ (F2 @ A3) @ Bs)) => (P2 @ F2 @ (cons_A1864255580le_alt @ A3 @ As) @ Bs))) => (P2 @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_57_list__nonempty__induct, axiom,
    ((![Xs : list_A2130511660le_alt, P2 : list_A2130511660le_alt > $o]: ((~ ((Xs = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((~ ((Xs2 = nil_Ar277507244le_alt))) => ((P2 @ Xs2) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2))))) => (P2 @ Xs))))))). % list_nonempty_induct
thf(fact_58_successively_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P2 @ P5 @ nil_Ar277507244le_alt)) => ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (P2 @ P5 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((P2 @ P5 @ (cons_A1864255580le_alt @ Y4 @ Xs2)) => (P2 @ P5 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y4 @ Xs2))))) => (P2 @ A0 @ A1))))))). % successively.induct
thf(fact_59_successively_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P5 @ nil_Ar277507244le_alt))))) => ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (~ ((X = (produc2047839287le_alt @ P5 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt)))))) => (~ ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P5 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y4 @ Xs2)))))))))))))). % successively.cases
thf(fact_60_remdups__adj_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (((X3 = Y4) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2))) => (((~ ((X3 = Y4))) => (P2 @ (cons_A1864255580le_alt @ Y4 @ Xs2))) => (P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y4 @ Xs2)))))) => (P2 @ A0))))))). % remdups_adj.induct
thf(fact_61_sorted__wrt_Oinduct, axiom,
    ((![P2 : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P2 @ P5 @ nil_Ar277507244le_alt)) => ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ P5 @ Ys) => (P2 @ P5 @ (cons_A1864255580le_alt @ X3 @ Ys)))) => (P2 @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_62_remdups__adj_Ocases, axiom,
    ((![X : list_A2130511660le_alt]: ((~ ((X = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y4 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_63_sorted__wrt_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P5 @ nil_Ar277507244le_alt))))) => (~ ((![P5 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P5 @ (cons_A1864255580le_alt @ X3 @ Ys)))))))))))). % sorted_wrt.cases
thf(fact_64_transpose_Ocases, axiom,
    ((![X : list_l1515872562le_alt]: ((~ ((X = nil_li2110134322le_alt))) => ((![Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ Xss))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Xss)))))))))))). % transpose.cases
thf(fact_65_shuffles_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ X_1)) => ((![Xs2 : list_A2130511660le_alt]: (P2 @ Xs2 @ nil_Ar277507244le_alt)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y4 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Xs2 @ (cons_A1864255580le_alt @ Y4 @ Ys)) => ((P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y4 @ Ys))))) => (P2 @ A0 @ A1))))))). % shuffles.induct
thf(fact_66_shuffles_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys))))) => ((![Xs2 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ Xs2 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y4 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y4 @ Ys))))))))))))). % shuffles.cases
thf(fact_67_induct__list012, axiom,
    ((![P2 : list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Zs : list_A2130511660le_alt]: ((P2 @ Zs) => ((P2 @ (cons_A1864255580le_alt @ Y4 @ Zs)) => (P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y4 @ Zs)))))) => (P2 @ Xs))))))). % induct_list012
thf(fact_68_splice_Oinduct, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ X_1)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Ys @ Xs2) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys))) => (P2 @ A0 @ A1)))))). % splice.induct
thf(fact_69_list__induct2_H, axiom,
    ((![P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ nil_Ar277507244le_alt)) => ((![Y4 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: (P2 @ nil_Ar277507244le_alt @ (cons_A1864255580le_alt @ Y4 @ Ys))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y4 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((P2 @ Xs2 @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y4 @ Ys)))) => (P2 @ Xs @ Ys2)))))))). % list_induct2'
thf(fact_70_splice_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys))))))))))). % splice.cases
thf(fact_71_neq__Nil__conv, axiom,
    ((![Xs : list_A2130511660le_alt]: ((~ ((Xs = nil_Ar277507244le_alt))) = (?[Y3 : arrow_1857593510le_alt]: (?[Ys3 : list_A2130511660le_alt]: (Xs = (cons_A1864255580le_alt @ Y3 @ Ys3)))))))). % neq_Nil_conv
thf(fact_72_list_Oinducts, axiom,
    ((![P2 : list_A2130511660le_alt > $o, List : list_A2130511660le_alt]: ((P2 @ nil_Ar277507244le_alt) => ((![X12 : arrow_1857593510le_alt, X23 : list_A2130511660le_alt]: ((P2 @ X23) => (P2 @ (cons_A1864255580le_alt @ X12 @ X23)))) => (P2 @ List)))))). % list.inducts
