% 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_281__5189280_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:16.035

% Could-be-implicit typings (18)
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,
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thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr720748555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
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thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $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__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (53)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
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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_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Finite__Set_Ocard_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    finite927127589e_indi : set_Ar1007576579e_indi > nat).
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_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat, type,
    inj_on_nat_nat : (nat > nat) > set_nat > $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_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    if_set550155277le_alt : $o > set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    ord_le2059613795e_indi : set_Ar1007576579e_indi > set_Ar1007576579e_indi > $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_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__Nat__Onat_J, type,
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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_Set_OCollect_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1382217680le_alt : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o) > set_Ar182050865le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
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thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
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thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
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thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_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__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_Lab____, type,
    lab : set_Pr367596371le_alt).
thf(sy_v_Lba____, type,
    lba : 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 (157)
thf(fact_0_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_1_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_2__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_3__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_4__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_5__092_060open_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lab))). % \<open>a <\<^bsub>Lab\<^esub> b\<close>
thf(fact_6__092_060open_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lba))). % \<open>b <\<^bsub>Lba\<^esub> a\<close>
thf(fact_7__092_060open_062_Ia_M_Ab_J_A_092_060notin_062_ALba_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lba))))). % \<open>(a, b) \<notin> Lba\<close>
thf(fact_8__092_060open_062_Ib_M_Aa_J_A_092_060notin_062_ALab_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lab))))). % \<open>(b, a) \<notin> Lab\<close>
thf(fact_9__092_060open_062_092_060exists_062n_060N_O_A_I_092_060forall_062m_092_060le_062n_O_Ab_A_060_092_060_094bsub_062F_A_I_092_060lambda_062i_O_Aif_Ah_Ai_A_060_Am_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Aa_J_A_092_060and_062_Aa_A_060_092_060_094bsub_062F_A_I_092_060lambda_062i_O_Aif_Ah_Ai_A_060_An_A_L_A1_Athen_ALab_Aelse_ALba_J_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((?[N : nat]: ((ord_less_nat @ N @ (finite927127589e_indi @ top_to1799531699e_indi)) & ((![M : nat]: ((ord_less_eq_nat @ M @ N) => (member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ M) @ lab @ lba)))))) & (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ (plus_plus_nat @ N @ one_one_nat)) @ lab @ lba))))))))). % \<open>\<exists>n<N. (\<forall>m\<le>n. b <\<^bsub>F (\<lambda>i. if h i < m then Lab else Lba)\<^esub> a) \<and> a <\<^bsub>F (\<lambda>i. if h i < n + 1 then Lab else Lba)\<^esub> b\<close>
thf(fact_10_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_11_PiProf, axiom,
    ((![N2 : nat]: (member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N2) @ lab @ lba)) @ arrow_1951607831e_Prof)))). % PiProf
