% 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_261__5189056_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:05.797

% Could-be-implicit typings (35)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_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(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,
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thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
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thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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(ty_n_t__Set__Oset_It__Product____Type__Oprod_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,
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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__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(ty_n_t__Product____Type__Oprod_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(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,
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    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_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,
    produc670815699le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__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(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,
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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,
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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,
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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,
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thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
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thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
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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 (101)
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,
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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,
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thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
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thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Pro1847889543le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Pro1122205927le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_set1343364587le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_set365323601le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_set1240805297le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1825994351le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1638831733le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc233791437le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt > produc1751271773le_alt).
thf(sy_c_Product__Type_OPair_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,
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thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc283291649le_alt : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1556693961le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc268611099le_alt : produc16571293le_alt > set_Pr367596371le_alt > produc1114386793le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1670879671le_alt : set_Pr367596371le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc552053119le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1659212421le_alt : set_Pr367596371le_alt > produc16571293le_alt > produc670815699le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1931840741le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > produc541234227le_alt).
thf(sy_c_Product__Type_OSigma_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc783065342le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Pr1877138731le_alt).
thf(sy_c_Product__Type_OSigma_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1711776894le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr319694141le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc712719070le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Pr696203165le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2062971558le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Pr367596371le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1761277106le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr80128425le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc1360152522le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr448479039le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1173532202le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr1043548575le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1576835688le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_Pr2052341855le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc416649876le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_Pr1113807113le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc223727860le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_Pr851393385le_alt).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_Omap__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1074667658le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    produc664345657le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    produc606635279le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    produc909656464_alt_o : (arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt > $o) > produc16571293le_alt > produc16571293le_alt > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc624247124_alt_o : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > produc16571293le_alt > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc846580013le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    produc1576739865le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt) > produc16571293le_alt > set_Ar182050865le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_Product__Type_Oprod_Ocase__prod_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_001_Eo, type,
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thf(sy_c_Product__Type_Oprod_Oswap_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_Product__Type_Oproduct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_Relation_Oinv__image_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
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thf(sy_c_Set_OCollect_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1382217680le_alt : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o) > set_Ar182050865le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec824848862le_alt : (produc1556433673le_alt > $o) > set_Pr448479039le_alt).
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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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001t__Product____Type__Oprod_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_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__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(sy_v_F, type,
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thf(sy_v_Lab____, type,
    lab : set_Pr367596371le_alt).
thf(sy_v_Lba____, type,
    lba : set_Pr367596371le_alt).
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thf(sy_v_b____, type,
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% Relevant facts (241)
thf(fact_0__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_1__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_2__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_3__092_060open_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lba))). % \<open>b <\<^bsub>Lba\<^esub> a\<close>
