% 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_132__5186784_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:05.607

% Could-be-implicit typings (26)
thf(ty_n_t__Set__Oset_I_062_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_M_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_J, type,
    set_Ar2014526681le_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_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_J, type,
    set_se720939393le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_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_Ar883249453le_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_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_J, type,
    set_Pr878102711le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Ar350387917le_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__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_J, type,
    set_se8691405le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_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_se1971956023le_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__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_J, type,
    set_Pr1275488279le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se1671167703le_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__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_se370278869le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr720748555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar1612966069e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1666424426le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar528567456e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1380421567le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (99)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1187035700le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Ar1380421567le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar415527999e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Ar528567456e_indi).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1084018769le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Ar1666424426le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar738911586e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Ar1612966069e_indi).
thf(sy_c_FuncSet_OPi_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_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,
    pi_Arr1706749621le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt) > set_Ar2014526681le_alt).
thf(sy_c_FuncSet_OPi_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1460089257le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar350387917le_alt).
thf(sy_c_FuncSet_OPi_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr2098764809le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar883249453le_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_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_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_set1402292231le_alt : set_se370278869le_alt > ((set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se1671167703le_alt).
thf(sy_c_FuncSet_OPi_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_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_set481180263le_alt : set_se370278869le_alt > ((set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_se1971956023le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_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,
    pi_Pro741994643le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar182050865le_alt) > set_Pr878102711le_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__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,
    pi_Pro353997839le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se370278869le_alt) > set_Pr1275488279le_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,
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thf(sy_c_member_001_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001_062_I_062_It__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_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_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,
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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__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,
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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,
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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,
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thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_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,
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thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_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,
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thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
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thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
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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,
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thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_i, type,
    i : arrow_1429744205e_indi).

% Relevant facts (249)
thf(fact_0_Lin__irrefl, axiom,
