% 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_274__5189194_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:12.955

% Could-be-implicit typings (17)
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__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__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).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (55)
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_Finite__Set_Ocard_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    finite927127589e_indi : set_Ar1007576579e_indi > nat).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    inj_on528257168di_nat : (arrow_1429744205e_indi > nat) > set_Ar1007576579e_indi > $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_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    if_set550155277le_alt : $o > set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_M_Eo_J, type,
    top_to1473733010indi_o : arrow_1429744205e_indi > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__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,
    top_to803745505le_alt : set_Ar182050865le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__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,
    top_to685525675le_alt : set_Ar809243995le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__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,
    top_to469035705le_alt : set_se2071012361le_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_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    collec1169676194e_indi : (arrow_1429744205e_indi > $o) > set_Ar1007576579e_indi).
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,
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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,
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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__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_Lab____, type,
    lab : set_Pr367596371le_alt).
thf(sy_v_Lba____, type,
    lba : set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).

% Relevant facts (204)
thf(fact_0__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_1_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_2_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_3_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_4__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_5_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_6__092_060open_062F_A_I_092_060lambda_062i_O_ALba_J_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ (f @ (^[I : arrow_1429744205e_indi]: lba)) @ arrow_1848678355le_Lin))). % \<open>F (\<lambda>i. Lba) \<in> Lin\<close>
thf(fact_7_const__Lin__Prof, axiom,
    ((![L2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P : arrow_1429744205e_indi]: L2) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_8_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L2 @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_9_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L2 @ X @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_10_mkbot__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L2 @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_11_mktop__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L2 @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_12__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_13__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((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 @ B @ A) @ (P3 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P3)))))))))). % "3"
thf(fact_14__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((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 @ B @ C) @ (P3 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P3)))))))))))). % "4"
thf(fact_15_pairwise__neutrality, 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))) => ((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))))))))))). % pairwise_neutrality
thf(fact_16__C0_C, axiom,
    ((![N : nat]: (member1334244458le_alt @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N) @ lab @ lba))) @ arrow_1848678355le_Lin)))). % "0"
thf(fact_17__092_060open_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lab))). % \<open>a <\<^bsub>Lab\<^esub> b\<close>
thf(fact_18__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_19__092_060open_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lba))). % \<open>b <\<^bsub>Lba\<^esub> a\<close>
thf(fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lba_O_A_092_060lbrakk_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lba : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ Lba) => (~ ((member1334244458le_alt @ Lba @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lba. \<lbrakk>b <\<^bsub>Lba\<^esub> a; Lba \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_21__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lab_O_A_092_060lbrakk_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lab : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ Lab) => (~ ((member1334244458le_alt @ Lab @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lab. \<lbrakk>a <\<^bsub>Lab\<^esub> b; Lab \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_22__092_060open_062_Ia_M_Ab_J_A_092_060notin_062_ALba_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lba))))). % \<open>(a, b) \<notin> Lba\<close>
thf(fact_23__092_060open_062_Ib_M_Aa_J_A_092_060notin_062_ALab_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lab))))). % \<open>(b, a) \<notin> Lab\<close>
thf(fact_24_PiProf, axiom,
    ((![N : nat]: (member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N) @ lab @ lba)) @ arrow_1951607831e_Prof)))). % PiProf
thf(fact_25_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ arrow_1951607831e_Prof)) => ((![Y2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y2 @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_26_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L2 @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))). % in_mkbot
thf(fact_27_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L2 @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))). % in_mktop
thf(fact_28_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X2))))))))))))). % unanimity_def
thf(fact_29_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L2 @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L2)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L2)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))))))))). % in_below
thf(fact_30_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L2 @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L2)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L2)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))))))))). % in_above
thf(fact_31_notin__Lin__iff, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L2))))))). % notin_Lin_iff
thf(fact_32_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_33_Lin__irrefl, axiom,
    ((![L2 : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L2) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L2)))))))). % Lin_irrefl
thf(fact_34__C1_C, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ zero_zero_nat) @ lab @ lba)))))))). % "1"
thf(fact_35_dictatorI, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F2 @ (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) => (![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((~ ((A4 = B4))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X3 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F2 @ X3))))))) => (arrow_960434986ctator @ F2 @ I3)))))). % dictatorI
