% 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_258__5188836_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:02.618

% Could-be-implicit typings (20)
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Ar1108837783le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_se1538189555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar182050865le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Pr1911398973le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Ar3481041le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_se370278869le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr720748555le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1556433673le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (94)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    inj_on528257168di_nat : (arrow_1429744205e_indi > nat) > set_Ar1007576579e_indi > $o).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Pro1164444725le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Pro1847889543le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Pro1122205927le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    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_Order__Relation_Ostrict__linear__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_257197092le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to803745505le_alt : set_Ar182050865le_alt).
thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to685525675le_alt : set_Ar809243995le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    top_to958727510le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to469035705le_alt : set_se2071012361le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_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_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_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).
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    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member167063198le_alt : (produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr1911398973le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1154116596le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr665675179le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1038100052le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr720748555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member1117110356le_alt : (set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se1538189555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member594528958le_alt : (set_Pr367596371le_alt > produc16571293le_alt) > set_se791007093le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1775590686le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se370278869le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (249)
thf(fact_0__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_1_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_2_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_3_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X))))))). % complete_Lin
thf(fact_4_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X2 = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X2) @ L))))))). % notin_Lin_iff
thf(fact_5_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X22 = Y2))))))). % prod.inject
thf(fact_6_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_7_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X2 = Y)))) & ((((((X2 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X2 = B)))) => ((((((Y = B)) => ((((X2 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))))))))). % in_above
thf(fact_8_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X2 = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X2 = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X2 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))))))))). % in_below
thf(fact_9_above__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_10_below__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_11_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X2) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_12_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X2) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_13_in__mkbot, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X2 = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((X2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))). % in_mkbot
thf(fact_14_in__mktop, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X2 = Z)))) & ((((((Y = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L))))))))))). % in_mktop
thf(fact_15_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X @ Y3)))))). % surj_pair
thf(fact_16_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_17_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_18_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_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_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_21_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_22_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_23_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F @ A @ B))))). % curryI
thf(fact_24_swap__simp, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X2 @ Y)) = (produc1494124311le_alt @ Y @ X2))))). % swap_simp
thf(fact_25_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_26_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_27__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "1"
thf(fact_28__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))))). % "2"
thf(fact_29_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_30_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_31_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_32_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_33_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_34_Collect__mem__eq, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_35_Collect__mem__eq, axiom,
    ((![A4 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_36_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_37_Collect__cong, axiom,
    ((![P2 : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X : set_Pr367596371le_alt]: ((P2 @ X) = (Q @ X))) => ((collec1399441576le_alt @ P2) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_38__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P3)))))))))). % "3"
thf(fact_39__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P3)))))))))))). % "4"