thf(fact_4__092_060open_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lab))). % \<open>a <\<^bsub>Lab\<^esub> b\<close>
thf(fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lab_O_A_092_060lbrakk_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lab : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ Lab) => (~ ((member1334244458le_alt @ Lab @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lab. \<lbrakk>a <\<^bsub>Lab\<^esub> b; Lab \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_6__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lba_O_A_092_060lbrakk_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lba : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ Lba) => (~ ((member1334244458le_alt @ Lba @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lba. \<lbrakk>b <\<^bsub>Lba\<^esub> a; Lba \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_7__092_060open_062_Ib_M_Aa_J_A_092_060notin_062_ALab_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lab))))). % \<open>(b, a) \<notin> Lab\<close>
thf(fact_8_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_9_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_10_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_11_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X))))))). % complete_Lin
thf(fact_12_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X3 = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X3) @ L))))))). % notin_Lin_iff
thf(fact_13_in__mkbot, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X3 = Z)) => ((~ ((X3 = Y)))))) & ((((~ ((X3 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L))))))))))). % in_mkbot
thf(fact_14_in__mktop, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X3 = Z)))) & ((((((Y = Z)) => ((~ ((X3 = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L))))))))))). % in_mktop
thf(fact_15_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X @ Y3)))))). % surj_pair
thf(fact_16_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_17_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_18_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X3) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_19_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X3) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_20_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_21_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_22_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_23_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X3 = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X3 = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X3 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L))))))))))))))))). % in_below
thf(fact_24_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X3 = Y)))) & ((((((X3 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X3 = B)))) => ((((((Y = B)) => ((((X3 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L))))))))))))))))). % in_above
thf(fact_25_below__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X3 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X3 @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_26_above__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X3 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X3 @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_27_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_28_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_29_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_30_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F @ A @ B))))). % curryI
thf(fact_31_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_32_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_33_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_34_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_35_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_36_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_37_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_39_Collect__mem__eq, axiom,
    ((![A4 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_40_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_41__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "1"
thf(fact_42__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "2"
thf(fact_43__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P3)))))))))). % "3"
thf(fact_44__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P3)))))))))))). % "4"
thf(fact_45_pairwise__neutrality, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))). % pairwise_neutrality
thf(fact_46_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4))))))))))))). % unanimity_def
thf(fact_47_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (Y4 @ I2))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ Y4))))))))))))))))). % IIA_def
thf(fact_48_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I2 : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F2 @ X4) = (X4 @ I2)))))))))). % dictator_def
thf(fact_49_swap__simp, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X3 @ Y)) = (produc1494124311le_alt @ Y @ X3))))). % swap_simp
thf(fact_50_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_51_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_52_mem__case__prodE, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, P : produc16571293le_alt]: ((member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member684274596le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_53_mem__case__prodE, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, P : produc16571293le_alt]: ((member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member183760530le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_54_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X3 : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X3) @ (image_1873259469le_alt @ produc1794822519le_alt @ A4)) = (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ A4))))). % pair_in_swap_image
thf(fact_55_assms_I1_J, axiom,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))). % assms(1)
thf(fact_56_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X3 @ Y)) = (produc1494124311le_alt @ X3 @ (F @ Y)))))). % apsnd_conv
thf(fact_57_case__prodI2, axiom,
    ((![P : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (C @ A3 @ B3))) => (produc624247124_alt_o @ C @ P))))). % case_prodI2
thf(fact_58_case__prodI, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ A @ B) => (produc624247124_alt_o @ F @ (produc1494124311le_alt @ A @ B)))))). % case_prodI
thf(fact_59_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member2048039092le_alt @ Z @ (C @ A3 @ B3)))) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_60_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member1334244458le_alt @ Z @ (C @ A3 @ B3)))) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_61_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member684274596le_alt @ Z @ (C @ A3 @ B3)))) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_62_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member183760530le_alt @ Z @ (C @ A3 @ B3)))) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_63_mem__case__prodI, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member2048039092le_alt @ Z @ (C @ A @ B)) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_64_mem__case__prodI, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ Z @ (C @ A @ B)) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_65_mem__case__prodI, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member684274596le_alt @ Z @ (C @ A @ B)) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_66_mem__case__prodI, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member183760530le_alt @ Z @ (C @ A @ B)) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ (produc1494124311le_alt @ A @ B))))))). % mem_case_prodI