thf(fact_12__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lab_O_A_092_060lbrakk_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lab : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ Lab) => (~ ((member1334244458le_alt @ Lab @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lab. \<lbrakk>a <\<^bsub>Lab\<^esub> b; Lab \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lba_O_A_092_060lbrakk_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lba : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ Lba) => (~ ((member1334244458le_alt @ Lba @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lba. \<lbrakk>b <\<^bsub>Lba\<^esub> a; Lba \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_14__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "1"
thf(fact_15__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "2"
thf(fact_16__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P2)))))))))). % "3"
thf(fact_17__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P2)))))))))))). % "4"
thf(fact_18_pairwise__neutrality, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))). % pairwise_neutrality
thf(fact_19_nat__add__left__cancel__le, axiom,
    ((![K : nat, M2 : nat, N2 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M2) @ (plus_plus_nat @ K @ N2)) = (ord_less_eq_nat @ M2 @ N2))))). % nat_add_left_cancel_le
thf(fact_20_nat__add__left__cancel__less, axiom,
    ((![K : nat, M2 : nat, N2 : nat]: ((ord_less_nat @ (plus_plus_nat @ K @ M2) @ (plus_plus_nat @ K @ N2)) = (ord_less_nat @ M2 @ N2))))). % nat_add_left_cancel_less
thf(fact_21_add__less__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_22_add__less__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_23_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_24_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_25_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_26_add__le__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_27_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_28_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_29_const__Lin__Prof, axiom,
    ((![L2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P3 : arrow_1429744205e_indi]: L2) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_30_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X))))))))))))). % unanimity_def
thf(fact_31_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![Y : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (Y @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ Y))))))))))))))))). % IIA_def
thf(fact_32_notin__Lin__iff, axiom,
    ((![L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((~ ((X2 = Y2))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y2) @ L2))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y2 @ X2) @ L2))))))). % notin_Lin_iff
thf(fact_33_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X3))))))). % complete_Lin
thf(fact_34_Lin__irrefl, axiom,
    ((![L2 : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L2) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L2)))))))). % Lin_irrefl
thf(fact_35_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_36_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_37_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_38_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A3 : nat]: (^[B3 : nat]: (plus_plus_nat @ B3 @ A3)))))). % add.commute
thf(fact_39_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_40_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_41_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_42_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_43_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_44_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_45_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_46_Collect__mem__eq, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_47_Collect__mem__eq, axiom,
    ((![A4 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A4))) = A4)))). % Collect_mem_eq
thf(fact_48_group__cancel_Oadd2, axiom,
    ((![B4 : nat, K : nat, B : nat, A : nat]: ((B4 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B4) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_49_group__cancel_Oadd1, axiom,
    ((![A4 : nat, K : nat, A : nat, B : nat]: ((A4 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A4 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_50_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((I3 = J) & (K = L3)) => ((plus_plus_nat @ I3 @ K) = (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_51_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_52_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_53_linorder__neqE__nat, axiom,