thf(fact_73_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ arrow_1951607831e_Prof) => (![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X3 @ I4)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F3 @ X3))))))) => (arrow_960434986ctator @ F3 @ I4)))))). % dictatorI
thf(fact_74_Pi__I, axiom,
    ((![A5 : set_Ar1007576579e_indi, F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_75_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_76_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_77_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_78_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_79_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_80_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_81_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_82_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_83_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_84_distinct__union, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((distin2037765919le_alt @ (union_420169888le_alt @ Xs @ Ys2)) = (distin2037765919le_alt @ Ys2))))). % distinct_union
thf(fact_85_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I3 : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F @ X4) = (X4 @ I3)))))))))). % dictator_def
thf(fact_86_funcsetI, axiom,
    ((![A5 : set_Ar1007576579e_indi, F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ B5))) => (member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_87_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ B5))) => (member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_88_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ B5))) => (member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_89_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ B5))) => (member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_90_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ B5))) => (member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_91_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ B5))) => (member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_92_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ B5))) => (member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_93_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ B5))) => (member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_94_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ B5))) => (member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_95_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ B5))) => (member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_96_PiE, axiom,
    ((![F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member1966420836e_indi @ X @ A5)))))))). % PiE
thf(fact_97_PiE, axiom,
    ((![F4 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_98_PiE, axiom,
    ((![F4 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_99_PiE, axiom,
    ((![F4 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_100_PiE, axiom,
    ((![F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_101_PiE, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_102_PiE, axiom,
    ((![F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_103_PiE, axiom,
    ((![F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_104_PiE, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_105_PiE, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F4 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_106_Pi__I_H, axiom,
    ((![A5 : set_Ar1007576579e_indi, F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_107_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_108_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_109_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_110_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_111_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_112_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_113_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_114_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_115_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F4 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_116_Pi__iff, axiom,
    ((![F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, I5 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ I5 @ X5)) = (![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ I5)) => ((member1334244458le_alt @ (F4 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_117_Pi__iff, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I5 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ I5 @ X5)) = (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ I5)) => ((member1334244458le_alt @ (F4 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_118_Pi__mem, axiom,
    ((![F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_119_Pi__mem, axiom,
    ((![F4 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_120_Pi__mem, axiom,
    ((![F4 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_121_Pi__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_122_Pi__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_123_Pi__mem, axiom,