thf(fact_40_pairwise__neutrality, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P3 @ arrow_1951607831e_Prof) => ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P3))))))))))). % pairwise_neutrality
thf(fact_41_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ arrow_1951607831e_Prof)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X3 @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (Y4 @ I2))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ Y4))))))))))))))))). % IIA_def
thf(fact_42_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I2 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X3 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X3))))))))))))). % unanimity_def
thf(fact_43_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I2 : arrow_1429744205e_indi]: (![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ arrow_1951607831e_Prof)) => (((F2 @ X3) = (X3 @ I2)))))))))). % dictator_def
thf(fact_44_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X2) @ (image_1873259469le_alt @ produc1794822519le_alt @ A4)) = (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ A4))))). % pair_in_swap_image
thf(fact_45_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_46_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X2 @ Y)) = (produc1494124311le_alt @ X2 @ (F @ Y)))))). % apsnd_conv
thf(fact_47_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member2048039092le_alt @ Z @ (C @ A3 @ B3)))) => (member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_48_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member1334244458le_alt @ Z @ (C @ A3 @ B3)))) => (member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_49_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member684274596le_alt @ Z @ (C @ A3 @ B3)))) => (member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_50_mem__case__prodI2, axiom,
    ((![P : produc16571293le_alt, Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (member183760530le_alt @ Z @ (C @ A3 @ B3)))) => (member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P)))))). % mem_case_prodI2
thf(fact_51_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_52_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_53_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_54_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_55_case__prodI2, axiom,
    ((![P : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ A3 @ B3)) => (C @ A3 @ B3))) => (produc624247124_alt_o @ C @ P))))). % case_prodI2
thf(fact_56_case__prodI, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ A @ B) => (produc624247124_alt_o @ F @ (produc1494124311le_alt @ A @ B)))))). % case_prodI
thf(fact_57_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member2048039092le_alt @ (F @ A @ B) @ (image_1873259469le_alt @ (produc846580013le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_58_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member1334244458le_alt @ (F @ A @ B) @ (image_715032109le_alt @ (produc860300173le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_59_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member684274596le_alt @ (F @ A @ B) @ (image_1481976431le_alt @ (produc606635279le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_60_pair__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ A4) => (member183760530le_alt @ (F @ A @ B) @ (image_1254321881le_alt @ (produc664345657le_alt @ F) @ A4)))))). % pair_imageI
thf(fact_61_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ arrow_1951607831e_Prof) => (![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F3 @ X))))))) => (arrow_960434986ctator @ F3 @ I3)))))). % dictatorI
thf(fact_62_case__prodE, axiom,
    ((![C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, P : produc16571293le_alt]: ((produc624247124_alt_o @ C @ P) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((C @ X @ Y3))))))))))). % case_prodE
thf(fact_63_case__prodD, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F @ (produc1494124311le_alt @ A @ B)) => (F @ A @ B))))). % case_prodD
thf(fact_64_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_65_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_66_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_67_mem__case__prodE, axiom,
    ((![Z : arrow_1429744205e_indi > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar809243995le_alt, P : produc16571293le_alt]: ((member684274596le_alt @ Z @ (produc773314629le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member684274596le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_68_mem__case__prodE, axiom,
    ((![Z : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Ar182050865le_alt, P : produc16571293le_alt]: ((member183760530le_alt @ Z @ (produc1576739865le_alt @ C @ P)) => (~ ((![X : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X @ Y3)) => (~ ((member183760530le_alt @ Z @ (C @ X @ Y3)))))))))))). % mem_case_prodE
thf(fact_69_Pi__I, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_70_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_71_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_72_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_73_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_74_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_75_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_76_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_77_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_78_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)))))). % Pi_I
thf(fact_79_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X2)) => ((member2048039092le_alt @ X2 @ A4) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % image_eqI
thf(fact_80_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X2)) => ((member2048039092le_alt @ X2 @ A4) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % image_eqI
thf(fact_81_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X2)) => ((member1334244458le_alt @ X2 @ A4) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % image_eqI
thf(fact_82_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X2)) => ((member1334244458le_alt @ X2 @ A4) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % image_eqI
thf(fact_83_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X2)) => ((member2048039092le_alt @ X2 @ A4) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4))))))). % image_eqI
thf(fact_84_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X2)) => ((member684274596le_alt @ X2 @ A4) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4))))))). % image_eqI