thf(fact_67_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member2048039092le_alt @ (F @ A @ B) @ (image_1873259469le_alt @ (produc846580013le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_68_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member1334244458le_alt @ (F @ A @ B) @ (image_715032109le_alt @ (produc860300173le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_69_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member684274596le_alt @ (F @ A @ B) @ (image_1481976431le_alt @ (produc606635279le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_70_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member183760530le_alt @ (F @ A @ B) @ (image_1254321881le_alt @ (produc664345657le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_71_case__prodE, axiom,
    ((![C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, P : produc16571293le_alt]: ((produc624247124_alt_o @ C @ P) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((C @ X @ Y3))))))))))). % case_prodE
thf(fact_72_case__prodD, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F @ (produc1494124311le_alt @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_73_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P4 : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_74_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ arrow_1951607831e_Prof) => (![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F3 @ X))))))) => (arrow_960434986ctator @ F3 @ I3)))))). % dictatorI
thf(fact_75_Pi__I, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_76_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_77_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_78_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_79_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_80_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_81_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_82_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_83_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_84_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_85_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X3)) => ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % image_eqI
thf(fact_86_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X3)) => ((member2048039092le_alt @ X3 @ A4) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % image_eqI
thf(fact_87_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X3)) => ((member1334244458le_alt @ X3 @ A4) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % image_eqI
thf(fact_88_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X3)) => ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % image_eqI
thf(fact_89_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X3)) => ((member2048039092le_alt @ X3 @ A4) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4))))))). % image_eqI
thf(fact_90_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X3)) => ((member684274596le_alt @ X3 @ A4) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4))))))). % image_eqI
thf(fact_91_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X3)) => ((member1334244458le_alt @ X3 @ A4) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4))))))). % image_eqI
thf(fact_92_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X3)) => ((member684274596le_alt @ X3 @ A4) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4))))))). % image_eqI
thf(fact_93_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X3)) => ((member684274596le_alt @ X3 @ A4) => (member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4))))))). % image_eqI
thf(fact_94_image__eqI, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X3)) => ((member2048039092le_alt @ X3 @ A4) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F @ A4))))))). % image_eqI
thf(fact_95_funcsetI, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_96_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_97_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_98_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_99_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_100_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_101_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_102_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_103_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_104_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_105_rev__image__eqI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_106_rev__image__eqI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_107_rev__image__eqI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_108_rev__image__eqI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_109_rev__image__eqI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_110_rev__image__eqI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_111_rev__image__eqI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_112_rev__image__eqI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_113_rev__image__eqI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_114_rev__image__eqI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => ((B = (F @ X3)) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_115_imageI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (image_1873259469le_alt @ F @ A4)))))). % imageI
thf(fact_116_imageI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (image_715032109le_alt @ F @ A4)))))). % imageI
thf(fact_117_imageI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (image_2105633431le_alt @ F @ A4)))))). % imageI
thf(fact_118_imageI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (image_71834871le_alt @ F @ A4)))))). % imageI
thf(fact_119_imageI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (image_1481976431le_alt @ F @ A4)))))). % imageI
thf(fact_120_imageI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (image_1432476219le_alt @ F @ A4)))))). % imageI
thf(fact_121_imageI, axiom,
    ((![X3 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (image_1576623141le_alt @ F @ A4)))))). % imageI
thf(fact_122_imageI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (image_712506523le_alt @ F @ A4)))))). % imageI
thf(fact_123_imageI, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (image_829063553le_alt @ F @ A4)))))). % imageI
thf(fact_124_imageI, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member183760530le_alt @ (F @ X3) @ (image_1254321881le_alt @ F @ A4)))))). % imageI
thf(fact_125_Pi__cong, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A4) => ((F @ W) = (G @ W)))) => ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A4 @ B5))))))). % Pi_cong
thf(fact_126_Pi__cong, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A4) => ((F @ W) = (G @ W)))) => ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A4 @ B5))))))). % Pi_cong