    ((![F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_124_Pi__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_125_Pi__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_126_Pi__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_127_Pi__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_128_Pi__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A5) => ((F4 @ W) = (G @ W)))) => ((member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_129_Pi__cong, axiom,
    ((![A5 : set_Ar809243995le_alt, F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A5) => ((F4 @ W) = (G @ W)))) => ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_130_funcset__mem, axiom,
    ((![F4 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F4 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_131_funcset__mem, axiom,
    ((![F4 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F4 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_132_funcset__mem, axiom,
    ((![F4 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F4 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_133_funcset__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F4 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_134_funcset__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F4 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_135_funcset__mem, axiom,
    ((![F4 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F4 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_136_funcset__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F4 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_137_funcset__mem, axiom,
    ((![F4 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F4 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_138_funcset__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_139_funcset__mem, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F4 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F4 @ X) @ B5)))))). % funcset_mem
thf(fact_140_product__lists_Osimps_I1_J, axiom,
    (((produc608939669le_alt @ nil_li2110134322le_alt) = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ nil_li2110134322le_alt)))). % product_lists.simps(1)
thf(fact_141_subseqs_Osimps_I1_J, axiom,
    (((subseq1380156923le_alt @ nil_Ar277507244le_alt) = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ nil_li2110134322le_alt)))). % subseqs.simps(1)
thf(fact_142_insert__Nil, axiom,
    ((![X : arrow_1857593510le_alt]: ((insert1859930562le_alt @ X @ nil_Ar277507244le_alt) = (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % insert_Nil
thf(fact_143_distinct__insert, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (insert1859930562le_alt @ X @ Xs)) = (distin2037765919le_alt @ Xs))))). % distinct_insert
thf(fact_144_lexord__Nil__left, axiom,
    ((![Y : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Y) @ (lexord1313992857le_alt @ R)) = (?[A4 : arrow_1857593510le_alt]: (?[X4 : list_A2130511660le_alt]: (Y = (cons_A1864255580le_alt @ A4 @ X4)))))))). % lexord_Nil_left
thf(fact_145_lexord__cons__cons, axiom,
    ((![A : arrow_1857593510le_alt, X : list_A2130511660le_alt, B : arrow_1857593510le_alt, Y : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ A @ X) @ (cons_A1864255580le_alt @ B @ Y)) @ (lexord1313992857le_alt @ R)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R)) | ((((A = B)) & ((member681312074le_alt @ (produc961395117le_alt @ X @ Y) @ (lexord1313992857le_alt @ R)))))))))). % lexord_cons_cons
thf(fact_146_listrel_Ocases, axiom,
    ((![A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ A1 @ A22) @ (listre1681044285le_alt @ R)) => (((A1 = nil_Ar277507244le_alt) => (~ ((A22 = nil_Ar277507244le_alt)))) => (~ ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((A1 = (cons_A1864255580le_alt @ X3 @ Xs2)) => (![Ys : list_A2130511660le_alt]: ((A22 = (cons_A1864255580le_alt @ Y4 @ Ys)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys) @ (listre1681044285le_alt @ R)))))))))))))))). % listrel.cases
thf(fact_147_listrel_ONil, axiom,
    ((![R : set_Pr367596371le_alt]: (member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) @ (listre1681044285le_alt @ R))))). % listrel.Nil
thf(fact_148_listrel__Nil1, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Xs) @ (listre1681044285le_alt @ R)) => (Xs = nil_Ar277507244le_alt))))). % listrel_Nil1
thf(fact_149_listrel__Nil2, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ nil_Ar277507244le_alt) @ (listre1681044285le_alt @ R)) => (Xs = nil_Ar277507244le_alt))))). % listrel_Nil2
thf(fact_150_lexord__irreflexive, axiom,
    ((![R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt]: ((![X3 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ X3) @ R)))) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Xs) @ (lexord1313992857le_alt @ R)))))))). % lexord_irreflexive
thf(fact_151_lexord__linear, axiom,
    ((![R : set_Pr367596371le_alt, X : list_A2130511660le_alt, Y : list_A2130511660le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ R) | ((A3 = B3) | (member2048039092le_alt @ (produc1494124311le_alt @ B3 @ A3) @ R)))) => ((member681312074le_alt @ (produc961395117le_alt @ X @ Y) @ (lexord1313992857le_alt @ R)) | ((X = Y) | (member681312074le_alt @ (produc961395117le_alt @ Y @ X) @ (lexord1313992857le_alt @ R)))))))). % lexord_linear