    ((![L : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L)))))))). % Lin_irrefl
thf(fact_1_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_2_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I : arrow_1429744205e_indi]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => (((F @ X) = (X @ I)))))))))). % dictator_def
thf(fact_3_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X2 = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X2) @ L))))))). % notin_Lin_iff
thf(fact_4_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ 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) @ (X @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_5_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![A2 : arrow_1857593510le_alt]: (![B2 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X))))))))))))). % unanimity_def
thf(fact_6_Pi__I, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_7_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_8_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_9_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_10_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_11_Pi__I, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_12_Pi__I, axiom,
    ((![A3 : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member2001237014le_alt @ F2 @ (pi_Arr1460089257le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_13_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Ar182050865le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member183760530le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1110545152le_alt @ F2 @ (pi_Pro741994643le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_14_Pi__I, axiom,
    ((![A3 : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member966567542le_alt @ F2 @ (pi_Arr2098764809le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_15_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_Ar182050865le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member183760530le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1377036490le_alt @ F2 @ (pi_set221036125le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_16_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_17_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A4 @ B4)) = (((A = A4)) & ((B = B4))))))). % old.prod.inject
thf(fact_18_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X2 = Y)))) & ((((((X2 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X2 = B)))) => ((((((Y = B)) => ((((X2 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))))))))). % in_above
thf(fact_19_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X2 = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X2 = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X2 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))))))))). % in_below
thf(fact_20_funcsetI, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: B3))))))). % funcsetI
thf(fact_21_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_22_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_23_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_24_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_25_funcsetI, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_26_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_se370278869le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1775590686le_alt @ (F2 @ X3) @ B3))) => (member1244701048le_alt @ F2 @ (pi_Pro353997839le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_27_funcsetI, axiom,
    ((![A3 : set_se370278869le_alt, F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1775590686le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member844470328le_alt @ F2 @ (pi_set1402292231le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_28_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_se370278869le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1775590686le_alt @ (F2 @ X3) @ B3))) => (member1032201006le_alt @ F2 @ (pi_set1572380101le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_29_funcsetI, axiom,
    ((![A3 : set_se370278869le_alt, F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1775590686le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member326648472le_alt @ F2 @ (pi_set481180263le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_30_funcset__id, axiom,
    ((![A3 : set_se2071012361le_alt]: (member1775590686le_alt @ (^[X : set_Pr367596371le_alt]: X) @ (pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: A3)))))). % funcset_id
thf(fact_31_funcset__id, axiom,
    ((![A3 : set_Ar182050865le_alt]: (member902395426le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: X) @ (pi_Arr1706749621le_alt @ A3 @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: A3)))))). % funcset_id