thf(fact_127_Pi__mem, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) => ((member1966420836e_indi @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_128_Pi__mem, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_129_Pi__mem, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_130_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_131_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_132_Pi__mem, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_133_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)) => ((member684274596le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_134_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_135_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) => ((member684274596le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_136_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)) => ((member684274596le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_137_Pi__iff, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ I4 @ X5)) = (![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ I4)) => ((member1334244458le_alt @ (F @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_138_Pi__iff, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ I4 @ X5)) = (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ I4)) => ((member1334244458le_alt @ (F @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_139_Pi__I_H, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_140_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_141_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_142_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_143_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_144_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_145_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_146_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_147_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_148_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_149_PiE, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member1966420836e_indi @ X3 @ A4)))))))). % PiE
thf(fact_150_PiE, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A4)))))))). % PiE
thf(fact_151_PiE, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A4)))))))). % PiE
thf(fact_152_PiE, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A4)))))))). % PiE
thf(fact_153_PiE, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A4)))))))). % PiE
thf(fact_154_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A4)))))))). % PiE
thf(fact_155_PiE, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A4)))))))). % PiE
thf(fact_156_PiE, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A4)))))))). % PiE
thf(fact_157_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A4)))))))). % PiE
thf(fact_158_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A4)))))))). % PiE
thf(fact_159_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1873259469le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_1873259469le_alt @ F @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_160_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_2105633431le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_2105633431le_alt @ F @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_161_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_715032109le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_715032109le_alt @ F @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_162_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_71834871le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_71834871le_alt @ F @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_163_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1432476219le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_1432476219le_alt @ F @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_164_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_1481976431le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_1481976431le_alt @ F @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_165_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_712506523le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_712506523le_alt @ F @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_166_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_1576623141le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_1576623141le_alt @ F @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_167_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_829063553le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_829063553le_alt @ F @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_168_Compr__image__eq, axiom,
    ((![F : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar182050865le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1972416495le_alt @ F @ A4))) & ((P2 @ X4))))) = (image_1972416495le_alt @ F @ (collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X4 @ A4)) & ((P2 @ (F @ X4))))))))))). % Compr_image_eq
thf(fact_169_imageE, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_170_imageE, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt]: ((member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_171_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_172_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_173_imageE, axiom,
    ((![B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt]: ((member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_174_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt]: ((member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_175_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_176_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_177_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_178_imageE, axiom,
    ((![B : produc16571293le_alt, F : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar182050865le_alt]: ((member2048039092le_alt @ B @ (image_1972416495le_alt @ F @ A4)) => (~ ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member183760530le_alt @ X @ A4))))))))))). % imageE
thf(fact_179_funcset__mem, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_180_funcset__mem, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_181_funcset__mem, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_182_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_183_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_184_funcset__mem, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_185_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_186_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_187_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A4) => (member1334244458le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_188_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A4) => (member684274596le_alt @ (F @ X3) @ B5)))))). % funcset_mem
thf(fact_189_case__prod__Pair__iden, axiom,
    ((![P : produc16571293le_alt]: ((produc846580013le_alt @ produc1494124311le_alt @ P) = P)))). % case_prod_Pair_iden
thf(fact_190_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S3 : set_Pr367596371le_alt]: (((^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R2))) = (^[X4 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_191_same__fstI, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R2 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P2 @ X3) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y) @ (R2 @ X3)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X3 @ Y5) @ (produc1494124311le_alt @ X3 @ Y)) @ (same_f554660482le_alt @ P2 @ R2))))))). % same_fstI
thf(fact_192_lex__prod__def, axiom,
    ((lex_pr3395839le_alt = (^[Ra : set_Pr367596371le_alt]: (^[Rb : set_Pr367596371le_alt]: (collec824848862le_alt @ (produc614564272_alt_o @ (produc909656464_alt_o @ (^[A5 : arrow_1857593510le_alt]: (^[B4 : arrow_1857593510le_alt]: (produc624247124_alt_o @ (^[A6 : arrow_1857593510le_alt]: (^[B6 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ A6) @ Ra)) | ((((A5 = A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ B6) @ Rb)))))))))))))))))). % lex_prod_def
