% 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_283__5189288_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:17.027

% Could-be-implicit typings (10)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__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__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__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__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 (65)
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_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_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_Finite__Set_Ocard_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    finite927127589e_indi : set_Ar1007576579e_indi > nat).
thf(sy_c_Fun_Ocomp_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__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_A1580130049e_indi : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > nat) > (arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > nat).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_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,
    comp_A255443021le_alt : (arrow_1429744205e_indi > nat) > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > nat).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_A2059482153e_indi : (arrow_1429744205e_indi > nat) > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > nat).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Nat__Onat, type,
    comp_A853618258at_nat : (arrow_1429744205e_indi > nat) > (nat > arrow_1429744205e_indi) > nat > nat).
thf(sy_c_Fun_Ocomp_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    comp_A708674671le_alt : (arrow_1429744205e_indi > nat) > (produc16571293le_alt > arrow_1429744205e_indi) > produc16571293le_alt > nat).
thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_n1073433769e_indi : (nat > arrow_1429744205e_indi) > (arrow_1429744205e_indi > nat) > arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_n330120530e_indi : (nat > nat) > (arrow_1429744205e_indi > nat) > arrow_1429744205e_indi > nat).
thf(sy_c_Fun_Ocomp_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    comp_P498338521e_indi : (produc16571293le_alt > nat) > (arrow_1429744205e_indi > produc16571293le_alt) > arrow_1429744205e_indi > nat).
thf(sy_c_Fun_Oid_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,
    id_Arr1104251884le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Fun_Oid_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    id_Arr152457500e_indi : arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Fun_Oid_001t__Nat__Onat, type,
    id_nat : nat > nat).
thf(sy_c_Fun_Oid_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    id_Pro1771394668le_alt : produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Fun_Oinj__on_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,
    inj_on1288490261le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_Fun_Oinj__on_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    inj_on1947401569e_indi : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi) > set_Ar809243995le_alt > $o).
thf(sy_c_Fun_Oinj__on_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__Nat__Onat, type,
    inj_on598967066lt_nat : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > nat) > set_Ar809243995le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    inj_on783451275le_alt : (arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    inj_on1663454827e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > set_Ar1007576579e_indi > $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_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on845182641le_alt : (arrow_1429744205e_indi > produc16571293le_alt) > 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_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    inj_on2029130011e_indi : (produc16571293le_alt > arrow_1429744205e_indi) > set_Pr367596371le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Nat__Onat, type,
    inj_on1748146656lt_nat : (produc16571293le_alt > nat) > set_Pr367596371le_alt > $o).
thf(sy_c_Fun_Oinj__on_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,
    inj_on616462689le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr367596371le_alt > $o).
thf(sy_c_Hilbert__Choice_Obijection_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,
    hilber759434986le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > $o).
thf(sy_c_Hilbert__Choice_Obijection_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    hilber1061076126e_indi : (arrow_1429744205e_indi > arrow_1429744205e_indi) > $o).
thf(sy_c_Hilbert__Choice_Obijection_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    hilber402823662le_alt : (produc16571293le_alt > produc16571293le_alt) > $o).
thf(sy_c_Hilbert__Choice_Oinv__into_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,
    hilber61073786le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_c_Hilbert__Choice_Oinv__into_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    hilber700257104e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > arrow_1429744205e_indi) > arrow_1429744205e_indi > arrow_1429744205e_indi).
thf(sy_c_Hilbert__Choice_Oinv__into_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    hilber1586975467di_nat : set_Ar1007576579e_indi > (arrow_1429744205e_indi > nat) > nat > arrow_1429744205e_indi).
thf(sy_c_Hilbert__Choice_Oinv__into_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,
    hilber790132294le_alt : set_Pr367596371le_alt > (produc16571293le_alt > produc16571293le_alt) > produc16571293le_alt > produc16571293le_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_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,
    ord_le875007495le_alt : set_Ar809243995le_alt > set_Ar809243995le_alt > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    ord_le1187139159e_indi : set_Ar1007576579e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    ord_le1510239143le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_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_Eo_J, type,
    top_to1344581618_alt_o : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_M_Eo_J, type,
    top_to1473733010indi_o : arrow_1429744205e_indi > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    top_to1074038850_alt_o : produc16571293le_alt > $o).
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__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
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_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_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1245692284le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_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_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    collec1169676194e_indi : (arrow_1429744205e_indi > $o) > set_Ar1007576579e_indi).
