% 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_166__5187506_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:21.682

% Could-be-implicit typings (24)
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_It__Product____Type__Oprod_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_Pr448479039le_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__Product____Type__Oprod_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,
    produc1556433673le_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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar1612966069e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1666424426le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar528567456e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1380421567le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $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__Product____Type__Ounit, type,
    product_unit : $tType).

% Explicit typings (104)
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_OPiE_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,
    piE_Ar1900467852le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar974971248le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar236171216le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1187035700le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Ar1380421567le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar415527999e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Ar528567456e_indi).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1084018769le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Ar1666424426le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar738911586e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Ar1612966069e_indi).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar1580347400le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr1024471460le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr2084141144le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr757114552le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se1100287834le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se232226le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se1902809474le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_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_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,
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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__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_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__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,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_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_Q____, type,
    q : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_a_H____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_a____, type,
    a2 : arrow_1857593510le_alt).
thf(sy_v_b_H____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b2 : arrow_1857593510le_alt).

% Relevant facts (232)
thf(fact_0_d2_I2_J, axiom,
    ((~ ((b2 = a))))). % d2(2)
thf(fact_1_d2_I1_J, axiom,
    ((~ ((a2 = b))))). % d2(1)
thf(fact_2__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_3_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_4_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_5_d1_I1_J, axiom,
    ((~ ((a2 = b2))))). % d1(1)
thf(fact_6__092_060open_062Q_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ q @ arrow_1951607831e_Prof))). % \<open>Q \<in> Prof\<close>
thf(fact_7__092_060open_062a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (f @ p2)))). % \<open>a <\<^bsub>F P\<^esub> b\<close>
thf(fact_8__C1_C, axiom,
    ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (p2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p @ I)))))). % "1"
thf(fact_9_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_10_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_11_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_12_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_13__092_060open_062Q_A_092_060equiv_062_A_092_060lambda_062i_O_Alet_AL_A_061_Aif_Aa_A_061_Aa_H_Athen_AP_Ai_Aelse_Abelow_A_IP_Ai_J_Aa_H_Aa_Ain_Aif_Ab_A_061_Ab_H_Athen_AL_Aelse_AArrow__Order__Mirabelle__riepwfubkl_Oabove_AL_Ab_Ab_H_092_060close_062, axiom,
    ((q = (^[I2 : arrow_1429744205e_indi]: (if_set550155277le_alt @ (b2 = b) @ (if_set550155277le_alt @ (a2 = a) @ (p2 @ I2) @ (arrow_887341619_below @ (p2 @ I2) @ a @ a2)) @ (arrow_1726226719_above @ (if_set550155277le_alt @ (a2 = a) @ (p2 @ I2) @ (arrow_887341619_below @ (p2 @ I2) @ a @ a2)) @ b2 @ b)))))). % \<open>Q \<equiv> \<lambda>i. let L = if a = a' then P i else below (P i) a' a in if b = b' then L else Arrow_Order_Mirabelle_riepwfubkl.above L b b'\<close>
thf(fact_14__092_060open_062F_AQ_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ (f @ q) @ arrow_1848678355le_Lin))). % \<open>F Q \<in> Lin\<close>
thf(fact_15_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_16_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_17_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_18_d1_I2_J, axiom,
