% 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_246__5188594_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:56.433

% 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_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_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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thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__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,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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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_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
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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 (102)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
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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,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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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,
    produc806763053le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt > produc1766186941le_alt).
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_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
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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,
    produc773314629le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt) > produc16571293le_alt > set_Ar809243995le_alt).
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_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_v_F, type,
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thf(sy_v_P_H____, type,
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% Relevant facts (239)
thf(fact_0_A_I4_J, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % A(4)
thf(fact_1_A_I3_J, axiom,
    ((member684274596le_alt @ p2 @ arrow_1951607831e_Prof))). % A(3)
thf(fact_2__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P2)))))))))))). % "4"
thf(fact_3_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_4_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_5_A_I2_J, axiom,
    ((~ ((a = b))))). % A(2)
thf(fact_6_A_I1_J, axiom,
    ((~ ((a2 = b2))))). % A(1)
thf(fact_7__092_060open_062a_A_061_Ab_H_A_092_060and_062_Ab_A_092_060noteq_062_Aa_H_092_060close_062, axiom,
    (((a2 = b) & (~ ((b2 = a)))))). % \<open>a = b' \<and> b \<noteq> a'\<close>
thf(fact_8__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "1"
thf(fact_9__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "2"
thf(fact_10__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P2 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P2)))))))))). % "3"
thf(fact_11_A_I5_J, axiom,
    ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (p2 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p @ I2)))))). % A(5)
thf(fact_12_calculation, axiom,
    ((((~ ((a2 = b))) & (~ ((b2 = a)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (f @ p2)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ p)))))). % calculation
thf(fact_13_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_14_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_15_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mkbot
thf(fact_16_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mktop
thf(fact_17_surj__pair, axiom,
    ((![P3 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_18_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P3 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ P3))))). % prod_cases
thf(fact_19_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_20_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4))))))))))))). % unanimity_def
thf(fact_21_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (Y4 @ I3))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ Y4))))))))))))))))). % IIA_def
thf(fact_22_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_23_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_24_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I3 : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F @ X4) = (X4 @ I3)))))))))). % dictator_def
thf(fact_25_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_26_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_27_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_28_curryI, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F2 @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F2 @ A @ B))))). % curryI
thf(fact_29_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_30_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_31_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X3))))))). % complete_Lin
thf(fact_32_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_33_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_34_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_35_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_36_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_37_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_39_Collect__mem__eq, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_40_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_41_curryD, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F2 @ A @ B) => (F2 @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_42_curryE, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F2 @ A @ B) => (F2 @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_43_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_above
thf(fact_44_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_below
thf(fact_45_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_46_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_47_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ Y @ X))))). % swap_simp
thf(fact_48_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P3 : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_49_mem__case__prodE, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, P3 : produc16571293le_alt]: ((member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member684274596le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_50_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P3 : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_51_mem__case__prodE, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, P3 : produc16571293le_alt]: ((member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member183760530le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_52_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ (image_1873259469le_alt @ produc1794822519le_alt @ A5)) = (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ A5))))). % pair_in_swap_image
thf(fact_53_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_54_case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A3 @ B3)) => (C @ A3 @ B3))) => (produc624247124_alt_o @ C @ P3))))). % case_prodI2
thf(fact_55_case__prodI, axiom,
    ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F2 @ A @ B) => (produc624247124_alt_o @ F2 @ (produc1494124311le_alt @ A @ B)))))). % case_prodI
