% 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_146__5187246_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:15.677

% Could-be-implicit typings (20)
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_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_Ar657346797le_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar1648870283e_indi : $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_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).

% Explicit typings (96)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    pi_Arr1556925371e_indi : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1007576579e_indi) > set_Ar1648870283e_indi).
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_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_Arr392975077le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar809243995le_alt) > set_Ar657346797le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    pi_Arr1561875345e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Ar1612966069e_indi).
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_FuncSet_Ocompose_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    compos1161645258le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Ocompose_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__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,
    compos239206496le_alt : set_Ar809243995le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Ocompose_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    compos848306234le_alt : set_Ar809243995le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Ocompose_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    compos1576979126le_alt : set_Ar1007576579e_indi > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Ocompose_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    compos450220916le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Ocompose_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    compos253629262le_alt : set_Ar1007576579e_indi > (set_Pr367596371le_alt > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_FuncSet_Oextensional_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,
    extens951643470le_alt : set_Ar809243995le_alt > set_Ar182050865le_alt).
thf(sy_c_FuncSet_Oextensional_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,
    extens1528283402le_alt : set_Ar1007576579e_indi > set_Ar809243995le_alt).
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    member225806060e_indi : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi) > set_Ar1648870283e_indi > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member361641010le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt) > set_Ar3481041le_alt > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member183760530le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    member1846093134le_alt : (arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar657346797le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    member1949987838e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > set_Ar1612966069e_indi > $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__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__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_thesis____, type,
    thesis : $o).

% Relevant facts (220)
thf(fact_0_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_1_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_2_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_3_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_4_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_5_converse__in__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ (conver1781819635le_alt @ L2) @ arrow_1848678355le_Lin) = (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin))))). % converse_in_Lin
thf(fact_6_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_7_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_8_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_9_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_10_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_11_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_12_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_13_converse__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converse_iff
thf(fact_14_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)) => ((![A2 : arrow_1857593510le_alt]: (![B2 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_15_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)) => ((![A2 : arrow_1857593510le_alt]: (![B2 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X2))))))))))))). % unanimity_def
thf(fact_16_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_17_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_18_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_19_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_20_converseD, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converseD
thf(fact_21_converseE, axiom,
    ((![Yx : produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ Yx @ (conver1781819635le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((Yx = (produc1494124311le_alt @ Y3 @ X3)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R))))))))))). % converseE
thf(fact_22_converse_Ocases, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ A22 @ A1) @ R))))). % converse.cases
thf(fact_23_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_24_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_25_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_26_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P3 : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A4 @ B4))) => (P2 @ P3))))). % prod_cases
thf(fact_27_surj__pair, axiom,
    ((![P3 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_28_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: (((^[X2 : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ R2))) = (^[X2 : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ S2)))) = (R2 = S2))))). % pred_equals_eq2
thf(fact_29_converse_Oinducts, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ (produc1494124311le_alt @ X1 @ X22) @ (conver1781819635le_alt @ R)) => ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ R) => (P2 @ B4 @ A4))) => (P2 @ X1 @ X22)))))). % converse.inducts
thf(fact_30_converse_Ointros, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (conver1781819635le_alt @ R)))))). % converse.intros
thf(fact_31_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A2 : arrow_1857593510le_alt]: (?[B2 : arrow_1857593510le_alt]: (((A1 = B2)) & ((((A22 = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ R))))))))))). % converse.simps