thf(fact_32_funcset__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: B3))) => ((member1966420836e_indi @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_33_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_34_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_35_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_36_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_37_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))) => ((member684274596le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_38_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : set_se370278869le_alt, X2 : produc16571293le_alt]: ((member1244701048le_alt @ F2 @ (pi_Pro353997839le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member1775590686le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_39_funcset__mem, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_se370278869le_alt, B3 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member844470328le_alt @ F2 @ (pi_set1402292231le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt > set_Pr367596371le_alt]: B3))) => ((member1775590686le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_40_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_se370278869le_alt, X2 : set_Pr367596371le_alt]: ((member1032201006le_alt @ F2 @ (pi_set1572380101le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member1775590686le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_41_funcset__mem, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_se370278869le_alt, B3 : set_se2071012361le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member326648472le_alt @ F2 @ (pi_set481180263le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt > set_Pr367596371le_alt]: B3))) => ((member1775590686le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_42_above__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_43_below__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_44_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A5 @ B5))) => (P @ Prod))))). % old.prod.inducts
thf(fact_45_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A5 @ B5)))))))))). % old.prod.exhaust
thf(fact_46_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A4 @ B4)) => (~ (((A = A4) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_47_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P2 : produc16571293le_alt]: ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A5 @ B5))) => (P @ P2))))). % prod_cases
thf(fact_48_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_49_Pi__cong, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_50_Pi__cong, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_51_Pi__cong, axiom,
    ((![A3 : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member2001237014le_alt @ F2 @ (pi_Arr1460089257le_alt @ A3 @ B3)) = (member2001237014le_alt @ G @ (pi_Arr1460089257le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_52_Pi__cong, axiom,
    ((![A3 : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member966567542le_alt @ F2 @ (pi_Arr2098764809le_alt @ A3 @ B3)) = (member966567542le_alt @ G @ (pi_Arr2098764809le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_53_Pi__cong, axiom,
    ((![A3 : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member902395426le_alt @ F2 @ (pi_Arr1706749621le_alt @ A3 @ B3)) = (member902395426le_alt @ G @ (pi_Arr1706749621le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_54_Pi__cong, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, G : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![W : set_Pr367596371le_alt]: ((member1334244458le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)) = (member1775590686le_alt @ G @ (pi_set1240805297le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_55_Pi__cong, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_Ar182050865le_alt]: ((![W : set_Pr367596371le_alt]: ((member1334244458le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member1377036490le_alt @ F2 @ (pi_set221036125le_alt @ A3 @ B3)) = (member1377036490le_alt @ G @ (pi_set221036125le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_56_Pi__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) => ((member1966420836e_indi @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_57_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_58_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_59_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_60_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_61_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) => ((member684274596le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_62_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se370278869le_alt, X2 : produc16571293le_alt]: ((member1244701048le_alt @ F2 @ (pi_Pro353997839le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member1775590686le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_63_Pi__mem, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_se370278869le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member844470328le_alt @ F2 @ (pi_set1402292231le_alt @ A3 @ B3)) => ((member1775590686le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_64_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se370278869le_alt, X2 : set_Pr367596371le_alt]: ((member1032201006le_alt @ F2 @ (pi_set1572380101le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member1775590686le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_65_Pi__mem, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_se370278869le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member326648472le_alt @ F2 @ (pi_set481180263le_alt @ A3 @ B3)) => ((member1775590686le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_66_Pi__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, I2 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ I2 @ X4)) = (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_67_Pi__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ I2 @ X4)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_68_Pi__iff, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, I2 : set_se2071012361le_alt, X4 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ I2 @ X4)) = (![X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_69_Pi__iff, axiom,