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_Wellfounded_Olex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lex_pr3395839le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Wellfounded_Omeasure_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    measur1447705966le_alt : (arrow_1857593510le_alt > nat) > set_Pr367596371le_alt).
thf(sy_c_Wellfounded_Omlex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    mlex_p1368559413le_alt : (arrow_1857593510le_alt > nat) > set_Pr367596371le_alt > set_Pr367596371le_alt).
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,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_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_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).
thf(sy_v_n____, type,
    n : nat).

% Relevant facts (143)
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_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_3_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_4_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_5_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_6_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_7_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_8_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_9_inv__equality, axiom,
    ((![G : nat > arrow_1429744205e_indi, F : arrow_1429744205e_indi > nat]: ((![X2 : arrow_1429744205e_indi]: ((G @ (F @ X2)) = X2)) => ((![Y : nat]: ((F @ (G @ Y)) = Y)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F) = G)))))). % inv_equality
thf(fact_10_n_I1_J, axiom,
    ((ord_less_nat @ n @ (finite927127589e_indi @ top_to1799531699e_indi)))). % n(1)
thf(fact_11_UNIV__eq__I, axiom,
    ((![A : set_Ar809243995le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ A)) => (top_to685525675le_alt = A))))). % UNIV_eq_I
thf(fact_12_UNIV__eq__I, axiom,
    ((![A : set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A)) => (top_to224369155le_alt = A))))). % UNIV_eq_I
thf(fact_13_UNIV__eq__I, axiom,
    ((![A : set_Ar1007576579e_indi]: ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ A)) => (top_to1799531699e_indi = A))))). % UNIV_eq_I
thf(fact_14_UNIV__witness, axiom,
    ((?[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_15_UNIV__witness, axiom,
    ((?[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_16_UNIV__witness, axiom,
    ((?[X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_17_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I : arrow_1429744205e_indi]: (![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X3 @ arrow_1951607831e_Prof)) => (((F2 @ X3) = (X3 @ I)))))))))). % dictator_def
thf(fact_18_bijection_Oeq__invI, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, A2 : arrow_1429744205e_indi, B : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => (((hilber700257104e_indi @ top_to1799531699e_indi @ F @ A2) = (hilber700257104e_indi @ top_to1799531699e_indi @ F @ B)) => (A2 = B)))))). % bijection.eq_invI
thf(fact_19_bijection_Oeq__invI, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A2 : produc16571293le_alt, B : produc16571293le_alt]: ((hilber402823662le_alt @ F) => (((hilber790132294le_alt @ top_to224369155le_alt @ F @ A2) = (hilber790132294le_alt @ top_to224369155le_alt @ F @ B)) => (A2 = B)))))). % bijection.eq_invI
thf(fact_20_bijection_Oeq__invI, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => (((hilber61073786le_alt @ top_to685525675le_alt @ F @ A2) = (hilber61073786le_alt @ top_to685525675le_alt @ F @ B)) => (A2 = B)))))). % bijection.eq_invI
thf(fact_21_bijection_Oinv__left, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, A2 : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => ((hilber700257104e_indi @ top_to1799531699e_indi @ F @ (F @ A2)) = A2))))). % bijection.inv_left
thf(fact_22_bijection_Oinv__left, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A2 : produc16571293le_alt]: ((hilber402823662le_alt @ F) => ((hilber790132294le_alt @ top_to224369155le_alt @ F @ (F @ A2)) = A2))))). % bijection.inv_left
thf(fact_23_bijection_Oinv__left, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => ((hilber61073786le_alt @ top_to685525675le_alt @ F @ (F @ A2)) = A2))))). % bijection.inv_left