thf(fact_36_Pi__I, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_37_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_38_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_39_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_40_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_41_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_42_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_43_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : 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 @ (F3 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_44_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_45_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_46_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y22 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_47_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_48_calculation, axiom,
    (((^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ (finite927127589e_indi @ top_to1799531699e_indi)) @ lab @ lba)) = (^[P : arrow_1429744205e_indi]: lab)))). % calculation
thf(fact_49_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I : arrow_1429744205e_indi]: (![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ arrow_1951607831e_Prof)) => (((F @ X2) = (X2 @ I)))))))))). % dictator_def
thf(fact_50_funcset__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_51_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_52_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_53_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_54_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_55_funcset__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_56_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_57_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_58_funcset__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_59_funcset__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ B5)))))). % funcset_mem
thf(fact_60_Pi__UNIV, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_61_Pi__UNIV, axiom,
    ((![A5 : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_62_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_63_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_64_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_65_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_66_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_67_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_68_Collect__mem__eq, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_69_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_70_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_71_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_72_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A4 @ B4))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_73_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_74_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_75_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A4 @ B4))) => (P2 @ P4))))). % prod_cases
thf(fact_76_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_77_Pi__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : 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) => ((F3 @ W) = (G @ W)))) => ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_78_Pi__cong, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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) => ((F3 @ W) = (G @ W)))) => ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_79_Pi__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_80_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_81_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_82_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_83_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_84_Pi__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_85_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_86_Pi__mem, axiom,
    ((![F3 : 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 @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_87_Pi__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_88_Pi__mem, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F3 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_89_Pi__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ I4 @ X4)) = (![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ I4)) => ((member1334244458le_alt @ (F3 @ X2) @ (X4 @ X2))))))))). % Pi_iff
thf(fact_90_Pi__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ I4 @ X4)) = (![X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ I4)) => ((member1334244458le_alt @ (F3 @ X2) @ (X4 @ X2))))))))). % Pi_iff
thf(fact_91_Pi__I_H, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_92_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_93_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_94_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_95_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_96_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_97_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_98_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : 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 @ (F3 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_99_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_100_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_101_PiE, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member1966420836e_indi @ X @ A5)))))))). % PiE
thf(fact_102_PiE, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_103_PiE, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_104_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_105_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_106_PiE, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_107_PiE, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_108_PiE, axiom,
    ((![F3 : 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 @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_109_PiE, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_110_PiE, axiom,
    ((![F3 : (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 @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_111_funcsetI, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_112_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_113_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_114_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_115_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_116_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ B5))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_117_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_118_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_119_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ B5))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_120_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (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 @ (F3 @ X3) @ B5))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_121_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_122_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_123_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_124_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_125_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_126_iso__tuple__UNIV__I, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt)))). % iso_tuple_UNIV_I
thf(fact_127_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_128_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_129_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_130_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_131_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_132_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_133_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_134_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_135_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_136_nat__less__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N2) => (P2 @ M2))) => (P2 @ N2))) => (P2 @ N))))). % nat_less_induct
thf(fact_137_infinite__descent, axiom,
    ((![P2 : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P2 @ N2))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N2) & (~ ((P2 @ M2))))))) => (P2 @ N))))). % infinite_descent