    ((![F2 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_se2071012361le_alt, X4 : set_Pr367596371le_alt > set_Ar182050865le_alt]: ((member1377036490le_alt @ F2 @ (pi_set221036125le_alt @ I2 @ X4)) = (![X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ I2)) => ((member183760530le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_70_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, I2 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2001237014le_alt @ F2 @ (pi_Arr1460089257le_alt @ I2 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I2)) => ((member2048039092le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_71_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member966567542le_alt @ F2 @ (pi_Arr2098764809le_alt @ I2 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_72_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((member902395426le_alt @ F2 @ (pi_Arr1706749621le_alt @ I2 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I2)) => ((member183760530le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_73_Pi__I_H, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_74_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_75_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_76_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_77_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_78_Pi__I_H, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_79_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se370278869le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1775590686le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1244701048le_alt @ F2 @ (pi_Pro353997839le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_80_Pi__I_H, axiom,
    ((![A3 : set_se370278869le_alt, F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc16571293le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1775590686le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member844470328le_alt @ F2 @ (pi_set1402292231le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_81_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se370278869le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1775590686le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1032201006le_alt @ F2 @ (pi_set1572380101le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_82_Pi__I_H, axiom,
    ((![A3 : set_se370278869le_alt, F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1775590686le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member326648472le_alt @ F2 @ (pi_set481180263le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_83_PiE, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1966420836e_indi @ X2 @ A3)))))))). % PiE
thf(fact_84_PiE, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_85_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_86_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_87_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_88_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A3)))))))). % PiE
thf(fact_89_PiE, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_se370278869le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member844470328le_alt @ F2 @ (pi_set1402292231le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1775590686le_alt @ X2 @ A3)))))))). % PiE
thf(fact_90_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se370278869le_alt, X2 : produc16571293le_alt]: ((member1244701048le_alt @ F2 @ (pi_Pro353997839le_alt @ A3 @ B3)) => ((~ ((member1775590686le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_91_PiE, axiom,
    ((![F2 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_se370278869le_alt, B3 : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member326648472le_alt @ F2 @ (pi_set481180263le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1775590686le_alt @ X2 @ A3)))))))). % PiE
thf(fact_92_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se370278869le_alt, X2 : set_Pr367596371le_alt]: ((member1032201006le_alt @ F2 @ (pi_set1572380101le_alt @ A3 @ B3)) => ((~ ((member1775590686le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_93_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X2) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_94_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X2) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_95_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ R))) = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_96_in__mktop, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X2 = Z)))) & ((((((Y = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))). % in_mktop
thf(fact_97_in__mkbot, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X2 = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((X2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))). % in_mkbot
thf(fact_98_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_99_ssubst__Pair__rhs, axiom,