thf(fact_56_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A3 @ B3)) => (member2048039092le_alt @ Z @ (C @ A3 @ B3)))) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P3)))))). % mem_case_prodI2
thf(fact_57_mem__case__prodI2, axiom,
    ((![P3 : 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]: ((P3 = (produc1494124311le_alt @ A3 @ B3)) => (member684274596le_alt @ Z @ (C @ A3 @ B3)))) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P3)))))). % mem_case_prodI2
thf(fact_58_mem__case__prodI2, axiom,
    ((![P3 : produc16571293le_alt, Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ A3 @ B3)) => (member1334244458le_alt @ Z @ (C @ A3 @ B3)))) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P3)))))). % mem_case_prodI2
thf(fact_59_mem__case__prodI2, axiom,
    ((![P3 : 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]: ((P3 = (produc1494124311le_alt @ A3 @ B3)) => (member183760530le_alt @ Z @ (C @ A3 @ B3)))) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P3)))))). % mem_case_prodI2
thf(fact_60_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_61_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_62_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_63_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_64_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A5) => (member2048039092le_alt @ (F2 @ A @ B) @ (image_1873259469le_alt @ (produc846580013le_alt @ F2) @ A5)))))). % pair_imageI
thf(fact_65_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A5) => (member684274596le_alt @ (F2 @ A @ B) @ (image_1481976431le_alt @ (produc606635279le_alt @ F2) @ A5)))))). % pair_imageI
thf(fact_66_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A5) => (member1334244458le_alt @ (F2 @ A @ B) @ (image_715032109le_alt @ (produc860300173le_alt @ F2) @ A5)))))). % pair_imageI
thf(fact_67_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A5) => (member183760530le_alt @ (F2 @ A @ B) @ (image_1254321881le_alt @ (produc664345657le_alt @ F2) @ A5)))))). % pair_imageI
thf(fact_68_case__prodE, axiom,
    ((![C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, P3 : produc16571293le_alt]: ((produc624247124_alt_o @ C @ P3) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P3 = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((C @ X3 @ Y3))))))))))). % case_prodE
thf(fact_69_case__prodD, axiom,
    ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F2 @ (produc1494124311le_alt @ A @ B)) => (F2 @ A @ B))))). % case_prodD
thf(fact_70_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_71_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ arrow_1951607831e_Prof) => (![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X3 @ I4)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F3 @ X3))))))) => (arrow_960434986ctator @ F3 @ I4)))))). % dictatorI
thf(fact_72_Pi__I, axiom,
    ((![A5 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_73_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_74_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_75_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_76_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_77_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_78_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_79_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_80_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_81_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_82_image__eqI, axiom,
    ((![B : produc16571293le_alt, F2 : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F2 @ X)) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_83_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F2 @ X)) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_84_image__eqI, axiom,
    ((![B : produc16571293le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F2 @ X)) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_85_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F2 @ X)) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_86_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F2 @ X)) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_87_image__eqI, axiom,
    ((![B : produc16571293le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((B = (F2 @ X)) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_88_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((B = (F2 @ X)) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_89_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((B = (F2 @ X)) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_90_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((B = (F2 @ X)) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ B @ (image_829063553le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_91_image__eqI, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F2 : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((B = (F2 @ X)) => ((member2048039092le_alt @ X @ A5) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F2 @ A5))))))). % image_eqI
thf(fact_92_funcset__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_93_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_94_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_95_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_96_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_97_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_98_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_99_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_100_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_101_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ B5)))))). % funcset_mem
thf(fact_102_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (image_1873259469le_alt @ F2 @ A5)))))). % imageI
thf(fact_103_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (image_715032109le_alt @ F2 @ A5)))))). % imageI
thf(fact_104_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (image_2105633431le_alt @ F2 @ A5)))))). % imageI
thf(fact_105_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (image_71834871le_alt @ F2 @ A5)))))). % imageI
thf(fact_106_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (image_1481976431le_alt @ F2 @ A5)))))). % imageI
thf(fact_107_imageI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (image_1432476219le_alt @ F2 @ A5)))))). % imageI
thf(fact_108_imageI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (image_712506523le_alt @ F2 @ A5)))))). % imageI
thf(fact_109_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (image_1576623141le_alt @ F2 @ A5)))))). % imageI
thf(fact_110_imageI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (image_829063553le_alt @ F2 @ A5)))))). % imageI
thf(fact_111_imageI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => (member183760530le_alt @ (F2 @ X) @ (image_1254321881le_alt @ F2 @ A5)))))). % imageI