    ((~ ((a = b))))). % d1(2)
thf(fact_19__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_20_Q__def, axiom,
    ((![I3 : arrow_1429744205e_indi]: ((q @ I3) = (if_set550155277le_alt @ (b2 = b) @ (if_set550155277le_alt @ (a2 = a) @ (p2 @ I3) @ (arrow_887341619_below @ (p2 @ I3) @ a @ a2)) @ (arrow_1726226719_above @ (if_set550155277le_alt @ (a2 = a) @ (p2 @ I3) @ (arrow_887341619_below @ (p2 @ I3) @ a @ a2)) @ b2 @ b)))))). % Q_def
thf(fact_21_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_22_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_23_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_24_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_25_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_26_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_27_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P3 : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_28_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_29_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_30_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_31_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_32_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_33_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]: (((![I2 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4))))))))))))). % unanimity_def
thf(fact_34_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)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (Y4 @ I2))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ Y4))))))))))))))))). % IIA_def
thf(fact_35_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_36_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_37_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_38_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_39_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_40_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_41_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_42_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_43_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_44_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_45_Collect__cong, axiom,
    ((![P2 : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P2 @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P2) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_46_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I2 : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F @ X4) = (X4 @ I2)))))))))). % dictator_def
thf(fact_47_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R))) = (^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_48_ssubst__Pair__rhs, axiom,
    ((![R2 : arrow_1857593510le_alt, S2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S2) @ R) => ((S3 = S2) => (member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_49_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) => (![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X3 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F2 @ X3))))))) => (arrow_960434986ctator @ F2 @ I3)))))). % dictatorI
thf(fact_50_curryI, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F3 @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F3 @ A @ B))))). % curryI
thf(fact_51_curryD, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F3 @ A @ B) => (F3 @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_52_curryE, axiom,
    ((![F3 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F3 @ A @ B) => (F3 @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_53_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_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_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_76_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_77_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_78_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_79_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_80_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_81_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_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_Pi__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ I4 @ X5)) = (![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ I4)) => ((member1334244458le_alt @ (F3 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_106_Pi__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ I4 @ X5)) = (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ I4)) => ((member1334244458le_alt @ (F3 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_107_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_108_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_109_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_110_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_111_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_112_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_113_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_114_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_115_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_116_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_117_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_118_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R2 @ F3)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F3 @ X) @ (F3 @ Y)) @ R2))))). % in_inv_image