thf(fact_152_lexord__Nil__right, axiom,
    ((![X : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ X @ nil_Ar277507244le_alt) @ (lexord1313992857le_alt @ R))))))). % lexord_Nil_right
thf(fact_153_listrel__Cons2, axiom,
    ((![Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1681044285le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((Xs = (cons_A1864255580le_alt @ X3 @ Xs2)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys2) @ (listre1681044285le_alt @ R))))))))))))). % listrel_Cons2
thf(fact_154_listrel__Cons1, axiom,
    ((![Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ Y @ Ys2) @ Xs) @ (listre1681044285le_alt @ R)) => (~ ((![Y4 : arrow_1857593510le_alt, Ys : list_A2130511660le_alt]: ((Xs = (cons_A1864255580le_alt @ Y4 @ Ys)) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Y4) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Ys2 @ Ys) @ (listre1681044285le_alt @ R))))))))))))). % listrel_Cons1
thf(fact_155_listrel_OCons, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1681044285le_alt @ R)) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1681044285le_alt @ R))))))). % listrel.Cons
thf(fact_156_listrel_Oinducts, axiom,
    ((![X1 : list_A2130511660le_alt, X2 : list_A2130511660le_alt, R : set_Pr367596371le_alt, P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o]: ((member681312074le_alt @ (produc961395117le_alt @ X1 @ X2) @ (listre1681044285le_alt @ R)) => ((P2 @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ R) => ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys) @ (listre1681044285le_alt @ R)) => ((P2 @ Xs2 @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y4 @ Ys)))))) => (P2 @ X1 @ X2))))))). % listrel.inducts
thf(fact_157_listrel_Osimps, axiom,
    ((![A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ A1 @ A22) @ (listre1681044285le_alt @ R)) = (((((A1 = nil_Ar277507244le_alt)) & ((A22 = nil_Ar277507244le_alt)))) | ((?[X4 : arrow_1857593510le_alt]: (?[Y3 : arrow_1857593510le_alt]: (?[Xs3 : list_A2130511660le_alt]: (?[Ys3 : list_A2130511660le_alt]: (((A1 = (cons_A1864255580le_alt @ X4 @ Xs3))) & ((((A22 = (cons_A1864255580le_alt @ Y3 @ Ys3))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ R)) & ((member681312074le_alt @ (produc961395117le_alt @ Xs3 @ Ys3) @ (listre1681044285le_alt @ R)))))))))))))))))). % listrel.simps
thf(fact_158_listrelp__listrel__eq, axiom,
    ((![R : set_Pr367596371le_alt]: ((listre1372300399le_alt @ (^[X4 : arrow_1857593510le_alt]: (^[Y3 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ R)))) = (^[X4 : list_A2130511660le_alt]: (^[Y3 : list_A2130511660le_alt]: (member681312074le_alt @ (produc961395117le_alt @ X4 @ Y3) @ (listre1681044285le_alt @ R)))))))). % listrelp_listrel_eq
thf(fact_159_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((^[X4 : arrow_1857593510le_alt]: (^[Y3 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ R2))) = (^[X4 : arrow_1857593510le_alt]: (^[Y3 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y3) @ S)))) = (R2 = S))))). % pred_equals_eq2
thf(fact_160_listrelp_ONil, axiom,
    ((![R : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (listre1372300399le_alt @ R @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt)))). % listrelp.Nil
thf(fact_161_listrelp_OCons, axiom,
    ((![R : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((R @ X @ Y) => ((listre1372300399le_alt @ R @ Xs @ Ys2) => (listre1372300399le_alt @ R @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2))))))). % listrelp.Cons
thf(fact_162_listrelp_Oinducts, axiom,
    ((![R : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X1 : list_A2130511660le_alt, X2 : list_A2130511660le_alt, P2 : list_A2130511660le_alt > list_A2130511660le_alt > $o]: ((listre1372300399le_alt @ R @ X1 @ X2) => ((P2 @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys : list_A2130511660le_alt]: ((R @ X3 @ Y4) => ((listre1372300399le_alt @ R @ Xs2 @ Ys) => ((P2 @ Xs2 @ Ys) => (P2 @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y4 @ Ys)))))) => (P2 @ X1 @ X2))))))). % listrelp.inducts
thf(fact_163_listrelp_Osimps, axiom,
    ((listre1372300399le_alt = (^[R3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (^[A12 : list_A2130511660le_alt]: (^[A23 : list_A2130511660le_alt]: (((((A12 = nil_Ar277507244le_alt)) & ((A23 = nil_Ar277507244le_alt)))) | ((?[X4 : arrow_1857593510le_alt]: (?[Y3 : arrow_1857593510le_alt]: (?[Xs3 : list_A2130511660le_alt]: (?[Ys3 : list_A2130511660le_alt]: (((A12 = (cons_A1864255580le_alt @ X4 @ Xs3))) & ((((A23 = (cons_A1864255580le_alt @ Y3 @ Ys3))) & ((((R3 @ X4 @ Y3)) & ((listre1372300399le_alt @ R3 @ Xs3 @ Ys3))))))))))))))))))). % listrelp.simps
thf(fact_164_listrelp_Ocases, axiom,
    ((![R : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt]: ((listre1372300399le_alt @ R @ A1 @ A22) => (((A1 = nil_Ar277507244le_alt) => (~ ((A22 = nil_Ar277507244le_alt)))) => (~ ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((A1 = (cons_A1864255580le_alt @ X3 @ Xs2)) => (![Ys : list_A2130511660le_alt]: ((A22 = (cons_A1864255580le_alt @ Y4 @ Ys)) => ((R @ X3 @ Y4) => (~ ((listre1372300399le_alt @ R @ Xs2 @ Ys))))))))))))))). % listrelp.cases