thf(fact_85_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X2)) => ((member1334244458le_alt @ X2 @ A4) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4))))))). % image_eqI
thf(fact_86_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X2)) => ((member684274596le_alt @ X2 @ A4) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4))))))). % image_eqI
thf(fact_87_image__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((B = (F @ X2)) => ((member684274596le_alt @ X2 @ A4) => (member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4))))))). % image_eqI
thf(fact_88_image__eqI, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X2)) => ((member2048039092le_alt @ X2 @ A4) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F @ A4))))))). % image_eqI
thf(fact_89_funcset__mem, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_90_funcset__mem, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_91_funcset__mem, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_92_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_93_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_94_funcset__mem, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_95_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_96_funcset__mem, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_97_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_98_funcset__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ B5)))))). % funcset_mem
thf(fact_99_imageI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (image_1873259469le_alt @ F @ A4)))))). % imageI
thf(fact_100_imageI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (image_715032109le_alt @ F @ A4)))))). % imageI
thf(fact_101_imageI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (image_2105633431le_alt @ F @ A4)))))). % imageI
thf(fact_102_imageI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (image_71834871le_alt @ F @ A4)))))). % imageI
thf(fact_103_imageI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (image_1481976431le_alt @ F @ A4)))))). % imageI
thf(fact_104_imageI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (image_1432476219le_alt @ F @ A4)))))). % imageI
thf(fact_105_imageI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (image_1576623141le_alt @ F @ A4)))))). % imageI
thf(fact_106_imageI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (image_712506523le_alt @ F @ A4)))))). % imageI
thf(fact_107_imageI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (image_829063553le_alt @ F @ A4)))))). % imageI
thf(fact_108_imageI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => (member183760530le_alt @ (F @ X2) @ (image_1254321881le_alt @ F @ A4)))))). % imageI
thf(fact_109_rev__image__eqI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_110_rev__image__eqI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_111_rev__image__eqI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_112_rev__image__eqI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_113_rev__image__eqI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_114_rev__image__eqI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt]: ((member684274596le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_115_rev__image__eqI, axiom,
    ((![X2 : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_116_rev__image__eqI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_117_rev__image__eqI, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_118_rev__image__eqI, axiom,
    ((![X2 : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2048039092le_alt @ X2 @ A4) => ((B = (F @ X2)) => (member183760530le_alt @ B @ (image_1254321881le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_119_PiE, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member1966420836e_indi @ X2 @ A4)))))))). % PiE
thf(fact_120_PiE, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_121_PiE, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_122_PiE, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_123_PiE, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_124_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)) => ((~ ((member2048039092le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE
thf(fact_125_PiE, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_126_PiE, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_127_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) => ((~ ((member1334244458le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE
thf(fact_128_PiE, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)) => ((~ ((member684274596le_alt @ (F @ X2) @ (B5 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE
thf(fact_129_Pi__I_H, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_130_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_131_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_132_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_133_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_134_Pi__I_H, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_135_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (B5 @ X)))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_136_Pi__I_H, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_137_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (B5 @ X)))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_138_Pi__I_H, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ (B5 @ X)))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)))))). % Pi_I'
thf(fact_139_Pi__iff, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ I4 @ X4)) = (![X3 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X3 @ I4)) => ((member1334244458le_alt @ (F @ X3) @ (X4 @ X3))))))))). % Pi_iff
thf(fact_140_Pi__iff, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ I4 @ X4)) = (![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ I4)) => ((member1334244458le_alt @ (F @ X3) @ (X4 @ X3))))))))). % Pi_iff