thf(fact_119_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_120_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_121_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_122_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_123_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_124_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_125_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_126_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_127_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_128_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_129_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_130_UNIV__I, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt)))). % UNIV_I
thf(fact_131_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_132_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_133_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_134_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_135_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X4 : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_136_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X4 : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_137_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_138_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_139_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_140_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_141_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_142_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_143_top__empty__eq, axiom,
    ((top_to1892800228_alt_o = (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X4 @ top_to803745505le_alt))))). % top_empty_eq
thf(fact_144_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X4 : arrow_1429744205e_indi]: (member1966420836e_indi @ X4 @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_145_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X4 : arrow_1857593510le_alt]: (member519365071le_alt @ X4 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_146_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_147_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_148_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_149_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_150_UNIV__witness, axiom,
    ((?[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_151_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_152_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_153_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_154_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_155_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_156_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_157_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_158_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A5)) => (top_to958727510le_alt = A5))))). % UNIV_eq_I
thf(fact_159_extensionalityI, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ F3 @ (extens1528283402le_alt @ A5)) => ((member684274596le_alt @ G @ (extens1528283402le_alt @ A5)) => ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => ((F3 @ X3) = (G @ X3)))) => (F3 = G))))))). % extensionalityI
thf(fact_160_extensionalityI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (extens951643470le_alt @ A5)) => ((member183760530le_alt @ G @ (extens951643470le_alt @ A5)) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => ((F3 @ X3) = (G @ X3)))) => (F3 = G))))))). % extensionalityI
thf(fact_161_same__fstI, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P2 @ X) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y) @ (R @ X)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X @ Y5) @ (produc1494124311le_alt @ X @ Y)) @ (same_f554660482le_alt @ P2 @ R))))))). % same_fstI
thf(fact_162_Pi__empty, axiom,
    ((![B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr479247969le_alt @ bot_bo365569479le_alt @ B5) = top_to803745505le_alt)))). % Pi_empty
thf(fact_163_Pi__empty, axiom,
    ((![B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B5) = top_to685525675le_alt)))). % Pi_empty
thf(fact_164_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P2)) = top_to469035705le_alt)) & ((~ (P2)) => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P2)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_165_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P2)) = top_to1799531699e_indi)) & ((~ (P2)) => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P2)) = bot_bo1390904983e_indi)))))). % Collect_const
thf(fact_166_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P2)) = top_to958727510le_alt)) & ((~ (P2)) => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P2)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_167_Pi__eq__empty, axiom,