thf(fact_193_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A4) => ((member519365071le_alt @ B @ (B5 @ A)) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_194_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_195_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member2048039092le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_196_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_197_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1334244458le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_198_SigmaI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member2048039092le_alt @ A @ A4) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_199_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ A @ A4) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_200_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member1334244458le_alt @ A @ A4) => ((member684274596le_alt @ B @ (B5 @ A)) => (member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_201_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member684274596le_alt @ A @ A4) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_202_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member684274596le_alt @ A @ A4) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A4 @ B5))))))). % SigmaI
thf(fact_203_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) = (((member519365071le_alt @ A @ A4)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_204_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_205_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_206_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_207_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_208_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A4 @ B5)) = (((member2048039092le_alt @ A @ A4)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_209_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A4 @ B5)) = (((member684274596le_alt @ A @ A4)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_210_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A4 @ B5)) = (((member1334244458le_alt @ A @ A4)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_211_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A4 @ B5)) = (((member684274596le_alt @ A @ A4)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_212_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A4 @ B5)) = (((member684274596le_alt @ A @ A4)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_213_in__lex__prod, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A @ B) @ (produc1494124311le_alt @ A2 @ B2)) @ (lex_pr3395839le_alt @ R @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ A2) @ R)) | ((((A = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B2) @ S))))))))). % in_lex_prod
thf(fact_214_SigmaE, axiom,
    ((![C : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (produc2062971558le_alt @ A4 @ B5)) => (~ ((![X : arrow_1857593510le_alt]: ((member519365071le_alt @ X @ A4) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc1494124311le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_215_SigmaE, axiom,
    ((![C : produc1556433673le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (produc1360152522le_alt @ A4 @ B5)) => (~ ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc41061307le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_216_SigmaE, axiom,
    ((![C : produc1114386793le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ C @ (produc1173532202le_alt @ A4 @ B5)) => (~ ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc268611099le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_217_SigmaE, axiom,
    ((![C : produc670815699le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ C @ (produc416649876le_alt @ A4 @ B5)) => (~ ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc1659212421le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_218_SigmaE, axiom,
    ((![C : produc541234227le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (produc223727860le_alt @ A4 @ B5)) => (~ ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc1931840741le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_219_SigmaE, axiom,
    ((![C : produc1556693961le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ C @ (produc1761277106le_alt @ A4 @ B5)) => (~ ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc283291649le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_220_SigmaE, axiom,
    ((![C : produc1751271773le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ C @ (produc1711776894le_alt @ A4 @ B5)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc233791437le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_221_SigmaE, axiom,
    ((![C : produc552053119le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ C @ (produc1576835688le_alt @ A4 @ B5)) => (~ ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc1670879671le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_222_SigmaE, axiom,
    ((![C : produc1766186941le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ C @ (produc712719070le_alt @ A4 @ B5)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc806763053le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_223_SigmaE, axiom,
    ((![C : produc1638831733le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ C @ (produc783065342le_alt @ A4 @ B5)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X)) => (~ ((C = (produc1825994351le_alt @ X @ Y3)))))))))))))). % SigmaE
thf(fact_224_SigmaD1, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (member519365071le_alt @ A @ A4))))). % SigmaD1
thf(fact_225_SigmaD2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (member519365071le_alt @ B @ (B5 @ A)))))). % SigmaD2
thf(fact_226_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A4 @ B5)) => (~ (((member519365071le_alt @ A @ A4) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_227_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_228_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_229_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_230_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_231_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A4 @ B5)) => (~ (((member2048039092le_alt @ A @ A4) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_232_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A4 @ B5)) => (~ (((member684274596le_alt @ A @ A4) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_233_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A4 @ B5)) => (~ (((member1334244458le_alt @ A @ A4) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_234_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A4 @ B5)) => (~ (((member684274596le_alt @ A @ A4) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_235_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A4 @ B5)) => (~ (((member684274596le_alt @ A @ A4) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_236_swap__product, axiom,
    ((![A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((image_1873259469le_alt @ (produc846580013le_alt @ (^[I2 : arrow_1857593510le_alt]: (^[J : arrow_1857593510le_alt]: (produc1494124311le_alt @ J @ I2)))) @ (produc2062971558le_alt @ A4 @ (^[Uu : arrow_1857593510le_alt]: B5))) = (produc2062971558le_alt @ B5 @ (^[Uu : arrow_1857593510le_alt]: A4)))))). % swap_product
thf(fact_237_member__product, axiom,
    ((![X3 : produc16571293le_alt, A4 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ X3 @ (produc961482780le_alt @ A4 @ B5)) = (member2048039092le_alt @ X3 @ (produc2062971558le_alt @ A4 @ (^[Uu : arrow_1857593510le_alt]: B5))))))). % member_product
thf(fact_238_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_239_in__inv__image, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (inv_im155136540le_alt @ R @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X3) @ (F @ Y)) @ R))))). % in_inv_image
thf(fact_240_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R2) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R2)))))). % map_prod_imageI

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lba))))).