    ((![X2 : nat, Y2 : nat]: ((~ ((X2 = Y2))) => ((~ ((ord_less_nat @ X2 @ Y2))) => (ord_less_nat @ Y2 @ X2)))))). % linorder_neqE_nat
thf(fact_54_infinite__descent, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N : nat]: ((~ ((P @ N))) => (?[M : nat]: ((ord_less_nat @ M @ N) & (~ ((P @ M))))))) => (P @ N2))))). % infinite_descent
thf(fact_55_nat__less__induct, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N : nat]: ((![M : nat]: ((ord_less_nat @ M @ N) => (P @ M))) => (P @ N))) => (P @ N2))))). % nat_less_induct
thf(fact_56_less__irrefl__nat, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_irrefl_nat
thf(fact_57_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_58_less__not__refl2, axiom,
    ((![N2 : nat, M2 : nat]: ((ord_less_nat @ N2 @ M2) => (~ ((M2 = N2))))))). % less_not_refl2
thf(fact_59_less__not__refl, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_not_refl
thf(fact_60_nat__neq__iff, axiom,
    ((![M2 : nat, N2 : nat]: ((~ ((M2 = N2))) = (((ord_less_nat @ M2 @ N2)) | ((ord_less_nat @ N2 @ M2))))))). % nat_neq_iff
thf(fact_61_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y3 : nat]: ((P @ Y3) => (ord_less_eq_nat @ Y3 @ B))) => (?[X3 : nat]: ((P @ X3) & (![Y4 : nat]: ((P @ Y4) => (ord_less_eq_nat @ Y4 @ X3)))))))))). % Nat.ex_has_greatest_nat
thf(fact_62_nat__le__linear, axiom,
    ((![M2 : nat, N2 : nat]: ((ord_less_eq_nat @ M2 @ N2) | (ord_less_eq_nat @ N2 @ M2))))). % nat_le_linear
thf(fact_63_le__antisym, axiom,
    ((![M2 : nat, N2 : nat]: ((ord_less_eq_nat @ M2 @ N2) => ((ord_less_eq_nat @ N2 @ M2) => (M2 = N2)))))). % le_antisym
thf(fact_64_eq__imp__le, axiom,
    ((![M2 : nat, N2 : nat]: ((M2 = N2) => (ord_less_eq_nat @ M2 @ N2))))). % eq_imp_le
thf(fact_65_le__trans, axiom,
    ((![I3 : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I3 @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I3 @ K)))))). % le_trans
thf(fact_66_le__refl, axiom,
    ((![N2 : nat]: (ord_less_eq_nat @ N2 @ N2)))). % le_refl
thf(fact_67_add__le__imp__le__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_68_add__le__imp__le__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_69_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B3 : nat]: (?[C2 : nat]: (B3 = (plus_plus_nat @ A3 @ C2)))))))). % le_iff_add
thf(fact_70_add__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_right_mono
thf(fact_71_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C3 : nat]: (~ ((B = (plus_plus_nat @ A @ C3))))))))))). % less_eqE
thf(fact_72_add__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_left_mono
thf(fact_73_add__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_mono
thf(fact_74_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_eq_nat @ I3 @ J) & (ord_less_eq_nat @ K @ L3)) => (ord_less_eq_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_75_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((I3 = J) & (ord_less_eq_nat @ K @ L3)) => (ord_less_eq_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_76_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_eq_nat @ I3 @ J) & (K = L3)) => (ord_less_eq_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_77_add__less__imp__less__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_right
thf(fact_78_add__less__imp__less__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_left
thf(fact_79_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_strict_right_mono
thf(fact_80_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_strict_left_mono
thf(fact_81_add__strict__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_strict_mono
thf(fact_82_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_nat @ I3 @ J) & (K = L3)) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_field(1)
thf(fact_83_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((I3 = J) & (ord_less_nat @ K @ L3)) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_field(2)
thf(fact_84_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_nat @ I3 @ J) & (ord_less_nat @ K @ L3)) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_field(5)
thf(fact_85_less__mono__imp__le__mono, axiom,
    ((![F2 : nat > nat, I3 : nat, J : nat]: ((![I2 : nat, J2 : nat]: ((ord_less_nat @ I2 @ J2) => (ord_less_nat @ (F2 @ I2) @ (F2 @ J2)))) => ((ord_less_eq_nat @ I3 @ J) => (ord_less_eq_nat @ (F2 @ I3) @ (F2 @ J))))))). % less_mono_imp_le_mono
thf(fact_86_le__neq__implies__less, axiom,
    ((![M2 : nat, N2 : nat]: ((ord_less_eq_nat @ M2 @ N2) => ((~ ((M2 = N2))) => (ord_less_nat @ M2 @ N2)))))). % le_neq_implies_less
thf(fact_87_less__or__eq__imp__le, axiom,