thf(fact_24_bijection_Oinv__right, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, A2 : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => ((F @ (hilber700257104e_indi @ top_to1799531699e_indi @ F @ A2)) = A2))))). % bijection.inv_right
thf(fact_25_bijection_Oinv__right, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A2 : produc16571293le_alt]: ((hilber402823662le_alt @ F) => ((F @ (hilber790132294le_alt @ top_to224369155le_alt @ F @ A2)) = A2))))). % bijection.inv_right
thf(fact_26_bijection_Oinv__right, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => ((F @ (hilber61073786le_alt @ top_to685525675le_alt @ F @ A2)) = A2))))). % bijection.inv_right
thf(fact_27_bijection_Oeq__inv__iff, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, A2 : arrow_1429744205e_indi, B : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => (((hilber700257104e_indi @ top_to1799531699e_indi @ F @ A2) = (hilber700257104e_indi @ top_to1799531699e_indi @ F @ B)) = (A2 = B)))))). % bijection.eq_inv_iff
thf(fact_28_bijection_Oeq__inv__iff, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A2 : produc16571293le_alt, B : produc16571293le_alt]: ((hilber402823662le_alt @ F) => (((hilber790132294le_alt @ top_to224369155le_alt @ F @ A2) = (hilber790132294le_alt @ top_to224369155le_alt @ F @ B)) = (A2 = B)))))). % bijection.eq_inv_iff
thf(fact_29_bijection_Oeq__inv__iff, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => (((hilber61073786le_alt @ top_to685525675le_alt @ F @ A2) = (hilber61073786le_alt @ top_to685525675le_alt @ F @ B)) = (A2 = B)))))). % bijection.eq_inv_iff
thf(fact_30_inv__into__f__f, axiom,
    ((![F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A) => ((member1966420836e_indi @ X @ A) => ((hilber1586975467di_nat @ A @ F @ (F @ X)) = X)))))). % inv_into_f_f
thf(fact_31_ord__eq__less__subst, axiom,
    ((![A2 : nat, F : nat > nat, B : nat, C : nat]: ((A2 = (F @ B)) => ((ord_less_nat @ B @ C) => ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (ord_less_nat @ (F @ X2) @ (F @ Y)))) => (ord_less_nat @ A2 @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_32_ord__less__eq__subst, axiom,
    ((![A2 : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_nat @ A2 @ B) => (((F @ B) = C) => ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (ord_less_nat @ (F @ X2) @ (F @ Y)))) => (ord_less_nat @ (F @ A2) @ C))))))). % ord_less_eq_subst
thf(fact_33_order__less__subst1, axiom,
    ((![A2 : nat, F : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A2 @ (F @ B)) => ((ord_less_nat @ B @ C) => ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (ord_less_nat @ (F @ X2) @ (F @ Y)))) => (ord_less_nat @ A2 @ (F @ C)))))))). % order_less_subst1
thf(fact_34_order__less__subst2, axiom,
    ((![A2 : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_nat @ A2 @ B) => ((ord_less_nat @ (F @ B) @ C) => ((![X2 : nat, Y : nat]: ((ord_less_nat @ X2 @ Y) => (ord_less_nat @ (F @ X2) @ (F @ Y)))) => (ord_less_nat @ (F @ A2) @ C))))))). % order_less_subst2
thf(fact_35_bijection_Oinj, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => (inj_on1663454827e_indi @ F @ top_to1799531699e_indi))))). % bijection.inj
thf(fact_36_bijection_Oinj, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt]: ((hilber402823662le_alt @ F) => (inj_on616462689le_alt @ F @ top_to224369155le_alt))))). % bijection.inj
thf(fact_37_bijection_Oinj, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => (inj_on1288490261le_alt @ F @ top_to685525675le_alt))))). % bijection.inj
thf(fact_38_gt__ex, axiom,
    ((![X : nat]: (?[X_1 : nat]: (ord_less_nat @ X @ X_1))))). % gt_ex
thf(fact_39_neqE, axiom,
    ((![X : nat, Y2 : nat]: ((~ ((X = Y2))) => ((~ ((ord_less_nat @ X @ Y2))) => (ord_less_nat @ Y2 @ X)))))). % neqE
thf(fact_40_neq__iff, axiom,
    ((![X : nat, Y2 : nat]: ((~ ((X = Y2))) = (((ord_less_nat @ X @ Y2)) | ((ord_less_nat @ Y2 @ X))))))). % neq_iff
thf(fact_41_order_Oasym, axiom,
    ((![A2 : nat, B : nat]: ((ord_less_nat @ A2 @ B) => (~ ((ord_less_nat @ B @ A2))))))). % order.asym
thf(fact_42_less__imp__neq, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_43_less__asym, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((ord_less_nat @ Y2 @ X))))))). % less_asym
thf(fact_44_less__asym_H, axiom,
    ((![A2 : nat, B : nat]: ((ord_less_nat @ A2 @ B) => (~ ((ord_less_nat @ B @ A2))))))). % less_asym'