thf(fact_32_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_33_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_34_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_35_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_36_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_37_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_38_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_39_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_40_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_41_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_42_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S3 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S3) @ R2)))))). % ssubst_Pair_rhs
thf(fact_43_dictatorI, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : 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 @ I2)) => (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F2 @ X3))))))) => (arrow_960434986ctator @ F2 @ I2)))))). % dictatorI
thf(fact_44_converse__inv__image, axiom,
    ((![R2 : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((conver1781819635le_alt @ (inv_im155136540le_alt @ R2 @ F3)) = (inv_im155136540le_alt @ (conver1781819635le_alt @ R2) @ F3))))). % converse_inv_image
thf(fact_45_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_46_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F3 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R @ F3)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F3 @ X) @ (F3 @ Y)) @ R))))). % in_inv_image
thf(fact_47_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_48_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_49_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_50_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_51_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_52_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_53_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_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_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_74_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_75_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_76_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_77_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_78_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_79_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_80_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_81_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_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_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_90_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_91_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_92_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_93_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_94_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_95_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_96_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_97_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_98_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_99_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_100_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_101_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_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_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_111_Pi__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I3 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ I3 @ X4)) = (![X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ I3)) => ((member1334244458le_alt @ (F3 @ X2) @ (X4 @ X2))))))))). % Pi_iff
thf(fact_112_Pi__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ I3 @ X4)) = (![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ I3)) => ((member1334244458le_alt @ (F3 @ X2) @ (X4 @ X2))))))))). % Pi_iff
thf(fact_113_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_114_funcset__compose, axiom,
    ((![F3 : arrow_1429744205e_indi > arrow_1429744205e_indi, A5 : set_Ar1007576579e_indi, B5 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member1949987838e_indi @ F3 @ (pi_Arr1561875345e_indi @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ B5 @ (^[Uu : arrow_1429744205e_indi]: C))) => (member684274596le_alt @ (compos450220916le_alt @ A5 @ G @ F3) @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: C)))))))). % funcset_compose
thf(fact_115_funcset__compose, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi, A5 : set_Ar809243995le_alt, B5 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member225806060e_indi @ F3 @ (pi_Arr1556925371e_indi @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ B5 @ (^[Uu : arrow_1429744205e_indi]: C))) => (member183760530le_alt @ (compos239206496le_alt @ A5 @ G @ F3) @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: C)))))))). % funcset_compose
thf(fact_116_funcset__compose, axiom,
    ((![F3 : arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_Ar809243995le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member1846093134le_alt @ F3 @ (pi_Arr392975077le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member183760530le_alt @ G @ (pi_Arr479247969le_alt @ B5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: C))) => (member684274596le_alt @ (compos1576979126le_alt @ A5 @ G @ F3) @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: C)))))))). % funcset_compose
thf(fact_117_funcset__compose, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member183760530le_alt @ G @ (pi_Arr479247969le_alt @ B5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: C))) => (member183760530le_alt @ (compos1161645258le_alt @ A5 @ G @ F3) @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: C)))))))). % funcset_compose
thf(fact_118_funcset__compose, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, G : set_Pr367596371le_alt > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1775590686le_alt @ G @ (pi_set1240805297le_alt @ B5 @ (^[Uu : set_Pr367596371le_alt]: C))) => (member684274596le_alt @ (compos253629262le_alt @ A5 @ G @ F3) @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: C)))))))). % funcset_compose
thf(fact_119_funcset__compose, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, G : set_Pr367596371le_alt > set_Pr367596371le_alt, C : set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member1775590686le_alt @ G @ (pi_set1240805297le_alt @ B5 @ (^[Uu : set_Pr367596371le_alt]: C))) => (member183760530le_alt @ (compos848306234le_alt @ A5 @ G @ F3) @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: C)))))))). % funcset_compose
thf(fact_120_The__split__eq, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((the_Pr821106518le_alt @ (produc624247124_alt_o @ (^[X5 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (((X = X5)) & ((Y = Y4))))))) = (produc1494124311le_alt @ X @ Y))))). % The_split_eq
thf(fact_121_case__prodI, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F3 @ A @ B) => (produc624247124_alt_o @ F3 @ (produc1494124311le_alt @ A @ B)))))). % case_prodI
thf(fact_122_case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A4 @ B4)) => (C2 @ A4 @ B4))) => (produc624247124_alt_o @ C2 @ P3))))). % case_prodI2