    ((![R2 : arrow_1857593510le_alt, S2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S2) @ R) => ((S3 = S2) => (member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_100_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_101_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_102_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt > set_Pr367596371le_alt, P : (set_Pr367596371le_alt > set_Pr367596371le_alt) > $o]: ((member1775590686le_alt @ A @ (collec1475725920le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_103_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : (set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member1377036490le_alt @ A @ (collec28207372le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_104_mem__Collect__eq, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, P : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt) > $o]: ((member2001237014le_alt @ A @ (collec1890909272le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_105_mem__Collect__eq, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member966567542le_alt @ A @ (collec1765222072le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_106_mem__Collect__eq, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member902395426le_alt @ A @ (collec1942128996le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_107_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_108_Collect__mem__eq, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_109_Collect__mem__eq, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_110_Collect__mem__eq, axiom,
    ((![A3 : set_se370278869le_alt]: ((collec1475725920le_alt @ (^[X : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_111_Collect__mem__eq, axiom,
    ((![A3 : set_se720939393le_alt]: ((collec28207372le_alt @ (^[X : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_112_Collect__mem__eq, axiom,
    ((![A3 : set_Ar350387917le_alt]: ((collec1890909272le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_113_Collect__mem__eq, axiom,
    ((![A3 : set_Ar883249453le_alt]: ((collec1765222072le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_114_Collect__mem__eq, axiom,
    ((![A3 : set_Ar2014526681le_alt]: ((collec1942128996le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_115_Collect__mem__eq, axiom,
    ((![A3 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_116_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_117_Pi__UNIV, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_118_Pi__UNIV, axiom,
    ((![A3 : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_119_Pi__UNIV, axiom,
    ((![A3 : set_se2071012361le_alt]: ((pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to1036171045le_alt)))). % Pi_UNIV
thf(fact_120_Pi__UNIV, axiom,
    ((![A3 : set_se2071012361le_alt]: ((pi_set221036125le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: top_to803745505le_alt)) = top_to1484314321le_alt)))). % Pi_UNIV
thf(fact_121_Pi__UNIV, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((pi_Arr1460089257le_alt @ A3 @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to224369155le_alt)) = top_to1430252573le_alt)))). % Pi_UNIV
thf(fact_122_Pi__UNIV, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((pi_Arr2098764809le_alt @ A3 @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to1646624381le_alt)))). % Pi_UNIV
thf(fact_123_Pi__UNIV, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((pi_Arr1706749621le_alt @ A3 @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to803745505le_alt)) = top_to1977016873le_alt)))). % Pi_UNIV
thf(fact_124_iso__tuple__UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % iso_tuple_UNIV_I
thf(fact_125_iso__tuple__UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_126_iso__tuple__UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_127_iso__tuple__UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X2 @ top_to1036171045le_alt)))). % iso_tuple_UNIV_I
thf(fact_128_iso__tuple__UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X2 @ top_to1484314321le_alt)))). % iso_tuple_UNIV_I
thf(fact_129_iso__tuple__UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X2 @ top_to1430252573le_alt)))). % iso_tuple_UNIV_I
thf(fact_130_iso__tuple__UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X2 @ top_to1646624381le_alt)))). % iso_tuple_UNIV_I
thf(fact_131_iso__tuple__UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X2 @ top_to1977016873le_alt)))). % iso_tuple_UNIV_I
thf(fact_132_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_133_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_134_UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % UNIV_I
thf(fact_135_UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_136_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_137_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X2 @ top_to1036171045le_alt)))). % UNIV_I
thf(fact_138_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X2 @ top_to1484314321le_alt)))). % UNIV_I
thf(fact_139_UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X2 @ top_to1430252573le_alt)))). % UNIV_I
thf(fact_140_UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X2 @ top_to1646624381le_alt)))). % UNIV_I
thf(fact_141_UNIV__I, axiom,
    ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X2 @ top_to1977016873le_alt)))). % UNIV_I
thf(fact_142_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_143_UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_144_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_145_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_146_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_147_UNIV__witness, axiom,
    ((?[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_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 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_150_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X3 @ top_to1036171045le_alt)))). % UNIV_witness