thf(fact_112_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : produc16571293le_alt, F2 : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F2 @ X)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_113_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F2 @ X)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_114_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : produc16571293le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F2 @ X)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_115_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F2 @ X)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_116_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F2 @ X)) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_117_rev__image__eqI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : produc16571293le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X @ A5) => ((B = (F2 @ X)) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_118_rev__image__eqI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A5) => ((B = (F2 @ X)) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_119_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A5) => ((B = (F2 @ X)) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_120_rev__image__eqI, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A5) => ((B = (F2 @ X)) => (member684274596le_alt @ B @ (image_829063553le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_121_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F2 : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A5) => ((B = (F2 @ X)) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F2 @ A5))))))). % rev_image_eqI
thf(fact_122_PiE, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member1966420836e_indi @ X @ A5)))))))). % PiE
thf(fact_123_PiE, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_124_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_125_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_126_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_127_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_128_PiE, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member2048039092le_alt @ X @ A5)))))))). % PiE
thf(fact_129_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member1334244458le_alt @ X @ A5)))))))). % PiE
thf(fact_130_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_131_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F2 @ X) @ (B5 @ X)))) => (~ ((member684274596le_alt @ X @ A5)))))))). % PiE
thf(fact_132_Pi__I_H, axiom,
    ((![A5 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_133_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_134_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_135_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_136_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_137_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_138_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_139_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_140_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_141_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ (B5 @ X3)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_142_Pi__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, I5 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ I5 @ X5)) = (![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ I5)) => ((member1334244458le_alt @ (F2 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_143_Pi__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I5 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ I5 @ X5)) = (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ I5)) => ((member1334244458le_alt @ (F2 @ X4) @ (X5 @ X4))))))))). % Pi_iff
thf(fact_144_Pi__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((member1966420836e_indi @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_145_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_146_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_147_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_148_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_149_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_150_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member2048039092le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_151_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_152_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member1334244458le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_153_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((member684274596le_alt @ X @ A5) => (member684274596le_alt @ (F2 @ X) @ (B5 @ X))))))). % Pi_mem
thf(fact_154_Pi__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A5) => ((F2 @ W) = (G @ W)))) => ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_155_Pi__cong, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A5) => ((F2 @ W) = (G @ W)))) => ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_156_imageE, axiom,
    ((![B : produc16571293le_alt, F2 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ B @ (image_1873259469le_alt @ F2 @ A5)) => (~ ((![X3 : produc16571293le_alt]: ((B = (F2 @ X3)) => (~ ((member2048039092le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_157_imageE, axiom,
    ((![B : produc16571293le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt]: ((member2048039092le_alt @ B @ (image_2105633431le_alt @ F2 @ A5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member1334244458le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_158_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt]: ((member1334244458le_alt @ B @ (image_715032109le_alt @ F2 @ A5)) => (~ ((![X3 : produc16571293le_alt]: ((B = (F2 @ X3)) => (~ ((member2048039092le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_159_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ B @ (image_71834871le_alt @ F2 @ A5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member1334244458le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_160_imageE, axiom,
    ((![B : produc16571293le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt]: ((member2048039092le_alt @ B @ (image_1432476219le_alt @ F2 @ A5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member684274596le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_161_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt]: ((member684274596le_alt @ B @ (image_1481976431le_alt @ F2 @ A5)) => (~ ((![X3 : produc16571293le_alt]: ((B = (F2 @ X3)) => (~ ((member2048039092le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_162_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member684274596le_alt @ B @ (image_1576623141le_alt @ F2 @ A5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member1334244458le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_163_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((member1334244458le_alt @ B @ (image_712506523le_alt @ F2 @ A5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member684274596le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_164_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt]: ((member684274596le_alt @ B @ (image_829063553le_alt @ F2 @ A5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member684274596le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_165_imageE, axiom,
    ((![B : produc16571293le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar182050865le_alt]: ((member2048039092le_alt @ B @ (image_1972416495le_alt @ F2 @ A5)) => (~ ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((B = (F2 @ X3)) => (~ ((member183760530le_alt @ X3 @ A5))))))))))). % imageE