thf(fact_123_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_124_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_125_case__prodD, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F3 @ (produc1494124311le_alt @ A @ B)) => (F3 @ A @ B))))). % case_prodD
thf(fact_126_case__prodE, axiom,
    ((![C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, P3 : produc16571293le_alt]: ((produc624247124_alt_o @ C2 @ P3) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((C2 @ X3 @ Y3))))))))))). % case_prodE
thf(fact_127_converse__unfold, axiom,
    ((conver1781819635le_alt = (^[R3 : set_Pr367596371le_alt]: (collec531981554le_alt @ (produc624247124_alt_o @ (^[Y2 : arrow_1857593510le_alt]: (^[X2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ R3))))))))). % converse_unfold
thf(fact_128_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_129_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_130_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_131_UNIV__I, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt)))). % UNIV_I
thf(fact_132_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_133_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_134_converse__UNIV, axiom,
    (((conver1781819635le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % converse_UNIV
thf(fact_135_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A4 @ B4)) => (member1334244458le_alt @ Z @ (C2 @ A4 @ B4)))) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C2 @ P3)))))). % mem_case_prodI2
thf(fact_136_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : produc16571293le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A4 @ B4)) => (member2048039092le_alt @ Z @ (C2 @ A4 @ B4)))) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C2 @ P3)))))). % mem_case_prodI2
thf(fact_137_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A4 @ B4)) => (member684274596le_alt @ Z @ (C2 @ A4 @ B4)))) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C2 @ P3)))))). % mem_case_prodI2
thf(fact_138_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A4 @ B4)) => (member183760530le_alt @ Z @ (C2 @ A4 @ B4)))) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C2 @ P3)))))). % mem_case_prodI2
thf(fact_139_mem__case__prodI, axiom,
    ((![Z : set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ Z @ (C2 @ A @ B)) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C2 @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_140_mem__case__prodI, axiom,
    ((![Z : produc16571293le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member2048039092le_alt @ Z @ (C2 @ A @ B)) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C2 @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_141_mem__case__prodI, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member684274596le_alt @ Z @ (C2 @ A @ B)) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C2 @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_142_mem__case__prodI, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member183760530le_alt @ Z @ (C2 @ A @ B)) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C2 @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_143_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P3 : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C2 @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_144_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P3 : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C2 @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_145_mem__case__prodE, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, P3 : produc16571293le_alt]: ((member684274596le_alt @ Z @ (produc773314629le_alt @ C2 @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member684274596le_alt @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_146_mem__case__prodE, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, P3 : produc16571293le_alt]: ((member183760530le_alt @ Z @ (produc1576739865le_alt @ C2 @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member183760530le_alt @ Z @ (C2 @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_147_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_148_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_149_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_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_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A5)) => (top_to469035705le_alt = A5))))). % UNIV_eq_I
thf(fact_154_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_155_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_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_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X2 : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_160_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X2 : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_161_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X2 : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_162_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_163_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_164_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_165_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_166_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_167_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_168_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_169_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_170_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_171_top__empty__eq, axiom,
    ((top_to1892800228_alt_o = (^[X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt))))). % top_empty_eq
thf(fact_172_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_173_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_174_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_175_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_176_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_177_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X2 : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_178_case__prod__Pair__iden, axiom,
    ((![P3 : produc16571293le_alt]: ((produc846580013le_alt @ produc1494124311le_alt @ P3) = P3)))). % case_prod_Pair_iden
thf(fact_179_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_180_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_181_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_182_compose__Id, axiom,
    ((![G : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt]: ((member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member684274596le_alt @ G @ (extens1528283402le_alt @ A5)) => ((compos450220916le_alt @ A5 @ G @ (restri908404718e_indi @ (^[X2 : arrow_1429744205e_indi]: X2) @ A5)) = G)))))). % compose_Id
thf(fact_183_compose__Id, axiom,
    ((![G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt]: ((member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member183760530le_alt @ G @ (extens951643470le_alt @ A5)) => ((compos1161645258le_alt @ A5 @ G @ (restri2097212184le_alt @ (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: X2) @ A5)) = G)))))). % compose_Id