thf(fact_151_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X3 @ top_to1484314321le_alt)))). % UNIV_witness
thf(fact_152_UNIV__witness, axiom,
    ((?[X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X3 @ top_to1430252573le_alt)))). % UNIV_witness
thf(fact_153_UNIV__witness, axiom,
    ((?[X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X3 @ top_to1646624381le_alt)))). % UNIV_witness
thf(fact_154_UNIV__witness, axiom,
    ((?[X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X3 @ top_to1977016873le_alt)))). % UNIV_witness
thf(fact_155_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_156_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_157_UNIV__eq__I, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ A3)) => (top_to803745505le_alt = A3))))). % UNIV_eq_I
thf(fact_158_UNIV__eq__I, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A3)) => (top_to224369155le_alt = A3))))). % UNIV_eq_I
thf(fact_159_UNIV__eq__I, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A3)) => (top_to469035705le_alt = A3))))). % UNIV_eq_I
thf(fact_160_UNIV__eq__I, axiom,
    ((![A3 : set_se370278869le_alt]: ((![X3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X3 @ A3)) => (top_to1036171045le_alt = A3))))). % UNIV_eq_I
thf(fact_161_UNIV__eq__I, axiom,
    ((![A3 : set_se720939393le_alt]: ((![X3 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X3 @ A3)) => (top_to1484314321le_alt = A3))))). % UNIV_eq_I
thf(fact_162_UNIV__eq__I, axiom,
    ((![A3 : set_Ar350387917le_alt]: ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X3 @ A3)) => (top_to1430252573le_alt = A3))))). % UNIV_eq_I
thf(fact_163_UNIV__eq__I, axiom,
    ((![A3 : set_Ar883249453le_alt]: ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X3 @ A3)) => (top_to1646624381le_alt = A3))))). % UNIV_eq_I
thf(fact_164_UNIV__eq__I, axiom,
    ((![A3 : set_Ar2014526681le_alt]: ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X3 @ A3)) => (top_to1977016873le_alt = A3))))). % UNIV_eq_I
thf(fact_165_UNIV__eq__I, axiom,
    ((![A3 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A3)) => (top_to1799531699e_indi = A3))))). % UNIV_eq_I
thf(fact_166_UNIV__eq__I, axiom,
    ((![A3 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A3)) => (top_to958727510le_alt = A3))))). % UNIV_eq_I
thf(fact_167_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_168_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_169_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_170_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_171_top__empty__eq, axiom,
    ((top_to1892800228_alt_o = (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt))))). % top_empty_eq
thf(fact_172_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_173_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_174_top__empty__eq, axiom,
    ((top_to1406106616_alt_o = (^[X : set_Pr367596371le_alt > set_Pr367596371le_alt]: (member1775590686le_alt @ X @ top_to1036171045le_alt))))). % top_empty_eq
thf(fact_175_top__empty__eq, axiom,
    ((top_to918230348_alt_o = (^[X : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member1377036490le_alt @ X @ top_to1484314321le_alt))))). % top_empty_eq
thf(fact_176_top__empty__eq, axiom,
    ((top_to369610496_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ top_to1430252573le_alt))))). % top_empty_eq
thf(fact_177_top__empty__eq, axiom,
    ((top_to491816096_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ top_to1646624381le_alt))))). % top_empty_eq
thf(fact_178_top__empty__eq, axiom,
    ((top_to2021186036_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X @ top_to1977016873le_alt))))). % top_empty_eq
thf(fact_179_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_180_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_181_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_182_Pi__empty, axiom,
    ((![B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr479247969le_alt @ bot_bo365569479le_alt @ B3) = top_to803745505le_alt)))). % Pi_empty
thf(fact_183_Pi__empty, axiom,
    ((![B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B3) = top_to685525675le_alt)))). % Pi_empty
thf(fact_184_Pi__empty, axiom,
    ((![B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((pi_set1240805297le_alt @ bot_bo1518363805le_alt @ B3) = top_to1036171045le_alt)))). % Pi_empty
thf(fact_185_Pi__empty, axiom,
    ((![B3 : set_Pr367596371le_alt > set_Ar182050865le_alt]: ((pi_set221036125le_alt @ bot_bo1518363805le_alt @ B3) = top_to1484314321le_alt)))). % Pi_empty
thf(fact_186_Pi__empty, axiom,
    ((![B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((pi_Arr1460089257le_alt @ bot_bo13098693le_alt @ B3) = top_to1430252573le_alt)))). % Pi_empty
thf(fact_187_Pi__empty, axiom,
    ((![B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr2098764809le_alt @ bot_bo13098693le_alt @ B3) = top_to1646624381le_alt)))). % Pi_empty
thf(fact_188_Pi__empty, axiom,
    ((![B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((pi_Arr1706749621le_alt @ bot_bo13098693le_alt @ B3) = top_to1977016873le_alt)))). % Pi_empty
thf(fact_189_PiE__UNIV, axiom,
    (((piE_Ar738911586e_indi @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to498310661e_indi))). % PiE_UNIV
thf(fact_190_PiE__UNIV, axiom,
    (((piE_Ar1084018769le_alt @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to1139905818le_alt))). % PiE_UNIV