thf(fact_45_less__trans, axiom,
    ((![X : nat, Y2 : nat, Z : nat]: ((ord_less_nat @ X @ Y2) => ((ord_less_nat @ Y2 @ Z) => (ord_less_nat @ X @ Z)))))). % less_trans
thf(fact_46_less__linear, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) | ((X = Y2) | (ord_less_nat @ Y2 @ X)))))). % less_linear
thf(fact_47_less__irrefl, axiom,
    ((![X : nat]: (~ ((ord_less_nat @ X @ X)))))). % less_irrefl
thf(fact_48_ord__eq__less__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((A2 = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A2 @ C)))))). % ord_eq_less_trans
thf(fact_49_ord__less__eq__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((ord_less_nat @ A2 @ B) => ((B = C) => (ord_less_nat @ A2 @ C)))))). % ord_less_eq_trans
thf(fact_50_dual__order_Oasym, axiom,
    ((![B : nat, A2 : nat]: ((ord_less_nat @ B @ A2) => (~ ((ord_less_nat @ A2 @ B))))))). % dual_order.asym
thf(fact_51_less__imp__not__eq, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_52_less__not__sym, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((ord_less_nat @ Y2 @ X))))))). % less_not_sym
thf(fact_53_less__induct, axiom,
    ((![P : nat > $o, A2 : nat]: ((![X2 : nat]: ((![Y3 : nat]: ((ord_less_nat @ Y3 @ X2) => (P @ Y3))) => (P @ X2))) => (P @ A2))))). % less_induct
thf(fact_54_antisym__conv3, axiom,
    ((![Y2 : nat, X : nat]: ((~ ((ord_less_nat @ Y2 @ X))) => ((~ ((ord_less_nat @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_55_less__imp__not__eq2, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_56_less__imp__triv, axiom,
    ((![X : nat, Y2 : nat, P : $o]: ((ord_less_nat @ X @ Y2) => ((ord_less_nat @ Y2 @ X) => P))))). % less_imp_triv
thf(fact_57_linorder__cases, axiom,
    ((![X : nat, Y2 : nat]: ((~ ((ord_less_nat @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_nat @ Y2 @ X)))))). % linorder_cases
thf(fact_58_mem__Collect__eq, axiom,
    ((![A2 : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A2 @ (collec1559089382le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_59_mem__Collect__eq, axiom,
    ((![A2 : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A2 @ (collec531981554le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_60_mem__Collect__eq, axiom,
    ((![A2 : arrow_1429744205e_indi, P : arrow_1429744205e_indi > $o]: ((member1966420836e_indi @ A2 @ (collec1169676194e_indi @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_61_Collect__mem__eq, axiom,
    ((![A : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_62_Collect__mem__eq, axiom,
    ((![A : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_63_Collect__mem__eq, axiom,
    ((![A : set_Ar1007576579e_indi]: ((collec1169676194e_indi @ (^[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_64_dual__order_Oirrefl, axiom,
    ((![A2 : nat]: (~ ((ord_less_nat @ A2 @ A2)))))). % dual_order.irrefl
thf(fact_65_order_Ostrict__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((ord_less_nat @ A2 @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A2 @ C)))))). % order.strict_trans
thf(fact_66_less__imp__not__less, axiom,
    ((![X : nat, Y2 : nat]: ((ord_less_nat @ X @ Y2) => (~ ((ord_less_nat @ Y2 @ X))))))). % less_imp_not_less
thf(fact_67_exists__least__iff, axiom,
    (((^[P2 : nat > $o]: (?[X4 : nat]: (P2 @ X4))) = (^[P3 : nat > $o]: (?[N : nat]: (((P3 @ N)) & ((![M : nat]: (((ord_less_nat @ M @ N)) => ((~ ((P3 @ M))))))))))))). % exists_least_iff
thf(fact_68_linorder__less__wlog, axiom,
    ((![P : nat > nat > $o, A2 : nat, B : nat]: ((![A3 : nat, B2 : nat]: ((ord_less_nat @ A3 @ B2) => (P @ A3 @ B2))) => ((![A3 : nat]: (P @ A3 @ A3)) => ((![A3 : nat, B2 : nat]: ((P @ B2 @ A3) => (P @ A3 @ B2))) => (P @ A2 @ B))))))). % linorder_less_wlog
thf(fact_69_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A2 : nat, C : nat]: ((ord_less_nat @ B @ A2) => ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A2)))))). % dual_order.strict_trans
thf(fact_70_not__less__iff__gr__or__eq, axiom,
    ((![X : nat, Y2 : nat]: ((~ ((ord_less_nat @ X @ Y2))) = (((ord_less_nat @ Y2 @ X)) | ((X = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_71_order_Ostrict__implies__not__eq, axiom,
    ((![A2 : nat, B : nat]: ((ord_less_nat @ A2 @ B) => (~ ((A2 = B))))))). % order.strict_implies_not_eq