thf(fact_165_list__ex1__simps_I1_J, axiom,
    ((![P2 : arrow_1857593510le_alt > $o]: (~ ((list_e746053615le_alt @ P2 @ nil_Ar277507244le_alt)))))). % list_ex1_simps(1)
thf(fact_166_Cons__listrel1__Cons, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1329599109le_alt @ R)) = (((((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R)) & ((Xs = Ys2)))) | ((((X = Y)) & ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)))))))))). % Cons_listrel1_Cons
thf(fact_167_listrel1I2, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ X @ Ys2)) @ (listre1329599109le_alt @ R)))))). % listrel1I2
thf(fact_168_not__listrel1__Nil, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ nil_Ar277507244le_alt) @ (listre1329599109le_alt @ R))))))). % not_listrel1_Nil
thf(fact_169_not__Nil__listrel1, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Xs) @ (listre1329599109le_alt @ R))))))). % not_Nil_listrel1
thf(fact_170_Cons__listrel1E2, axiom,
    ((![Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1329599109le_alt @ R)) => ((![X3 : arrow_1857593510le_alt]: ((Xs = (cons_A1864255580le_alt @ X3 @ Ys2)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R))))) => (~ ((![Zs : list_A2130511660le_alt]: ((Xs = (cons_A1864255580le_alt @ Y @ Zs)) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Zs @ Ys2) @ (listre1329599109le_alt @ R))))))))))))). % Cons_listrel1E2
thf(fact_171_Cons__listrel1E1, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ Ys2) @ (listre1329599109le_alt @ R)) => ((![Y4 : arrow_1857593510le_alt]: ((Ys2 = (cons_A1864255580le_alt @ Y4 @ Xs)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y4) @ R))))) => (~ ((![Zs : list_A2130511660le_alt]: ((Ys2 = (cons_A1864255580le_alt @ X @ Zs)) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Zs) @ (listre1329599109le_alt @ R))))))))))))). % Cons_listrel1E1
thf(fact_172_listrel1I1, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Xs)) @ (listre1329599109le_alt @ R)))))). % listrel1I1
thf(fact_173_snoc__listrel1__snoc__iff, axiom,
    ((![Xs : list_A2130511660le_alt, X : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (append714424641le_alt @ Xs @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt)) @ (append714424641le_alt @ Ys2 @ (cons_A1864255580le_alt @ Y @ nil_Ar277507244le_alt))) @ (listre1329599109le_alt @ R)) = (((((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R))) & ((X = Y)))) | ((((Xs = Ys2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R))))))))). % snoc_listrel1_snoc_iff
thf(fact_174_list__ex1__simps_I2_J, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((list_e746053615le_alt @ P2 @ (cons_A1864255580le_alt @ X @ Xs)) = (((((P2 @ X)) => ((list_a501266778le_alt @ (^[Y3 : arrow_1857593510le_alt]: (((~ ((P2 @ Y3)))) | ((X = Y3)))) @ Xs)))) & ((((~ ((P2 @ X)))) => ((list_e746053615le_alt @ P2 @ Xs))))))))). % list_ex1_simps(2)
thf(fact_175_append__Nil2, axiom,
    ((![Xs : list_A2130511660le_alt]: ((append714424641le_alt @ Xs @ nil_Ar277507244le_alt) = Xs)))). % append_Nil2
thf(fact_176_append__self__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = Xs) = (Ys2 = nil_Ar277507244le_alt))))). % append_self_conv
thf(fact_177_self__append__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((Xs = (append714424641le_alt @ Xs @ Ys2)) = (Ys2 = nil_Ar277507244le_alt))))). % self_append_conv
thf(fact_178_append__self__conv2, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = Ys2) = (Xs = nil_Ar277507244le_alt))))). % append_self_conv2
thf(fact_179_self__append__conv2, axiom,
    ((![Ys2 : list_A2130511660le_alt, Xs : list_A2130511660le_alt]: ((Ys2 = (append714424641le_alt @ Xs @ Ys2)) = (Xs = nil_Ar277507244le_alt))))). % self_append_conv2
thf(fact_180_Nil__is__append__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((nil_Ar277507244le_alt = (append714424641le_alt @ Xs @ Ys2)) = (((Xs = nil_Ar277507244le_alt)) & ((Ys2 = nil_Ar277507244le_alt))))))). % Nil_is_append_conv
thf(fact_181_append__is__Nil__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = nil_Ar277507244le_alt) = (((Xs = nil_Ar277507244le_alt)) & ((Ys2 = nil_Ar277507244le_alt))))))). % append_is_Nil_conv
thf(fact_182_append_Oright__neutral, axiom,
    ((![A : list_A2130511660le_alt]: ((append714424641le_alt @ A @ nil_Ar277507244le_alt) = A)))). % append.right_neutral
thf(fact_183_list__all__simps_I1_J, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((list_a501266778le_alt @ P2 @ (cons_A1864255580le_alt @ X @ Xs)) = (((P2 @ X)) & ((list_a501266778le_alt @ P2 @ Xs))))))). % list_all_simps(1)
thf(fact_184_list_Opred__inject_I2_J, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, Aa : list_A2130511660le_alt]: ((list_a501266778le_alt @ P2 @ (cons_A1864255580le_alt @ A @ Aa)) = (((P2 @ A)) & ((list_a501266778le_alt @ P2 @ Aa))))))). % list.pred_inject(2)

% Conjectures (1)
thf(conj_0, conjecture,
    ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ c) @ (arrow_887341619_below @ (p2 @ I2) @ c @ b)) = (member2048039092le_alt @ (produc1494124311le_alt @ b @ c) @ (arrow_887341619_below @ (arrow_887341619_below @ (p2 @ I2) @ c @ b) @ b @ a)))))).