thf(fact_138_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_139_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_140_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_141_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_142_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_143_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_144_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_145_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_146_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_147_gr__implies__not0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_148_infinite__descent0, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P2 @ N2))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N2) & (~ ((P2 @ M2)))))))) => (P2 @ N)))))). % infinite_descent0
thf(fact_149_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_150_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_151_UNIV__I, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt)))). % UNIV_I
thf(fact_152_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_153_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_154_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_155_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_156_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_157_order_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_158_not__less__iff__gr__or__eq, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) = (((ord_less_nat @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_159_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_nat @ B @ A) => ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))))). % dual_order.strict_trans
thf(fact_160_linorder__less__wlog, axiom,
    ((![P2 : nat > nat > $o, A : nat, B : nat]: ((![A4 : nat, B4 : nat]: ((ord_less_nat @ A4 @ B4) => (P2 @ A4 @ B4))) => ((![A4 : nat]: (P2 @ A4 @ A4)) => ((![A4 : nat, B4 : nat]: ((P2 @ B4 @ A4) => (P2 @ A4 @ B4))) => (P2 @ A @ B))))))). % linorder_less_wlog
thf(fact_161_exists__least__iff, axiom,
    (((^[P5 : nat > $o]: (?[X5 : nat]: (P5 @ X5))) = (^[P6 : nat > $o]: (?[N3 : nat]: (((P6 @ N3)) & ((![M3 : nat]: (((ord_less_nat @ M3 @ N3)) => ((~ ((P6 @ M3))))))))))))). % exists_least_iff
thf(fact_162_less__imp__not__less, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_imp_not_less
thf(fact_163_order_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % order.strict_trans
thf(fact_164_dual__order_Oirrefl, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % dual_order.irrefl
thf(fact_165_linorder__cases, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) => ((~ ((X = Y))) => (ord_less_nat @ Y @ X)))))). % linorder_cases
thf(fact_166_less__imp__triv, axiom,
    ((![X : nat, Y : nat, P2 : $o]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ X) => P2))))). % less_imp_triv
thf(fact_167_less__imp__not__eq2, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_168_antisym__conv3, axiom,
    ((![Y : nat, X : nat]: ((~ ((ord_less_nat @ Y @ X))) => ((~ ((ord_less_nat @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_169_less__induct, axiom,
    ((![P2 : nat > $o, A : nat]: ((![X3 : nat]: ((![Y4 : nat]: ((ord_less_nat @ Y4 @ X3) => (P2 @ Y4))) => (P2 @ X3))) => (P2 @ A))))). % less_induct
thf(fact_170_less__not__sym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_not_sym
thf(fact_171_less__imp__not__eq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_172_dual__order_Oasym, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((ord_less_nat @ A @ B))))))). % dual_order.asym
thf(fact_173_ord__less__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C)))))). % ord_less_eq_trans
thf(fact_174_ord__eq__less__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % ord_eq_less_trans
thf(fact_175_less__irrefl, axiom,
    ((![X : nat]: (~ ((ord_less_nat @ X @ X)))))). % less_irrefl
thf(fact_176_less__linear, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) | ((X = Y) | (ord_less_nat @ Y @ X)))))). % less_linear
thf(fact_177_less__trans, axiom,
    ((![X : nat, Y : nat, Z : nat]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ Z) => (ord_less_nat @ X @ Z)))))). % less_trans
thf(fact_178_less__asym_H, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % less_asym'
thf(fact_179_less__asym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_asym
thf(fact_180_less__imp__neq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_181_order_Oasym, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % order.asym
thf(fact_182_neq__iff, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) = (((ord_less_nat @ X @ Y)) | ((ord_less_nat @ Y @ X))))))). % neq_iff
thf(fact_183_neqE, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % neqE
thf(fact_184_gt__ex, axiom,
    ((![X : nat]: (?[X_1 : nat]: (ord_less_nat @ X @ X_1))))). % gt_ex
thf(fact_185_order__less__subst2, axiom,
    ((![A : nat, B : nat, F3 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (F3 @ B) @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F3 @ X3) @ (F3 @ Y3)))) => (ord_less_nat @ (F3 @ A) @ C))))))). % order_less_subst2
thf(fact_186_order__less__subst1, axiom,
    ((![A : nat, F3 : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A @ (F3 @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F3 @ X3) @ (F3 @ Y3)))) => (ord_less_nat @ A @ (F3 @ C)))))))). % order_less_subst1
thf(fact_187_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F3 : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => (((F3 @ B) = C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F3 @ X3) @ (F3 @ Y3)))) => (ord_less_nat @ (F3 @ A) @ C))))))). % ord_less_eq_subst
thf(fact_188_ord__eq__less__subst, axiom,
    ((![A : nat, F3 : nat > nat, B : nat, C : nat]: ((A = (F3 @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F3 @ X3) @ (F3 @ Y3)))) => (ord_less_nat @ A @ (F3 @ C)))))))). % ord_eq_less_subst
thf(fact_189_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_190_UNIV__witness, axiom,
    ((?[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_191_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_192_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_193_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_194_UNIV__eq__I, axiom,
    ((![A5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A5)) => (top_to469035705le_alt = A5))))). % UNIV_eq_I
thf(fact_195_UNIV__eq__I, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ A5)) => (top_to803745505le_alt = A5))))). % UNIV_eq_I
thf(fact_196_UNIV__eq__I, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A5)) => (top_to685525675le_alt = A5))))). % UNIV_eq_I
thf(fact_197_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_198_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A5)) => (top_to1799531699e_indi = A5))))). % UNIV_eq_I
thf(fact_199_inj__on__inverseI, axiom,
    ((![A5 : set_Ar1007576579e_indi, G : nat > arrow_1429744205e_indi, F3 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => ((G @ (F3 @ X3)) = X3))) => (inj_on528257168di_nat @ F3 @ A5))))). % inj_on_inverseI
thf(fact_200_inj__on__contraD, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F3 @ A5) => ((~ ((X = Y))) => ((member1966420836e_indi @ X @ A5) => ((member1966420836e_indi @ Y @ A5) => (~ (((F3 @ X) = (F3 @ Y))))))))))). % inj_on_contraD
thf(fact_201_inj__on__eq__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > nat, A5 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F3 @ A5) => ((member1966420836e_indi @ X @ A5) => ((member1966420836e_indi @ Y @ A5) => (((F3 @ X) = (F3 @ Y)) = (X = Y)))))))). % inj_on_eq_iff
thf(fact_202_inj__on__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > nat]: ((![A4 : arrow_1429744205e_indi]: ((member1966420836e_indi @ A4 @ A5) => ((F3 @ A4) = (G @ A4)))) => ((inj_on528257168di_nat @ F3 @ A5) = (inj_on528257168di_nat @ G @ A5)))))). % inj_on_cong
thf(fact_203_inj__on__def, axiom,
    ((inj_on528257168di_nat = (^[F4 : arrow_1429744205e_indi > nat]: (^[A6 : set_Ar1007576579e_indi]: (![X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ A6)) => ((![Y2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ Y2 @ A6)) => (((((F4 @ X2) = (F4 @ Y2))) => ((X2 = Y2)))))))))))))). % inj_on_def

% Helper facts (3)
thf(help_If_3_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((member1334244458le_alt @ (f @ (^[I : arrow_1429744205e_indi]: lab)) @ arrow_1848678355le_Lin))).