thf(fact_72_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A2 : nat]: ((ord_less_nat @ B @ A2) => (~ ((A2 = B))))))). % dual_order.strict_implies_not_eq
thf(fact_73_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_74_top__set__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ top_to1074038850_alt_o)))). % top_set_def
thf(fact_75_top__set__def, axiom,
    ((top_to685525675le_alt = (collec1559089382le_alt @ top_to1344581618_alt_o)))). % top_set_def
thf(fact_76_top_Onot__eq__extremum, axiom,
    ((![A2 : set_Ar1007576579e_indi]: ((~ ((A2 = top_to1799531699e_indi))) = (ord_le1187139159e_indi @ A2 @ top_to1799531699e_indi))))). % top.not_eq_extremum
thf(fact_77_top_Onot__eq__extremum, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((~ ((A2 = top_to224369155le_alt))) = (ord_le1510239143le_alt @ A2 @ top_to224369155le_alt))))). % top.not_eq_extremum
thf(fact_78_top_Onot__eq__extremum, axiom,
    ((![A2 : set_Ar809243995le_alt]: ((~ ((A2 = top_to685525675le_alt))) = (ord_le875007495le_alt @ A2 @ top_to685525675le_alt))))). % top.not_eq_extremum
thf(fact_79_top_Oextremum__strict, axiom,
    ((![A2 : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ top_to1799531699e_indi @ A2)))))). % top.extremum_strict
thf(fact_80_top_Oextremum__strict, axiom,
    ((![A2 : set_Pr367596371le_alt]: (~ ((ord_le1510239143le_alt @ top_to224369155le_alt @ A2)))))). % top.extremum_strict
thf(fact_81_top_Oextremum__strict, axiom,
    ((![A2 : set_Ar809243995le_alt]: (~ ((ord_le875007495le_alt @ top_to685525675le_alt @ A2)))))). % top.extremum_strict
thf(fact_82_inv__into__f__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y2 : nat]: ((inj_on528257168di_nat @ F @ A) => ((member1966420836e_indi @ X @ A) => (((F @ X) = Y2) => ((hilber1586975467di_nat @ A @ F @ Y2) = X))))))). % inv_into_f_eq
thf(fact_83_bijection_Oinj__inv, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => (inj_on1663454827e_indi @ (hilber700257104e_indi @ top_to1799531699e_indi @ F) @ top_to1799531699e_indi))))). % bijection.inj_inv
thf(fact_84_bijection_Oinj__inv, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt]: ((hilber402823662le_alt @ F) => (inj_on616462689le_alt @ (hilber790132294le_alt @ top_to224369155le_alt @ F) @ top_to224369155le_alt))))). % bijection.inj_inv
thf(fact_85_bijection_Oinj__inv, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => (inj_on1288490261le_alt @ (hilber61073786le_alt @ top_to685525675le_alt @ F) @ top_to685525675le_alt))))). % bijection.inj_inv
thf(fact_86_inj__imp__inv__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : nat > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((![X2 : nat]: ((F @ (G @ X2)) = X2)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F) = G)))))). % inj_imp_inv_eq
thf(fact_87_inv__f__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y2 : nat]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = Y2) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F @ Y2) = X)))))). % inv_f_eq
thf(fact_88_inv__f__f, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F @ (F @ X)) = X))))). % inv_f_f
thf(fact_89_bijection_Oinv__right__eq__iff, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, B : arrow_1429744205e_indi, A2 : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => ((B = (hilber700257104e_indi @ top_to1799531699e_indi @ F @ A2)) = ((F @ B) = A2)))))). % bijection.inv_right_eq_iff
thf(fact_90_bijection_Oinv__right__eq__iff, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, B : produc16571293le_alt, A2 : produc16571293le_alt]: ((hilber402823662le_alt @ F) => ((B = (hilber790132294le_alt @ top_to224369155le_alt @ F @ A2)) = ((F @ B) = A2)))))). % bijection.inv_right_eq_iff
thf(fact_91_bijection_Oinv__right__eq__iff, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => ((B = (hilber61073786le_alt @ top_to685525675le_alt @ F @ A2)) = ((F @ B) = A2)))))). % bijection.inv_right_eq_iff
thf(fact_92_bijection_Oinv__left__eq__iff, axiom,
    ((![F : arrow_1429744205e_indi > arrow_1429744205e_indi, A2 : arrow_1429744205e_indi, B : arrow_1429744205e_indi]: ((hilber1061076126e_indi @ F) => (((hilber700257104e_indi @ top_to1799531699e_indi @ F @ A2) = B) = ((F @ B) = A2)))))). % bijection.inv_left_eq_iff
thf(fact_93_bijection_Oinv__left__eq__iff, axiom,