thf(fact_141_Pi__mem, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) => ((member1966420836e_indi @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_142_Pi__mem, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_143_Pi__mem, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_144_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_145_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_146_Pi__mem, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ B5)) => ((member2048039092le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_147_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ B5)) => ((member684274596le_alt @ X2 @ A4) => (member2048039092le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_148_Pi__mem, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ B5)) => ((member1334244458le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_149_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) => ((member684274596le_alt @ X2 @ A4) => (member1334244458le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_150_Pi__mem, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ B5)) => ((member684274596le_alt @ X2 @ A4) => (member684274596le_alt @ (F @ X2) @ (B5 @ X2))))))). % Pi_mem
thf(fact_151_Pi__cong, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A4) => ((F @ W) = (G @ W)))) => ((member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A4 @ B5))))))). % Pi_cong
thf(fact_152_Pi__cong, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A4) => ((F @ W) = (G @ W)))) => ((member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A4 @ B5))))))). % Pi_cong
thf(fact_153_imageE, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_154_imageE, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt]: ((member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_155_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_156_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_157_imageE, axiom,
    ((![B : produc16571293le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt]: ((member2048039092le_alt @ B @ (image_1432476219le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_158_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt]: ((member684274596le_alt @ B @ (image_1481976431le_alt @ F @ A4)) => (~ ((![X : produc16571293le_alt]: ((B = (F @ X)) => (~ ((member2048039092le_alt @ X @ A4))))))))))). % imageE
thf(fact_159_imageE, axiom,
    ((![B : set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((member1334244458le_alt @ B @ (image_712506523le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_160_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((member684274596le_alt @ B @ (image_1576623141le_alt @ F @ A4)) => (~ ((![X : set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member1334244458le_alt @ X @ A4))))))))))). % imageE
thf(fact_161_imageE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt]: ((member684274596le_alt @ B @ (image_829063553le_alt @ F @ A4)) => (~ ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member684274596le_alt @ X @ A4))))))))))). % imageE
thf(fact_162_imageE, axiom,
    ((![B : produc16571293le_alt, F : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar182050865le_alt]: ((member2048039092le_alt @ B @ (image_1972416495le_alt @ F @ A4)) => (~ ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((B = (F @ X)) => (~ ((member183760530le_alt @ X @ A4))))))))))). % imageE
thf(fact_163_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ (image_1873259469le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_1873259469le_alt @ F @ (collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_164_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ (image_2105633431le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_2105633431le_alt @ F @ (collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_165_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ (image_715032109le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_715032109le_alt @ F @ (collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_166_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ (image_71834871le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_71834871le_alt @ F @ (collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_167_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ (image_1432476219le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_1432476219le_alt @ F @ (collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_168_Compr__image__eq, axiom,
    ((![F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ (image_1481976431le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_1481976431le_alt @ F @ (collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_169_Compr__image__eq, axiom,
    ((![F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ (image_1576623141le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_1576623141le_alt @ F @ (collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_170_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, P2 : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (((member1334244458le_alt @ X3 @ (image_712506523le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_712506523le_alt @ F @ (collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_171_Compr__image__eq, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ (image_829063553le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_829063553le_alt @ F @ (collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_172_Compr__image__eq, axiom,
    ((![F : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar182050865le_alt, P2 : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (((member2048039092le_alt @ X3 @ (image_1972416495le_alt @ F @ A4))) & ((P2 @ X3))))) = (image_1972416495le_alt @ F @ (collec1382217680le_alt @ (^[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X3 @ A4)) & ((P2 @ (F @ X3))))))))))). % Compr_image_eq
thf(fact_173_funcsetI, axiom,
    ((![A4 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi]: ((member1966420836e_indi @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member684274596le_alt @ F @ (pi_Arr1981691447le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_174_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member1154116596le_alt @ F @ (pi_Pro1847889543le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_175_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member1038100052le_alt @ F @ (pi_Pro1122205927le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_176_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member594528958le_alt @ F @ (pi_set365323601le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_177_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member1775590686le_alt @ F @ (pi_set1240805297le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_178_funcsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member167063198le_alt @ F @ (pi_Pro1164444725le_alt @ A4 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_179_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ B5))) => (member361641010le_alt @ F @ (pi_Arr1114944513le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_180_funcsetI, axiom,