    ((![A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr479247969le_alt @ A5 @ B5) = bot_bo13098693le_alt) = (?[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A5)) & (((B5 @ X4) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_168_Pi__eq__empty, axiom,
    ((![A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A5 @ B5) = bot_bo365569479le_alt) = (?[X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ A5)) & (((B5 @ X4) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_169_empty__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: $false))))). % empty_def
thf(fact_170_empty__not__UNIV, axiom,
    ((~ ((bot_bo1390904983e_indi = top_to1799531699e_indi))))). % empty_not_UNIV
thf(fact_171_empty__not__UNIV, axiom,
    ((~ ((bot_bo1127707250le_alt = top_to958727510le_alt))))). % empty_not_UNIV
thf(fact_172_funcset__to__empty__iff, axiom,
    ((![A5 : set_Ar809243995le_alt]: (((A5 = bot_bo365569479le_alt) => ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = top_to803745505le_alt)) & ((~ ((A5 = bot_bo365569479le_alt))) => ((pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = bot_bo13098693le_alt)))))). % funcset_to_empty_iff
thf(fact_173_funcset__to__empty__iff, axiom,
    ((![A5 : set_Ar1007576579e_indi]: (((A5 = bot_bo1390904983e_indi) => ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = top_to685525675le_alt)) & ((~ ((A5 = bot_bo1390904983e_indi))) => ((pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = bot_bo365569479le_alt)))))). % funcset_to_empty_iff
thf(fact_174_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A @ B) @ (produc1494124311le_alt @ A2 @ B2)) @ (lex_pr3395839le_alt @ R2 @ S2)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R2)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S2))))))))). % in_lex_prod
thf(fact_175_PiE__UNIV, axiom,
    (((piE_Ar738911586e_indi @ top_to1799531699e_indi @ (^[I2 : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to498310661e_indi))). % PiE_UNIV
thf(fact_176_PiE__UNIV, axiom,
    (((piE_Ar1084018769le_alt @ top_to1799531699e_indi @ (^[I2 : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to1139905818le_alt))). % PiE_UNIV
thf(fact_177_PiE__UNIV, axiom,
    (((piE_Ar415527999e_indi @ top_to958727510le_alt @ (^[I2 : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to2048848e_indi))). % PiE_UNIV
thf(fact_178_PiE__UNIV, axiom,
    (((piE_Ar1187035700le_alt @ top_to958727510le_alt @ (^[I2 : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to290516239le_alt))). % PiE_UNIV
thf(fact_179_top__unit__def, axiom,
    ((top_top_Product_unit = product_Unity))). % top_unit_def
thf(fact_180_PiE__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (piE_Ar1580347400le_alt @ I4 @ X5)) = (((![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ I4)) => ((member1334244458le_alt @ (F3 @ X4) @ (X5 @ X4)))))) & ((member684274596le_alt @ F3 @ (extens1528283402le_alt @ I4)))))))). % PiE_iff
thf(fact_181_PiE__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (piE_Ar236171216le_alt @ I4 @ X5)) = (((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ I4)) => ((member1334244458le_alt @ (F3 @ X4) @ (X5 @ X4)))))) & ((member183760530le_alt @ F3 @ (extens951643470le_alt @ I4)))))))). % PiE_iff
thf(fact_182_PiE__ext, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, K : set_Ar1007576579e_indi, S2 : arrow_1429744205e_indi > set_se2071012361le_alt, Y : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ (piE_Ar1580347400le_alt @ K @ S2)) => ((member684274596le_alt @ Y @ (piE_Ar1580347400le_alt @ K @ S2)) => ((![I5 : arrow_1429744205e_indi]: ((member1966420836e_indi @ I5 @ K) => ((X @ I5) = (Y @ I5)))) => (X = Y))))))). % PiE_ext
thf(fact_183_PiE__ext, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, K : set_Ar809243995le_alt, S2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, Y : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X @ (piE_Ar236171216le_alt @ K @ S2)) => ((member183760530le_alt @ Y @ (piE_Ar236171216le_alt @ K @ S2)) => ((![I5 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ I5 @ K) => ((X @ I5) = (Y @ I5)))) => (X = Y))))))). % PiE_ext
thf(fact_184_PiE__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, S : set_Ar1007576579e_indi, T : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (piE_Ar1580347400le_alt @ S @ T)) => ((member1966420836e_indi @ X @ S) => (member1334244458le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_185_PiE__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, S : set_Pr367596371le_alt, T : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (piE_Pr2084141144le_alt @ S @ T)) => ((member2048039092le_alt @ X @ S) => (member2048039092le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_186_PiE__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, S : set_Pr367596371le_alt, T : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (piE_Pr757114552le_alt @ S @ T)) => ((member2048039092le_alt @ X @ S) => (member1334244458le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_187_PiE__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, S : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (piE_se232226le_alt @ S @ T)) => ((member1334244458le_alt @ X @ S) => (member2048039092le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_188_PiE__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, S : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (piE_se1902809474le_alt @ S @ T)) => ((member1334244458le_alt @ X @ S) => (member1334244458le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_189_PiE__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, S : set_Pr367596371le_alt, T : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (piE_Pr1024471460le_alt @ S @ T)) => ((member2048039092le_alt @ X @ S) => (member684274596le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_190_PiE__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, S : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (piE_Ar974971248le_alt @ S @ T)) => ((member684274596le_alt @ X @ S) => (member2048039092le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_191_PiE__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, S : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (piE_se1100287834le_alt @ S @ T)) => ((member1334244458le_alt @ X @ S) => (member684274596le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_192_PiE__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, S : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (piE_Ar236171216le_alt @ S @ T)) => ((member684274596le_alt @ X @ S) => (member1334244458le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_193_PiE__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, S : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (piE_Ar1900467852le_alt @ S @ T)) => ((member684274596le_alt @ X @ S) => (member684274596le_alt @ (F3 @ X) @ (T @ X))))))). % PiE_mem
thf(fact_194_old_Ounit_Oexhaust, axiom,
    ((![Y : product_unit]: (Y = product_Unity)))). % old.unit.exhaust
thf(fact_195_old_Ounit_Oinducts, axiom,
    ((![P2 : product_unit > $o, Unit : product_unit]: ((P2 @ product_Unity) => (P2 @ Unit))))). % old.unit.inducts
thf(fact_196_PiE__UNIV__domain, axiom,
    ((![T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((piE_Ar236171216le_alt @ top_to685525675le_alt @ T) = (pi_Arr479247969le_alt @ top_to685525675le_alt @ T))))). % PiE_UNIV_domain
thf(fact_197_PiE__UNIV__domain, axiom,
    ((![T : arrow_1429744205e_indi > set_se2071012361le_alt]: ((piE_Ar1580347400le_alt @ top_to1799531699e_indi @ T) = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ T))))). % PiE_UNIV_domain
thf(fact_198_default__unit__def, axiom,
    ((defaul1399868459t_unit = product_Unity))). % default_unit_def
thf(fact_199_extensional__funcset__def, axiom,
    ((![S : set_Ar809243995le_alt, T : set_se2071012361le_alt]: ((piE_Ar236171216le_alt @ S @ (^[I2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: T)) = (inf_in2014612675le_alt @ (pi_Arr479247969le_alt @ S @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: T)) @ (extens951643470le_alt @ S)))))). % extensional_funcset_def
thf(fact_200_extensional__funcset__def, axiom,
    ((![S : set_Ar1007576579e_indi, T : set_se2071012361le_alt]: ((piE_Ar1580347400le_alt @ S @ (^[I2 : arrow_1429744205e_indi]: T)) = (inf_in82880073le_alt @ (pi_Arr1981691447le_alt @ S @ (^[Uu : arrow_1429744205e_indi]: T)) @ (extens1528283402le_alt @ S)))))). % extensional_funcset_def
thf(fact_201_Int__UNIV, axiom,
    ((![A5 : set_Ar1007576579e_indi, B5 : set_Ar1007576579e_indi]: (((inf_in1270134677e_indi @ A5 @ B5) = top_to1799531699e_indi) = (((A5 = top_to1799531699e_indi)) & ((B5 = top_to1799531699e_indi))))))). % Int_UNIV
thf(fact_202_Int__UNIV, axiom,
    ((![A5 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: (((inf_in840442356le_alt @ A5 @ B5) = top_to958727510le_alt) = (((A5 = top_to958727510le_alt)) & ((B5 = top_to958727510le_alt))))))). % Int_UNIV
thf(fact_203_Collect__conj__eq, axiom,
    ((![P2 : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((P2 @ X4)) & ((Q @ X4))))) = (inf_in322684315le_alt @ (collec1399441576le_alt @ P2) @ (collec1399441576le_alt @ Q)))))). % Collect_conj_eq
thf(fact_204_Int__Collect, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ X @ (inf_in607321317le_alt @ A5 @ (collec531981554le_alt @ P2))) = (((member2048039092le_alt @ X @ A5)) & ((P2 @ X))))))). % Int_Collect
thf(fact_205_Int__Collect, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ X @ (inf_in82880073le_alt @ A5 @ (collec1559089382le_alt @ P2))) = (((member684274596le_alt @ X @ A5)) & ((P2 @ X))))))). % Int_Collect
thf(fact_206_Int__Collect, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar182050865le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ X @ (inf_in2014612675le_alt @ A5 @ (collec1382217680le_alt @ P2))) = (((member183760530le_alt @ X @ A5)) & ((P2 @ X))))))). % Int_Collect
thf(fact_207_Int__Collect, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ X @ (inf_in322684315le_alt @ A5 @ (collec1399441576le_alt @ P2))) = (((member1334244458le_alt @ X @ A5)) & ((P2 @ X))))))). % Int_Collect
thf(fact_208_Int__def, axiom,