    ((![F : produc16571293le_alt > produc16571293le_alt, A2 : produc16571293le_alt, B : produc16571293le_alt]: ((hilber402823662le_alt @ F) => (((hilber790132294le_alt @ top_to224369155le_alt @ F @ A2) = B) = ((F @ B) = A2)))))). % bijection.inv_left_eq_iff
thf(fact_94_bijection_Oinv__left__eq__iff, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((hilber759434986le_alt @ F) => (((hilber61073786le_alt @ top_to685525675le_alt @ F @ A2) = B) = ((F @ B) = A2)))))). % bijection.inv_left_eq_iff
thf(fact_95_pairwise__neutrality, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A2 = B))) => ((~ ((A4 = B3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P4 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (P4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (f @ P4))))))))))). % pairwise_neutrality
thf(fact_96__C4_C, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A2 = B))) => ((~ ((B = C))) => ((~ ((A2 = C))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P4 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P4)))))))))))). % "4"
thf(fact_97__C3_C, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A2 = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P4 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ (P4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ (f @ P4)))))))))). % "3"
thf(fact_98__C2_C, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A2 = B))) => ((~ ((A4 = B3))) => ((~ ((A2 = B3))) => ((~ ((B = A4))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P4 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (P4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (f @ P4))))))))))))). % "2"
thf(fact_99__C1_C, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A2 = B))) => ((~ ((A4 = B3))) => ((~ ((A2 = B3))) => ((~ ((B = A4))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P4 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (P4 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B3) @ (f @ P4))))))))))))). % "1"
thf(fact_100_inj__def, axiom,
    ((![F : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) = (![X3 : arrow_1429744205e_indi]: (![Y4 : arrow_1429744205e_indi]: ((((F @ X3) = (F @ Y4))) => ((X3 = Y4))))))))). % inj_def
thf(fact_101_inj__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = (F @ Y2)) = (X = Y2)))))). % inj_eq
thf(fact_102_injI, axiom,
    ((![F : arrow_1429744205e_indi > nat]: ((![X2 : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: (((F @ X2) = (F @ Y)) => (X2 = Y))) => (inj_on528257168di_nat @ F @ top_to1799531699e_indi))))). % injI
thf(fact_103_injD, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = (F @ Y2)) => (X = Y2)))))). % injD
thf(fact_104_inj__on__inverseI, axiom,
    ((![A : set_Ar1007576579e_indi, G : nat > arrow_1429744205e_indi, F : arrow_1429744205e_indi > nat]: ((![X2 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X2 @ A) => ((G @ (F @ X2)) = X2))) => (inj_on528257168di_nat @ F @ A))))). % inj_on_inverseI
thf(fact_105_inj__on__contraD, axiom,
    ((![F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A) => ((~ ((X = Y2))) => ((member1966420836e_indi @ X @ A) => ((member1966420836e_indi @ Y2 @ A) => (~ (((F @ X) = (F @ Y2))))))))))). % inj_on_contraD
thf(fact_106_inj__on__eq__iff, axiom,
    ((![F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A) => ((member1966420836e_indi @ X @ A) => ((member1966420836e_indi @ Y2 @ A) => (((F @ X) = (F @ Y2)) = (X = Y2)))))))). % inj_on_eq_iff
thf(fact_107_inj__on__cong, axiom,
    ((![A : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > nat]: ((![A3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ A3 @ A) => ((F @ A3) = (G @ A3)))) => ((inj_on528257168di_nat @ F @ A) = (inj_on528257168di_nat @ G @ A)))))). % inj_on_cong
thf(fact_108_inj__on__def, axiom,
    ((inj_on528257168di_nat = (^[F3 : arrow_1429744205e_indi > nat]: (^[A5 : set_Ar1007576579e_indi]: (![X3 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X3 @ A5)) => ((![Y4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ Y4 @ A5)) => (((((F3 @ X3) = (F3 @ Y4))) => ((X3 = Y4)))))))))))))). % inj_on_def
thf(fact_109_inj__onI, axiom,
    ((![A : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > nat]: ((![X2 : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((member1966420836e_indi @ X2 @ A) => ((member1966420836e_indi @ Y @ A) => (((F @ X2) = (F @ Y)) => (X2 = Y))))) => (inj_on528257168di_nat @ F @ A))))). % inj_onI