thf(fact_184_Id__compose, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member684274596le_alt @ F3 @ (extens1528283402le_alt @ A5)) => ((compos253629262le_alt @ A5 @ (restri12751886le_alt @ (^[Y2 : set_Pr367596371le_alt]: Y2) @ B5) @ F3) = F3)))))). % Id_compose
thf(fact_185_Id__compose, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member183760530le_alt @ F3 @ (extens951643470le_alt @ A5)) => ((compos848306234le_alt @ A5 @ (restri12751886le_alt @ (^[Y2 : set_Pr367596371le_alt]: Y2) @ B5) @ F3) = F3)))))). % Id_compose
thf(fact_186_restrictI, 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 @ (restri1835750036le_alt @ F3 @ A5) @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % restrictI
thf(fact_187_restrictI, 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 @ (restri1395776228le_alt @ F3 @ A5) @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % restrictI
thf(fact_188_restrictI, 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 @ (restri114015662le_alt @ F3 @ A5) @ (pi_set365323601le_alt @ A5 @ B5)))))). % restrictI
thf(fact_189_restrictI, 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 @ (restri870897988le_alt @ F3 @ A5) @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % restrictI
thf(fact_190_restrictI, 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 @ (restri12751886le_alt @ F3 @ A5) @ (pi_set1240805297le_alt @ A5 @ B5)))))). % restrictI
thf(fact_191_restrictI, 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 @ (restri2038060568le_alt @ F3 @ A5) @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % restrictI
thf(fact_192_restrictI, 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 @ (restri1988560356le_alt @ F3 @ A5) @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % restrictI
thf(fact_193_restrictI, 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 @ (restri143877070le_alt @ F3 @ A5) @ (pi_set1343364587le_alt @ A5 @ B5)))))). % restrictI
thf(fact_194_restrictI, 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 @ (restri1427244100le_alt @ F3 @ A5) @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % restrictI
thf(fact_195_restrictI, 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 @ (restri2097212184le_alt @ F3 @ A5) @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % restrictI
thf(fact_196_extensional__restrict, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi]: ((member684274596le_alt @ F3 @ (extens1528283402le_alt @ A5)) => ((restri1835750036le_alt @ F3 @ A5) = F3))))). % extensional_restrict
thf(fact_197_extensional__restrict, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((member183760530le_alt @ F3 @ (extens951643470le_alt @ A5)) => ((restri1427244100le_alt @ F3 @ A5) = F3))))). % extensional_restrict
thf(fact_198_restrict__extensional, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi]: (member684274596le_alt @ (restri1835750036le_alt @ F3 @ A5) @ (extens1528283402le_alt @ A5))))). % restrict_extensional
thf(fact_199_restrict__extensional, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: (member183760530le_alt @ (restri1427244100le_alt @ F3 @ A5) @ (extens951643470le_alt @ A5))))). % restrict_extensional
thf(fact_200_restrict__in__funcset, 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 @ (restri1835750036le_alt @ F3 @ A5) @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % restrict_in_funcset
thf(fact_201_restrict__in__funcset, 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 @ (restri1395776228le_alt @ F3 @ A5) @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % restrict_in_funcset
thf(fact_202_restrict__in__funcset, 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 @ (restri114015662le_alt @ F3 @ A5) @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_203_restrict__in__funcset, 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 @ (restri870897988le_alt @ F3 @ A5) @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % restrict_in_funcset
thf(fact_204_restrict__in__funcset, 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 @ (restri12751886le_alt @ F3 @ A5) @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_205_restrict__in__funcset, 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 @ (restri2038060568le_alt @ F3 @ A5) @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % restrict_in_funcset
thf(fact_206_restrict__in__funcset, 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 @ (restri1988560356le_alt @ F3 @ A5) @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_207_restrict__in__funcset, 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 @ (restri143877070le_alt @ F3 @ A5) @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_208_restrict__in__funcset, 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 @ (restri1427244100le_alt @ F3 @ A5) @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_209_restrict__in__funcset, 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 @ (restri2097212184le_alt @ F3 @ A5) @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % restrict_in_funcset
thf(fact_210_restrict__Pi__cancel, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, I3 : set_Ar1007576579e_indi, A5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ (restri1835750036le_alt @ X @ I3) @ (pi_Arr1981691447le_alt @ I3 @ A5)) = (member684274596le_alt @ X @ (pi_Arr1981691447le_alt @ I3 @ A5)))))). % restrict_Pi_cancel
thf(fact_211_restrict__Pi__cancel, axiom,
    ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar809243995le_alt, A5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ (restri1427244100le_alt @ X @ I3) @ (pi_Arr479247969le_alt @ I3 @ A5)) = (member183760530le_alt @ X @ (pi_Arr479247969le_alt @ I3 @ A5)))))). % restrict_Pi_cancel
thf(fact_212_converse__empty, axiom,
    (((conver1781819635le_alt @ bot_bo1596236775le_alt) = bot_bo1596236775le_alt))). % converse_empty
thf(fact_213_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_214_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_215_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_216_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) = (?[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X2 @ A5)) & (((B5 @ X2) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_217_Pi__eq__empty, axiom,
    ((![A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A5 @ B5) = bot_bo365569479le_alt) = (?[X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ A5)) & (((B5 @ X2) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_218_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_219_Pi__empty, axiom,
    ((![B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B5) = top_to685525675le_alt)))). % Pi_empty

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![R4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ R4 @ arrow_1848678355le_Lin) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