    ((![M2 : nat, N2 : nat]: (((ord_less_nat @ M2 @ N2) | (M2 = N2)) => (ord_less_eq_nat @ M2 @ N2))))). % less_or_eq_imp_le
thf(fact_88_le__eq__less__or__eq, axiom,
    ((ord_less_eq_nat = (^[M3 : nat]: (^[N3 : nat]: (((ord_less_nat @ M3 @ N3)) | ((M3 = N3)))))))). % le_eq_less_or_eq
thf(fact_89_less__imp__le__nat, axiom,
    ((![M2 : nat, N2 : nat]: ((ord_less_nat @ M2 @ N2) => (ord_less_eq_nat @ M2 @ N2))))). % less_imp_le_nat
thf(fact_90_nat__less__le, axiom,
    ((ord_less_nat = (^[M3 : nat]: (^[N3 : nat]: (((ord_less_eq_nat @ M3 @ N3)) & ((~ ((M3 = N3)))))))))). % nat_less_le
thf(fact_91_less__add__eq__less, axiom,
    ((![K : nat, L3 : nat, M2 : nat, N2 : nat]: ((ord_less_nat @ K @ L3) => (((plus_plus_nat @ M2 @ L3) = (plus_plus_nat @ K @ N2)) => (ord_less_nat @ M2 @ N2)))))). % less_add_eq_less
thf(fact_92_trans__less__add2, axiom,
    ((![I3 : nat, J : nat, M2 : nat]: ((ord_less_nat @ I3 @ J) => (ord_less_nat @ I3 @ (plus_plus_nat @ M2 @ J)))))). % trans_less_add2
thf(fact_93_trans__less__add1, axiom,
    ((![I3 : nat, J : nat, M2 : nat]: ((ord_less_nat @ I3 @ J) => (ord_less_nat @ I3 @ (plus_plus_nat @ J @ M2)))))). % trans_less_add1
thf(fact_94_add__less__mono1, axiom,
    ((![I3 : nat, J : nat, K : nat]: ((ord_less_nat @ I3 @ J) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ K)))))). % add_less_mono1
thf(fact_95_not__add__less2, axiom,
    ((![J : nat, I3 : nat]: (~ ((ord_less_nat @ (plus_plus_nat @ J @ I3) @ I3)))))). % not_add_less2
thf(fact_96_not__add__less1, axiom,
    ((![I3 : nat, J : nat]: (~ ((ord_less_nat @ (plus_plus_nat @ I3 @ J) @ I3)))))). % not_add_less1
thf(fact_97_add__less__mono, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: ((ord_less_nat @ I3 @ J) => ((ord_less_nat @ K @ L3) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3))))))). % add_less_mono
thf(fact_98_add__lessD1, axiom,
    ((![I3 : nat, J : nat, K : nat]: ((ord_less_nat @ (plus_plus_nat @ I3 @ J) @ K) => (ord_less_nat @ I3 @ K))))). % add_lessD1
thf(fact_99_nat__le__iff__add, axiom,
    ((ord_less_eq_nat = (^[M3 : nat]: (^[N3 : nat]: (?[K2 : nat]: (N3 = (plus_plus_nat @ M3 @ K2)))))))). % nat_le_iff_add
thf(fact_100_trans__le__add2, axiom,
    ((![I3 : nat, J : nat, M2 : nat]: ((ord_less_eq_nat @ I3 @ J) => (ord_less_eq_nat @ I3 @ (plus_plus_nat @ M2 @ J)))))). % trans_le_add2
thf(fact_101_trans__le__add1, axiom,
    ((![I3 : nat, J : nat, M2 : nat]: ((ord_less_eq_nat @ I3 @ J) => (ord_less_eq_nat @ I3 @ (plus_plus_nat @ J @ M2)))))). % trans_le_add1
thf(fact_102_add__le__mono1, axiom,
    ((![I3 : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I3 @ J) => (ord_less_eq_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ K)))))). % add_le_mono1
thf(fact_103_add__le__mono, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: ((ord_less_eq_nat @ I3 @ J) => ((ord_less_eq_nat @ K @ L3) => (ord_less_eq_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3))))))). % add_le_mono
thf(fact_104_le__Suc__ex, axiom,
    ((![K : nat, L3 : nat]: ((ord_less_eq_nat @ K @ L3) => (?[N : nat]: (L3 = (plus_plus_nat @ K @ N))))))). % le_Suc_ex
thf(fact_105_add__leD2, axiom,
    ((![M2 : nat, K : nat, N2 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M2 @ K) @ N2) => (ord_less_eq_nat @ K @ N2))))). % add_leD2
thf(fact_106_add__leD1, axiom,
    ((![M2 : nat, K : nat, N2 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M2 @ K) @ N2) => (ord_less_eq_nat @ M2 @ N2))))). % add_leD1
thf(fact_107_le__add2, axiom,
    ((![N2 : nat, M2 : nat]: (ord_less_eq_nat @ N2 @ (plus_plus_nat @ M2 @ N2))))). % le_add2
thf(fact_108_le__add1, axiom,
    ((![N2 : nat, M2 : nat]: (ord_less_eq_nat @ N2 @ (plus_plus_nat @ N2 @ M2))))). % le_add1
thf(fact_109_add__leE, axiom,
    ((![M2 : nat, K : nat, N2 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M2 @ K) @ N2) => (~ (((ord_less_eq_nat @ M2 @ N2) => (~ ((ord_less_eq_nat @ K @ N2)))))))))). % add_leE
thf(fact_110_add__less__le__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_less_le_mono
thf(fact_111_add__le__less__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_le_less_mono
thf(fact_112_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_nat @ I3 @ J) & (ord_less_eq_nat @ K @ L3)) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_field(3)
thf(fact_113_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I3 : nat, J : nat, K : nat, L3 : nat]: (((ord_less_eq_nat @ I3 @ J) & (ord_less_nat @ K @ L3)) => (ord_less_nat @ (plus_plus_nat @ I3 @ K) @ (plus_plus_nat @ J @ L3)))))). % add_mono_thms_linordered_field(4)