thf(fact_166_Compr__image__eq, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1873259469le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_1873259469le_alt @ F2 @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_167_Compr__image__eq, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, P : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_2105633431le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_2105633431le_alt @ F2 @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_168_Compr__image__eq, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_715032109le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_715032109le_alt @ F2 @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_169_Compr__image__eq, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_71834871le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_71834871le_alt @ F2 @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_170_Compr__image__eq, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, P : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1432476219le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_1432476219le_alt @ F2 @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_171_Compr__image__eq, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_1481976431le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_1481976431le_alt @ F2 @ (collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_172_Compr__image__eq, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_1576623141le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_1576623141le_alt @ F2 @ (collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_173_Compr__image__eq, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, P : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X4 @ (image_712506523le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_712506523le_alt @ F2 @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_174_Compr__image__eq, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ (image_829063553le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_829063553le_alt @ F2 @ (collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_175_Compr__image__eq, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar182050865le_alt, P : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (((member2048039092le_alt @ X4 @ (image_1972416495le_alt @ F2 @ A5))) & ((P @ X4))))) = (image_1972416495le_alt @ F2 @ (collec1382217680le_alt @ (^[X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X4 @ A5)) & ((P @ (F2 @ X4))))))))))). % Compr_image_eq
thf(fact_176_funcsetI, axiom,
    ((![A5 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ B5))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_177_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ B5))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_178_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ B5))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_179_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ B5))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_180_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ B5))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_181_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ B5))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_182_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F2 @ X3) @ B5))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_183_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F2 @ X3) @ B5))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_184_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ B5))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_185_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F2 @ X3) @ B5))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_186_case__prod__Pair__iden, axiom,
    ((![P3 : produc16571293le_alt]: ((produc846580013le_alt @ produc1494124311le_alt @ P3) = P3)))). % case_prod_Pair_iden
thf(fact_187_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_188_same__fstI, axiom,
    ((![P : arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R2 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P @ X) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y) @ (R2 @ X)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X @ Y5) @ (produc1494124311le_alt @ X @ Y)) @ (same_f554660482le_alt @ P @ R2))))))). % same_fstI
thf(fact_189_lex__prod__def, axiom,
    ((lex_pr3395839le_alt = (^[Ra : set_Pr367596371le_alt]: (^[Rb : set_Pr367596371le_alt]: (collec824848862le_alt @ (produc614564272_alt_o @ (produc909656464_alt_o @ (^[A4 : arrow_1857593510le_alt]: (^[B4 : arrow_1857593510le_alt]: (produc624247124_alt_o @ (^[A6 : arrow_1857593510le_alt]: (^[B6 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ A6) @ Ra)) | ((((A4 = A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ B6) @ Rb)))))))))))))))))). % lex_prod_def
thf(fact_190_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) = (((member519365071le_alt @ A @ A5)) & ((member519365071le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_191_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_192_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_193_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_194_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_195_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5)) = (((member2048039092le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_196_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member2048039092le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_197_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member1334244458le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_198_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5)) = (((member1334244458le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_199_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5)) = (((member684274596le_alt @ A @ A5)) & ((member684274596le_alt @ B @ (B5 @ A)))))))). % mem_Sigma_iff
thf(fact_200_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A5) => ((member519365071le_alt @ B @ (B5 @ A)) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_201_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_202_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member2048039092le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_203_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_204_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1334244458le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_205_SigmaI, axiom,
    ((![A : produc16571293le_alt, A5 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member2048039092le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_206_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ A @ A5) => ((member2048039092le_alt @ B @ (B5 @ A)) => (member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_207_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member684274596le_alt @ A @ A5) => ((member1334244458le_alt @ B @ (B5 @ A)) => (member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_208_SigmaI, axiom,