    ((inf_in607321317le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B6 : set_Pr367596371le_alt]: (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A6)) & ((member2048039092le_alt @ X4 @ B6)))))))))). % Int_def
thf(fact_209_Int__def, axiom,
    ((inf_in82880073le_alt = (^[A6 : set_Ar809243995le_alt]: (^[B6 : set_Ar809243995le_alt]: (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A6)) & ((member684274596le_alt @ X4 @ B6)))))))))). % Int_def
thf(fact_210_Int__def, axiom,
    ((inf_in2014612675le_alt = (^[A6 : set_Ar182050865le_alt]: (^[B6 : set_Ar182050865le_alt]: (collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X4 @ A6)) & ((member183760530le_alt @ X4 @ B6)))))))))). % Int_def
thf(fact_211_Int__def, axiom,
    ((inf_in322684315le_alt = (^[A6 : set_se2071012361le_alt]: (^[B6 : set_se2071012361le_alt]: (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A6)) & ((member1334244458le_alt @ X4 @ B6)))))))))). % Int_def
thf(fact_212_Pi__Int, axiom,
    ((![I4 : set_Ar809243995le_alt, E : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((inf_in2014612675le_alt @ (pi_Arr479247969le_alt @ I4 @ E) @ (pi_Arr479247969le_alt @ I4 @ F2)) = (pi_Arr479247969le_alt @ I4 @ (^[I2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (inf_in322684315le_alt @ (E @ I2) @ (F2 @ I2)))))))). % Pi_Int
thf(fact_213_Pi__Int, axiom,
    ((![I4 : set_Ar1007576579e_indi, E : arrow_1429744205e_indi > set_se2071012361le_alt, F2 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((inf_in82880073le_alt @ (pi_Arr1981691447le_alt @ I4 @ E) @ (pi_Arr1981691447le_alt @ I4 @ F2)) = (pi_Arr1981691447le_alt @ I4 @ (^[I2 : arrow_1429744205e_indi]: (inf_in322684315le_alt @ (E @ I2) @ (F2 @ I2)))))))). % Pi_Int
thf(fact_214_Int__UNIV__left, axiom,
    ((![B5 : set_Ar1007576579e_indi]: ((inf_in1270134677e_indi @ top_to1799531699e_indi @ B5) = B5)))). % Int_UNIV_left
thf(fact_215_Int__UNIV__left, axiom,
    ((![B5 : set_Ar1665529862le_alt]: ((inf_in840442356le_alt @ top_to958727510le_alt @ B5) = B5)))). % Int_UNIV_left
thf(fact_216_Int__UNIV__right, axiom,
    ((![A5 : set_Ar1007576579e_indi]: ((inf_in1270134677e_indi @ A5 @ top_to1799531699e_indi) = A5)))). % Int_UNIV_right
thf(fact_217_Int__UNIV__right, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((inf_in840442356le_alt @ A5 @ top_to958727510le_alt) = A5)))). % Int_UNIV_right
thf(fact_218_PiE__def, axiom,
    ((piE_Ar236171216le_alt = (^[S5 : set_Ar809243995le_alt]: (^[T2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (inf_in2014612675le_alt @ (pi_Arr479247969le_alt @ S5 @ T2) @ (extens951643470le_alt @ S5))))))). % PiE_def
thf(fact_219_PiE__def, axiom,
    ((piE_Ar1580347400le_alt = (^[S5 : set_Ar1007576579e_indi]: (^[T2 : arrow_1429744205e_indi > set_se2071012361le_alt]: (inf_in82880073le_alt @ (pi_Arr1981691447le_alt @ S5 @ T2) @ (extens1528283402le_alt @ S5))))))). % PiE_def
thf(fact_220_inf__top__left, axiom,
    ((![X : set_Ar1007576579e_indi]: ((inf_in1270134677e_indi @ top_to1799531699e_indi @ X) = X)))). % inf_top_left
thf(fact_221_inf__top__left, axiom,
    ((![X : set_Ar1665529862le_alt]: ((inf_in840442356le_alt @ top_to958727510le_alt @ X) = X)))). % inf_top_left
thf(fact_222_inf__top__left, axiom,
    ((![X : product_unit]: ((inf_inf_Product_unit @ top_top_Product_unit @ X) = X)))). % inf_top_left
thf(fact_223_inf__top__right, axiom,
    ((![X : set_Ar1007576579e_indi]: ((inf_in1270134677e_indi @ X @ top_to1799531699e_indi) = X)))). % inf_top_right
thf(fact_224_inf__top__right, axiom,
    ((![X : set_Ar1665529862le_alt]: ((inf_in840442356le_alt @ X @ top_to958727510le_alt) = X)))). % inf_top_right
thf(fact_225_inf__top__right, axiom,
    ((![X : product_unit]: ((inf_inf_Product_unit @ X @ top_top_Product_unit) = X)))). % inf_top_right
thf(fact_226_inf__top_Oright__neutral, axiom,
    ((![A : set_Ar1007576579e_indi]: ((inf_in1270134677e_indi @ A @ top_to1799531699e_indi) = A)))). % inf_top.right_neutral
thf(fact_227_inf__top_Oright__neutral, axiom,
    ((![A : set_Ar1665529862le_alt]: ((inf_in840442356le_alt @ A @ top_to958727510le_alt) = A)))). % inf_top.right_neutral
thf(fact_228_inf__top_Oright__neutral, axiom,
    ((![A : product_unit]: ((inf_inf_Product_unit @ A @ top_top_Product_unit) = A)))). % inf_top.right_neutral
thf(fact_229_inf__top_Oneutr__eq__iff, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi]: ((top_to1799531699e_indi = (inf_in1270134677e_indi @ A @ B)) = (((A = top_to1799531699e_indi)) & ((B = top_to1799531699e_indi))))))). % inf_top.neutr_eq_iff
thf(fact_230_inf__top_Oneutr__eq__iff, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((top_to958727510le_alt = (inf_in840442356le_alt @ A @ B)) = (((A = top_to958727510le_alt)) & ((B = top_to958727510le_alt))))))). % inf_top.neutr_eq_iff
thf(fact_231_inf__top_Oneutr__eq__iff, axiom,
    ((![A : product_unit, B : product_unit]: ((top_top_Product_unit = (inf_inf_Product_unit @ A @ B)) = (((A = top_top_Product_unit)) & ((B = top_top_Product_unit))))))). % inf_top.neutr_eq_iff

% 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,
    ((![I5 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (p2 @ I5)) = (member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (q @ I5)))))).