    ((![A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member1117110356le_alt @ F @ (pi_set1343364587le_alt @ A4 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_181_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ B5))) => (member183760530le_alt @ F @ (pi_Arr479247969le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_182_funcsetI, axiom,
    ((![A4 : set_Ar809243995le_alt, F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X @ A4) => (member684274596le_alt @ (F @ X) @ B5))) => (member896258016le_alt @ F @ (pi_Arr1849985851le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_183_case__prod__Pair__iden, axiom,
    ((![P : produc16571293le_alt]: ((produc846580013le_alt @ produc1494124311le_alt @ P) = P)))). % case_prod_Pair_iden
thf(fact_184_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S3 : set_Pr367596371le_alt]: (((^[X3 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ R2))) = (^[X3 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ S3)))) = (R2 = S3))))). % pred_equals_eq2
thf(fact_185_UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_186_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_187_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % UNIV_I
thf(fact_188_UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % UNIV_I
thf(fact_189_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_190_UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_191_Pi__UNIV, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_192_Pi__UNIV, axiom,
    ((![A4 : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A4 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_193_same__fstI, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, X2 : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R2 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((P2 @ X2) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ Y) @ (R2 @ X2)) => (member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ X2 @ Y5) @ (produc1494124311le_alt @ X2 @ Y)) @ (same_f554660482le_alt @ P2 @ R2))))))). % same_fstI
thf(fact_194_UNIV__witness, axiom,
    ((?[X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_195_UNIV__witness, axiom,
    ((?[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_196_UNIV__witness, axiom,
    ((?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_197_UNIV__witness, axiom,
    ((?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_198_UNIV__witness, axiom,
    ((?[X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_199_UNIV__witness, axiom,
    ((?[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_200_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_201_UNIV__eq__I, axiom,
    ((![A4 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A4)) => (top_to469035705le_alt = A4))))). % UNIV_eq_I
thf(fact_202_UNIV__eq__I, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A4)) => (top_to685525675le_alt = A4))))). % UNIV_eq_I
thf(fact_203_UNIV__eq__I, axiom,
    ((![A4 : set_Ar182050865le_alt]: ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A4)) => (top_to803745505le_alt = A4))))). % UNIV_eq_I
thf(fact_204_UNIV__eq__I, axiom,
    ((![A4 : set_Ar1007576579e_indi]: ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ A4)) => (top_to1799531699e_indi = A4))))). % UNIV_eq_I
thf(fact_205_UNIV__eq__I, axiom,
    ((![A4 : set_Ar1665529862le_alt]: ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ A4)) => (top_to958727510le_alt = A4))))). % UNIV_eq_I
thf(fact_206_rangeE, axiom,
    ((![B : produc16571293le_alt, F : arrow_1429744205e_indi > produc16571293le_alt]: ((member2048039092le_alt @ B @ (image_2120751389le_alt @ F @ top_to1799531699e_indi)) => (~ ((![X : arrow_1429744205e_indi]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_207_rangeE, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member1334244458le_alt @ B @ (image_444707709le_alt @ F @ top_to1799531699e_indi)) => (~ ((![X : arrow_1429744205e_indi]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_208_rangeE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ B @ (image_836174111le_alt @ F @ top_to1799531699e_indi)) => (~ ((![X : arrow_1429744205e_indi]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_209_rangeE, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : arrow_1429744205e_indi > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ B @ (image_1735005225le_alt @ F @ top_to1799531699e_indi)) => (~ ((![X : arrow_1429744205e_indi]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_210_rangeE, axiom,
    ((![B : produc16571293le_alt, F : arrow_1857593510le_alt > produc16571293le_alt]: ((member2048039092le_alt @ B @ (image_2110916560le_alt @ F @ top_to958727510le_alt)) => (~ ((![X : arrow_1857593510le_alt]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_211_rangeE, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ B @ (image_1862227504le_alt @ F @ top_to958727510le_alt)) => (~ ((![X : arrow_1857593510le_alt]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_212_rangeE, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ B @ (image_2059429932le_alt @ F @ top_to958727510le_alt)) => (~ ((![X : arrow_1857593510le_alt]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_213_rangeE, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ B @ (image_1195412316le_alt @ F @ top_to958727510le_alt)) => (~ ((![X : arrow_1857593510le_alt]: (~ ((B = (F @ X))))))))))). % rangeE
thf(fact_214_rangeI, axiom,
    ((![F : arrow_1429744205e_indi > produc16571293le_alt, X2 : arrow_1429744205e_indi]: (member2048039092le_alt @ (F @ X2) @ (image_2120751389le_alt @ F @ top_to1799531699e_indi))))). % rangeI
thf(fact_215_rangeI, axiom,
    ((![F : arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: (member1334244458le_alt @ (F @ X2) @ (image_444707709le_alt @ F @ top_to1799531699e_indi))))). % rangeI
thf(fact_216_rangeI, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: (member684274596le_alt @ (F @ X2) @ (image_836174111le_alt @ F @ top_to1799531699e_indi))))). % rangeI
thf(fact_217_rangeI, axiom,
    ((![F : arrow_1429744205e_indi > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: (member183760530le_alt @ (F @ X2) @ (image_1735005225le_alt @ F @ top_to1799531699e_indi))))). % rangeI