thf(fact_114_mono__nat__linear__lb, axiom,
    ((![F2 : nat > nat, M2 : nat, K : nat]: ((![M4 : nat, N : nat]: ((ord_less_nat @ M4 @ N) => (ord_less_nat @ (F2 @ M4) @ (F2 @ N)))) => (ord_less_eq_nat @ (plus_plus_nat @ (F2 @ M2) @ K) @ (F2 @ (plus_plus_nat @ M2 @ K))))))). % mono_nat_linear_lb
thf(fact_115_discrete, axiom,
    ((ord_less_nat = (^[A3 : nat]: (ord_less_eq_nat @ (plus_plus_nat @ A3 @ one_one_nat)))))). % discrete
thf(fact_116_inj__add__left, axiom,
    ((![A : nat]: (inj_on_nat_nat @ (plus_plus_nat @ A) @ top_top_set_nat)))). % inj_add_left
thf(fact_117_add__mono1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat)))))). % add_mono1
thf(fact_118_less__add__one, axiom,
    ((![A : nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat))))). % less_add_one
thf(fact_119_inj__on__subset, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, B4 : set_Ar1007576579e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((ord_le2059613795e_indi @ B4 @ A4) => (inj_on528257168di_nat @ F2 @ B4)))))). % inj_on_subset
thf(fact_120_subset__inj__on, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, B4 : set_Ar1007576579e_indi, A4 : set_Ar1007576579e_indi]: ((inj_on528257168di_nat @ F2 @ B4) => ((ord_le2059613795e_indi @ A4 @ B4) => (inj_on528257168di_nat @ F2 @ A4)))))). % subset_inj_on
thf(fact_121_bounded__Max__nat, axiom,
    ((![P : nat > $o, X2 : nat, M5 : nat]: ((P @ X2) => ((![X3 : nat]: ((P @ X3) => (ord_less_eq_nat @ X3 @ M5))) => (~ ((![M4 : nat]: ((P @ M4) => (~ ((![X4 : nat]: ((P @ X4) => (ord_less_eq_nat @ X4 @ M4)))))))))))))). % bounded_Max_nat
thf(fact_122_inj__on__inverseI, axiom,
    ((![A4 : set_Ar1007576579e_indi, G : nat > arrow_1429744205e_indi, F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A4) => ((G @ (F2 @ X3)) = X3))) => (inj_on528257168di_nat @ F2 @ A4))))). % inj_on_inverseI
thf(fact_123_inj__on__contraD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((~ ((X2 = Y2))) => ((member1966420836e_indi @ X2 @ A4) => ((member1966420836e_indi @ Y2 @ A4) => (~ (((F2 @ X2) = (F2 @ Y2))))))))))). % inj_on_contraD
thf(fact_124_inj__on__eq__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((member1966420836e_indi @ X2 @ A4) => ((member1966420836e_indi @ Y2 @ A4) => (((F2 @ X2) = (F2 @ Y2)) = (X2 = Y2)))))))). % inj_on_eq_iff
thf(fact_125_inj__on__cong, axiom,
    ((![A4 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > nat]: ((![A5 : arrow_1429744205e_indi]: ((member1966420836e_indi @ A5 @ A4) => ((F2 @ A5) = (G @ A5)))) => ((inj_on528257168di_nat @ F2 @ A4) = (inj_on528257168di_nat @ G @ A4)))))). % inj_on_cong
thf(fact_126_inj__on__def, axiom,
    ((inj_on528257168di_nat = (^[F3 : arrow_1429744205e_indi > nat]: (^[A6 : set_Ar1007576579e_indi]: (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ A6)) => ((![Y : arrow_1429744205e_indi]: (((member1966420836e_indi @ Y @ A6)) => (((((F3 @ X) = (F3 @ Y))) => ((X = Y)))))))))))))). % inj_on_def
thf(fact_127_inj__onI, axiom,
    ((![A4 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A4) => ((member1966420836e_indi @ Y3 @ A4) => (((F2 @ X3) = (F2 @ Y3)) => (X3 = Y3))))) => (inj_on528257168di_nat @ F2 @ A4))))). % inj_onI
thf(fact_128_inj__onD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => (((F2 @ X2) = (F2 @ Y2)) => ((member1966420836e_indi @ X2 @ A4) => ((member1966420836e_indi @ Y2 @ A4) => (X2 = Y2)))))))). % inj_onD
thf(fact_129_inj__on__add, axiom,
    ((![A : nat, A4 : set_nat]: (inj_on_nat_nat @ (plus_plus_nat @ A) @ A4)))). % inj_on_add
thf(fact_130_injD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => (((F2 @ X2) = (F2 @ Y2)) => (X2 = Y2)))))). % injD
thf(fact_131_injI, axiom,
    ((![F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: (((F2 @ X3) = (F2 @ Y3)) => (X3 = Y3))) => (inj_on528257168di_nat @ F2 @ top_to1799531699e_indi))))). % injI
thf(fact_132_inj__eq, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X2 : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => (((F2 @ X2) = (F2 @ Y2)) = (X2 = Y2)))))). % inj_eq
thf(fact_133_inj__def, axiom,
    ((![F2 : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) = (![X : arrow_1429744205e_indi]: (![Y : arrow_1429744205e_indi]: ((((F2 @ X) = (F2 @ Y))) => ((X = Y))))))))). % inj_def
thf(fact_134_inj__on__add_H, axiom,
    ((![A : nat, A4 : set_nat]: (inj_on_nat_nat @ (^[B3 : nat]: (plus_plus_nat @ B3 @ A)) @ A4)))). % inj_on_add'
thf(fact_135_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_136_dictatorI, axiom,