    ((![A : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member1334244458le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_209_SigmaI, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member684274596le_alt @ A @ A5) => ((member684274596le_alt @ B @ (B5 @ A)) => (member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5))))))). % SigmaI
thf(fact_210_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_211_SigmaE2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (~ (((member519365071le_alt @ A @ A5) => (~ ((member519365071le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_212_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_213_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_214_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ (produc1659212421le_alt @ A @ B) @ (produc416649876le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_215_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ A @ B) @ (produc223727860le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_216_SigmaE2, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A5 @ B5)) => (~ (((member2048039092le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_217_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ (produc233791437le_alt @ A @ B) @ (produc1711776894le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member2048039092le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_218_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ (produc806763053le_alt @ A @ B) @ (produc712719070le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member1334244458le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_219_SigmaE2, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ (produc1670879671le_alt @ A @ B) @ (produc1576835688le_alt @ A5 @ B5)) => (~ (((member1334244458le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_220_SigmaE2, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ (produc1825994351le_alt @ A @ B) @ (produc783065342le_alt @ A5 @ B5)) => (~ (((member684274596le_alt @ A @ A5) => (~ ((member684274596le_alt @ B @ (B5 @ A))))))))))). % SigmaE2
thf(fact_221_SigmaD2, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (member519365071le_alt @ B @ (B5 @ A)))))). % SigmaD2
thf(fact_222_SigmaD1, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A5 @ B5)) => (member519365071le_alt @ A @ A5))))). % SigmaD1
thf(fact_223_SigmaE, axiom,
    ((![C : produc16571293le_alt, A5 : set_Ar1665529862le_alt, B5 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (produc2062971558le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A5) => (![Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1494124311le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_224_SigmaE, axiom,
    ((![C : produc1556433673le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (produc1360152522le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc41061307le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_225_SigmaE, axiom,
    ((![C : produc1114386793le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((member1923768064le_alt @ C @ (produc1173532202le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc268611099le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_226_SigmaE, axiom,
    ((![C : produc670815699le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1480196970le_alt @ C @ (produc416649876le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1659212421le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_227_SigmaE, axiom,
    ((![C : produc541234227le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (produc223727860le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1931840741le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_228_SigmaE, axiom,
    ((![C : produc1556693961le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((member1263449330le_alt @ C @ (produc1761277106le_alt @ A5 @ B5)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc283291649le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_229_SigmaE, axiom,
    ((![C : produc1751271773le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member1458027142le_alt @ C @ (produc1711776894le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : produc16571293le_alt]: ((member2048039092le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc233791437le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_230_SigmaE, axiom,
    ((![C : produc1766186941le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member1902783718le_alt @ C @ (produc712719070le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc806763053le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_231_SigmaE, axiom,
    ((![C : produc552053119le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((member688649896le_alt @ C @ (produc1576835688le_alt @ A5 @ B5)) => (~ ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1670879671le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_232_SigmaE, axiom,
    ((![C : produc1638831733le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1926142604le_alt @ C @ (produc783065342le_alt @ A5 @ B5)) => (~ ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A5) => (![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ Y3 @ (B5 @ X3)) => (~ ((C = (produc1825994351le_alt @ X3 @ Y3)))))))))))))). % SigmaE
thf(fact_233_swap__product, axiom,
    ((![A5 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((image_1873259469le_alt @ (produc846580013le_alt @ (^[I3 : arrow_1857593510le_alt]: (^[J : arrow_1857593510le_alt]: (produc1494124311le_alt @ J @ I3)))) @ (produc2062971558le_alt @ A5 @ (^[Uu : arrow_1857593510le_alt]: B5))) = (produc2062971558le_alt @ B5 @ (^[Uu : arrow_1857593510le_alt]: A5)))))). % swap_product
thf(fact_234_member__product, axiom,
    ((![X : produc16571293le_alt, A5 : set_Ar1665529862le_alt, B5 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ X @ (produc961482780le_alt @ A5 @ B5)) = (member2048039092le_alt @ X @ (produc2062971558le_alt @ A5 @ (^[Uu : arrow_1857593510le_alt]: B5))))))). % member_product
thf(fact_235_map__prod__simp, axiom,
    ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F2 @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F2 @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_236_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R @ F2)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F2 @ X) @ (F2 @ Y)) @ R))))). % in_inv_image
thf(fact_237_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R2) => (member2048039092le_alt @ (produc1494124311le_alt @ (F2 @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F2 @ G) @ R2)))))). % map_prod_imageI
thf(fact_238_prod__fun__imageE, axiom,
    ((![C : produc16571293le_alt, F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, R2 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (image_1873259469le_alt @ (produc1074667658le_alt @ F2 @ G) @ R2)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((C = (produc1494124311le_alt @ (F2 @ X3) @ (G @ Y3))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R2))))))))))). % prod_fun_imageE

% Conjectures (1)
thf(conj_0, conjecture,
    (((member2048039092le_alt @ (produc1494124311le_alt @ a2 @ b2) @ (f @ p2)) = (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ p))))).