thf(fact_218_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > produc16571293le_alt, X2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (F @ X2) @ (image_2110916560le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_219_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: (member1334244458le_alt @ (F @ X2) @ (image_1862227504le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_220_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: (member684274596le_alt @ (F @ X2) @ (image_2059429932le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_221_rangeI, axiom,
    ((![F : arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: (member183760530le_alt @ (F @ X2) @ (image_1195412316le_alt @ F @ top_to958727510le_alt))))). % rangeI
thf(fact_222_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_223_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X3 : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_224_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X3 : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_225_range__eqI, axiom,
    ((![B : produc16571293le_alt, F : arrow_1429744205e_indi > produc16571293le_alt, X2 : arrow_1429744205e_indi]: ((B = (F @ X2)) => (member2048039092le_alt @ B @ (image_2120751389le_alt @ F @ top_to1799531699e_indi)))))). % range_eqI
thf(fact_226_range__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: ((B = (F @ X2)) => (member1334244458le_alt @ B @ (image_444707709le_alt @ F @ top_to1799531699e_indi)))))). % range_eqI
thf(fact_227_range__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: ((B = (F @ X2)) => (member684274596le_alt @ B @ (image_836174111le_alt @ F @ top_to1799531699e_indi)))))). % range_eqI
thf(fact_228_range__eqI, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : arrow_1429744205e_indi > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi]: ((B = (F @ X2)) => (member183760530le_alt @ B @ (image_1735005225le_alt @ F @ top_to1799531699e_indi)))))). % range_eqI
thf(fact_229_range__eqI, axiom,
    ((![B : produc16571293le_alt, F : arrow_1857593510le_alt > produc16571293le_alt, X2 : arrow_1857593510le_alt]: ((B = (F @ X2)) => (member2048039092le_alt @ B @ (image_2110916560le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_230_range__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : arrow_1857593510le_alt > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((B = (F @ X2)) => (member1334244458le_alt @ B @ (image_1862227504le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_231_range__eqI, axiom,
    ((![B : arrow_1429744205e_indi > set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((B = (F @ X2)) => (member684274596le_alt @ B @ (image_2059429932le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_232_range__eqI, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, F : arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((B = (F @ X2)) => (member183760530le_alt @ B @ (image_1195412316le_alt @ F @ top_to958727510le_alt)))))). % range_eqI
thf(fact_233_lex__prod__def, axiom,
    ((lex_pr3395839le_alt = (^[Ra : set_Pr367596371le_alt]: (^[Rb : set_Pr367596371le_alt]: (collec824848862le_alt @ (produc614564272_alt_o @ (produc909656464_alt_o @ (^[A5 : arrow_1857593510le_alt]: (^[B4 : arrow_1857593510le_alt]: (produc624247124_alt_o @ (^[A6 : arrow_1857593510le_alt]: (^[B6 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ A6) @ Ra)) | ((((A5 = A6)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ B6) @ Rb)))))))))))))))))). % lex_prod_def
thf(fact_234_surjD, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: (((image_688677079e_indi @ F @ top_to1799531699e_indi) = top_to1799531699e_indi) => (?[X : arrow_1429744205e_indi]: (Y = (F @ X))))))). % surjD
thf(fact_235_surjD, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (((image_582756252le_alt @ F @ top_to1799531699e_indi) = top_to958727510le_alt) => (?[X : arrow_1429744205e_indi]: (Y = (F @ X))))))). % surjD
thf(fact_236_surjD, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: (((image_2061749130e_indi @ F @ top_to958727510le_alt) = top_to1799531699e_indi) => (?[X : arrow_1857593510le_alt]: (Y = (F @ X))))))). % surjD
thf(fact_237_surjD, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) => (?[X : arrow_1857593510le_alt]: (Y = (F @ X))))))). % surjD
thf(fact_238_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_239_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_240_surj__def, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi]: (((image_688677079e_indi @ F @ top_to1799531699e_indi) = top_to1799531699e_indi) = (![Y4 : arrow_1429744205e_indi]: (?[X3 : arrow_1429744205e_indi]: (Y4 = (F @ X3)))))))). % surj_def
thf(fact_241_surj__def, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1857593510le_alt]: (((image_582756252le_alt @ F @ top_to1799531699e_indi) = top_to958727510le_alt) = (![Y4 : arrow_1857593510le_alt]: (?[X3 : arrow_1429744205e_indi]: (Y4 = (F @ X3)))))))). % surj_def
thf(fact_242_surj__def, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1429744205e_indi]: (((image_2061749130e_indi @ F @ top_to958727510le_alt) = top_to1799531699e_indi) = (![Y4 : arrow_1429744205e_indi]: (?[X3 : arrow_1857593510le_alt]: (Y4 = (F @ X3)))))))). % surj_def
thf(fact_243_surj__def, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt]: (((image_1918885929le_alt @ F @ top_to958727510le_alt) = top_to958727510le_alt) = (![Y4 : arrow_1857593510le_alt]: (?[X3 : arrow_1857593510le_alt]: (Y4 = (F @ X3)))))))). % surj_def
thf(fact_244_surjI, axiom,
    ((![G : arrow_1429744205e_indi > arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1429744205e_indi]: ((![X : arrow_1857593510le_alt]: ((G @ (F @ X)) = X)) => ((image_582756252le_alt @ G @ top_to1799531699e_indi) = top_to958727510le_alt))))). % surjI
thf(fact_245_surjI, axiom,
    ((![G : arrow_1857593510le_alt > arrow_1429744205e_indi, F : arrow_1429744205e_indi > arrow_1857593510le_alt]: ((![X : arrow_1429744205e_indi]: ((G @ (F @ X)) = X)) => ((image_2061749130e_indi @ G @ top_to958727510le_alt) = top_to1799531699e_indi))))). % surjI
thf(fact_246_surjI, axiom,
    ((![G : arrow_1857593510le_alt > arrow_1857593510le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((![X : arrow_1857593510le_alt]: ((G @ (F @ X)) = X)) => ((image_1918885929le_alt @ G @ top_to958727510le_alt) = top_to958727510le_alt))))). % surjI
thf(fact_247_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_248_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![Lab : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ Lab) => ((member1334244458le_alt @ Lab @ arrow_1848678355le_Lin) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