    ((![F4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F4 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ arrow_1951607831e_Prof) => (![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: ((~ ((A5 = B5))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B5) @ (X3 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B5) @ (F4 @ X3))))))) => (arrow_960434986ctator @ F4 @ I3)))))). % dictatorI
thf(fact_137_Pi__I, axiom,
    ((![A4 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A4) => (member1334244458le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_138_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B4 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_139_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B4 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member1334244458le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_140_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B4 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member2048039092le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_141_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B4 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_142_Pi__I, axiom,
    ((![A4 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member684274596le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_143_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => (member2048039092le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_144_Pi__I, axiom,
    ((![A4 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member684274596le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_145_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => (member1334244458le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_146_Pi__I, axiom,
    ((![A4 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A4) => (member684274596le_alt @ (F2 @ X3) @ (B4 @ X3)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A4 @ B4)))))). % Pi_I
thf(fact_147_PiE, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar1007576579e_indi, B4 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A4 @ B4)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member1966420836e_indi @ X2 @ A4)))))))). % PiE
thf(fact_148_PiE, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A4 : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A4 @ B4)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_149_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A4 : set_se2071012361le_alt, B4 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A4 @ B4)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_150_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A4 @ B4)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_151_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B4 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A4 @ B4)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_152_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A4 : set_Ar809243995le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A4 @ B4)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE
thf(fact_153_PiE, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A4 @ B4)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A4)))))))). % PiE
thf(fact_154_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B4 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A4 @ B4)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A4)))))))). % PiE
thf(fact_155_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A4 @ B4)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE
thf(fact_156_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A4 : set_Ar809243995le_alt, B4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A4 @ B4)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B4 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A4)))))))). % PiE

% Helper facts (3)
thf(help_If_3_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X2 : set_Pr367596371le_alt, Y2 : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $false @ X2 @ Y2) = Y2)))).
thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X2 : set_Pr367596371le_alt, Y2 : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $true @ X2 @ Y2) = X2)))).

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![N4 : nat]: ((ord_less_nat @ N4 @ (finite927127589e_indi @ top_to1799531699e_indi)) => ((![M4 : nat]: ((ord_less_eq_nat @ M4 @ N4) => (member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ M4) @ lab @ lba)))))) => ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ (plus_plus_nat @ N4 @ one_one_nat)) @ lab @ lba)))) => thesis)))))).
thf(conj_1, conjecture,
    (thesis)).