thf(fact_191_PiE__UNIV, axiom,
    (((piE_Ar415527999e_indi @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to2048848e_indi))). % PiE_UNIV
thf(fact_192_PiE__UNIV, axiom,
    (((piE_Ar1187035700le_alt @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to290516239le_alt))). % PiE_UNIV
thf(fact_193_curryI, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F2 @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F2 @ A @ B))))). % curryI
thf(fact_194_empty__iff, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ C @ bot_bo13098693le_alt)))))). % empty_iff
thf(fact_195_empty__iff, axiom,
    ((![C : produc16571293le_alt]: (~ ((member2048039092le_alt @ C @ bot_bo1596236775le_alt)))))). % empty_iff
thf(fact_196_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ C @ bot_bo1518363805le_alt)))))). % empty_iff
thf(fact_197_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt > set_Pr367596371le_alt]: (~ ((member1775590686le_alt @ C @ bot_bo869397057le_alt)))))). % empty_iff
thf(fact_198_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member1377036490le_alt @ C @ bot_bo1631280109le_alt)))))). % empty_iff
thf(fact_199_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ C @ bot_bo709157177le_alt)))))). % empty_iff
thf(fact_200_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ C @ bot_bo1793590169le_alt)))))). % empty_iff
thf(fact_201_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ C @ bot_bo1697362245le_alt)))))). % empty_iff
thf(fact_202_all__not__in__conv, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ X @ A3)))) = (A3 = bot_bo13098693le_alt))))). % all_not_in_conv
thf(fact_203_all__not__in__conv, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: (~ ((member2048039092le_alt @ X @ A3)))) = (A3 = bot_bo1596236775le_alt))))). % all_not_in_conv
thf(fact_204_all__not__in__conv, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ X @ A3)))) = (A3 = bot_bo1518363805le_alt))))). % all_not_in_conv
thf(fact_205_all__not__in__conv, axiom,
    ((![A3 : set_se370278869le_alt]: ((![X : set_Pr367596371le_alt > set_Pr367596371le_alt]: (~ ((member1775590686le_alt @ X @ A3)))) = (A3 = bot_bo869397057le_alt))))). % all_not_in_conv
thf(fact_206_all__not__in__conv, axiom,
    ((![A3 : set_se720939393le_alt]: ((![X : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member1377036490le_alt @ X @ A3)))) = (A3 = bot_bo1631280109le_alt))))). % all_not_in_conv
thf(fact_207_all__not__in__conv, axiom,
    ((![A3 : set_Ar350387917le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ X @ A3)))) = (A3 = bot_bo709157177le_alt))))). % all_not_in_conv
thf(fact_208_all__not__in__conv, axiom,
    ((![A3 : set_Ar883249453le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ X @ A3)))) = (A3 = bot_bo1793590169le_alt))))). % all_not_in_conv
thf(fact_209_all__not__in__conv, axiom,
    ((![A3 : set_Ar2014526681le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ X @ A3)))) = (A3 = bot_bo1697362245le_alt))))). % all_not_in_conv
thf(fact_210_Collect__empty__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: (((collec1399441576le_alt @ P) = bot_bo1518363805le_alt) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_211_empty__Collect__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: ((bot_bo1518363805le_alt = (collec1399441576le_alt @ P)) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_212_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = top_to469035705le_alt)) & ((~ (P)) => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_213_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = top_to1799531699e_indi)) & ((~ (P)) => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = bot_bo1390904983e_indi)))))). % Collect_const
thf(fact_214_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = top_to958727510le_alt)) & ((~ (P)) => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_215_Pi__eq__empty, axiom,
    ((![A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr479247969le_alt @ A3 @ B3) = bot_bo13098693le_alt) = (?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_216_Pi__eq__empty, axiom,
    ((![A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A3 @ B3) = bot_bo365569479le_alt) = (?[X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_217_Pi__eq__empty, axiom,
    ((![A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: (((pi_set1240805297le_alt @ A3 @ B3) = bot_bo869397057le_alt) = (?[X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_218_Pi__eq__empty, axiom,
    ((![A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Ar182050865le_alt]: (((pi_set221036125le_alt @ A3 @ B3) = bot_bo1631280109le_alt) = (?[X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A3)) & (((B3 @ X) = bot_bo13098693le_alt)))))))). % Pi_eq_empty
thf(fact_219_Pi__eq__empty, axiom,
    ((![A3 : set_Ar182050865le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((pi_Arr1460089257le_alt @ A3 @ B3) = bot_bo709157177le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A3)) & (((B3 @ X) = bot_bo1596236775le_alt)))))))). % Pi_eq_empty
thf(fact_220_Pi__eq__empty, axiom,
    ((![A3 : set_Ar182050865le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr2098764809le_alt @ A3 @ B3) = bot_bo1793590169le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_221_Pi__eq__empty, axiom,
    ((![A3 : set_Ar182050865le_alt, B3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: (((pi_Arr1706749621le_alt @ A3 @ B3) = bot_bo1697362245le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A3)) & (((B3 @ X) = bot_bo13098693le_alt)))))))). % Pi_eq_empty
thf(fact_222_emptyE, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ A @ bot_bo13098693le_alt)))))). % emptyE
thf(fact_223_emptyE, axiom,
    ((![A : produc16571293le_alt]: (~ ((member2048039092le_alt @ A @ bot_bo1596236775le_alt)))))). % emptyE
thf(fact_224_emptyE, axiom,
    ((![A : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ A @ bot_bo1518363805le_alt)))))). % emptyE
thf(fact_225_emptyE, axiom,
    ((![A : set_Pr367596371le_alt > set_Pr367596371le_alt]: (~ ((member1775590686le_alt @ A @ bot_bo869397057le_alt)))))). % emptyE
thf(fact_226_emptyE, axiom,
    ((![A : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member1377036490le_alt @ A @ bot_bo1631280109le_alt)))))). % emptyE
thf(fact_227_emptyE, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ A @ bot_bo709157177le_alt)))))). % emptyE
thf(fact_228_emptyE, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ A @ bot_bo1793590169le_alt)))))). % emptyE
thf(fact_229_emptyE, axiom,
    ((![A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ A @ bot_bo1697362245le_alt)))))). % emptyE
thf(fact_230_equals0D, axiom,
    ((![A3 : set_Ar182050865le_alt, A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((A3 = bot_bo13098693le_alt) => (~ ((member183760530le_alt @ A @ A3))))))). % equals0D
thf(fact_231_equals0D, axiom,
    ((![A3 : set_Pr367596371le_alt, A : produc16571293le_alt]: ((A3 = bot_bo1596236775le_alt) => (~ ((member2048039092le_alt @ A @ A3))))))). % equals0D
thf(fact_232_equals0D, axiom,
    ((![A3 : set_se2071012361le_alt, A : set_Pr367596371le_alt]: ((A3 = bot_bo1518363805le_alt) => (~ ((member1334244458le_alt @ A @ A3))))))). % equals0D
thf(fact_233_equals0D, axiom,
    ((![A3 : set_se370278869le_alt, A : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((A3 = bot_bo869397057le_alt) => (~ ((member1775590686le_alt @ A @ A3))))))). % equals0D
thf(fact_234_equals0D, axiom,
    ((![A3 : set_se720939393le_alt, A : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((A3 = bot_bo1631280109le_alt) => (~ ((member1377036490le_alt @ A @ A3))))))). % equals0D
thf(fact_235_equals0D, axiom,
    ((![A3 : set_Ar350387917le_alt, A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: ((A3 = bot_bo709157177le_alt) => (~ ((member2001237014le_alt @ A @ A3))))))). % equals0D
thf(fact_236_equals0D, axiom,
    ((![A3 : set_Ar883249453le_alt, A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((A3 = bot_bo1793590169le_alt) => (~ ((member966567542le_alt @ A @ A3))))))). % equals0D
thf(fact_237_equals0D, axiom,
    ((![A3 : set_Ar2014526681le_alt, A : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((A3 = bot_bo1697362245le_alt) => (~ ((member902395426le_alt @ A @ A3))))))). % equals0D
thf(fact_238_equals0I, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![Y3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ Y3 @ A3)))) => (A3 = bot_bo13098693le_alt))))). % equals0I
thf(fact_239_equals0I, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![Y3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ Y3 @ A3)))) => (A3 = bot_bo1596236775le_alt))))). % equals0I
thf(fact_240_equals0I, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![Y3 : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ Y3 @ A3)))) => (A3 = bot_bo1518363805le_alt))))). % equals0I
thf(fact_241_equals0I, axiom,
    ((![A3 : set_se370278869le_alt]: ((![Y3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: (~ ((member1775590686le_alt @ Y3 @ A3)))) => (A3 = bot_bo869397057le_alt))))). % equals0I
thf(fact_242_equals0I, axiom,
    ((![A3 : set_se720939393le_alt]: ((![Y3 : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member1377036490le_alt @ Y3 @ A3)))) => (A3 = bot_bo1631280109le_alt))))). % equals0I
thf(fact_243_equals0I, axiom,
    ((![A3 : set_Ar350387917le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ Y3 @ A3)))) => (A3 = bot_bo709157177le_alt))))). % equals0I
thf(fact_244_equals0I, axiom,
    ((![A3 : set_Ar883249453le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ Y3 @ A3)))) => (A3 = bot_bo1793590169le_alt))))). % equals0I
thf(fact_245_equals0I, axiom,
    ((![A3 : set_Ar2014526681le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ Y3 @ A3)))) => (A3 = bot_bo1697362245le_alt))))). % equals0I
thf(fact_246_ex__in__conv, axiom,
    ((![A3 : set_Ar350387917le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ A3)) = (~ ((A3 = bot_bo709157177le_alt))))))). % ex_in_conv
thf(fact_247_ex__in__conv, axiom,
    ((![A3 : set_Ar883249453le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ A3)) = (~ ((A3 = bot_bo1793590169le_alt))))))). % ex_in_conv
thf(fact_248_ex__in__conv, axiom,
    ((![A3 : set_Ar2014526681le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X @ A3)) = (~ ((A3 = bot_bo1697362245le_alt))))))). % ex_in_conv

% Conjectures (3)
thf(conj_0, hypothesis,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))).
thf(conj_1, hypothesis,
    ((![X5 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X5 @ arrow_1951607831e_Prof) => (![A6 : arrow_1857593510le_alt, B6 : arrow_1857593510le_alt]: ((~ ((A6 = B6))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B6) @ (X5 @ i)) => (member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B6) @ (f @ X5))))))))).
thf(conj_2, conjecture,
    ((arrow_960434986ctator @ f @ i))).