thf(fact_110_inj__onD, axiom,
    ((![F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y2 : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A) => (((F @ X) = (F @ Y2)) => ((member1966420836e_indi @ X @ A) => ((member1966420836e_indi @ Y2 @ A) => (X = Y2)))))))). % inj_onD
thf(fact_111_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)) => ((![A6 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (X3 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (F2 @ X3))))))))))))). % unanimity_def
thf(fact_112_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)) => ((![A6 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (X3 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (Y4 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (F2 @ X3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A6 @ B4) @ (F2 @ Y4))))))))))))))))). % IIA_def
thf(fact_113_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_114_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_115_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_116_old_Oprod_Oinject, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B) = (produc1494124311le_alt @ A4 @ B3)) = (((A2 = A4)) & ((B = B3))))))). % old.prod.inject
thf(fact_117_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y22 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_118_surj__pair, axiom,
    ((![P5 : produc16571293le_alt]: (?[X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (P5 = (produc1494124311le_alt @ X2 @ Y)))))). % surj_pair
thf(fact_119_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P5 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B2))) => (P @ P5))))). % prod_cases
thf(fact_120_Pair__inject, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B) = (produc1494124311le_alt @ A4 @ B3)) => (~ (((A2 = A4) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_121_old_Oprod_Oexhaust, axiom,
    ((![Y2 : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (~ ((Y2 = (produc1494124311le_alt @ A3 @ B2)))))))))). % old.prod.exhaust
thf(fact_122_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B2))) => (P @ Prod))))). % old.prod.inducts
thf(fact_123_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y2 = Z)))) & ((((((X = Z)) => ((~ ((X = Y2)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ L))))))))))). % in_mkbot
thf(fact_124_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y2 = Z)) => ((~ ((X = Y2)))))) & ((((~ ((Y2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ L))))))))))). % in_mktop
thf(fact_125_in__measure, axiom,
    ((![X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, F : arrow_1857593510le_alt > nat]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ (measur1447705966le_alt @ F)) = (ord_less_nat @ (F @ X) @ (F @ Y2)))))). % in_measure
thf(fact_126_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y2)) = (produc1494124311le_alt @ X @ (F @ Y2)))))). % apsnd_conv
thf(fact_127_mlex__less, axiom,
    ((![F : arrow_1857593510le_alt > nat, X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((ord_less_nat @ (F @ X) @ (F @ Y2)) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ (mlex_p1368559413le_alt @ F @ R)))))). % mlex_less
thf(fact_128_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y2)) = (produc1494124311le_alt @ (F @ X) @ Y2))))). % apfst_conv
thf(fact_129_mlex__iff, axiom,
    ((![X : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt, F : arrow_1857593510le_alt > nat, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ (mlex_p1368559413le_alt @ F @ R)) = (((ord_less_nat @ (F @ X) @ (F @ Y2))) | (((((F @ X) = (F @ Y2))) & ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ R))))))))). % mlex_iff
thf(fact_130_in__lex__prod, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ (produc1494124311le_alt @ A2 @ B) @ (produc1494124311le_alt @ A4 @ B3)) @ (lex_pr3395839le_alt @ R2 @ S)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ A4) @ R2)) | ((((A2 = A4)) & ((member2048039092le_alt @ (produc1494124311le_alt @ B @ B3) @ S))))))))). % in_lex_prod
thf(fact_131_inj__on__imageI2, axiom,
    ((![F4 : nat > nat, F : arrow_1429744205e_indi > nat, A : set_Ar1007576579e_indi]: ((inj_on528257168di_nat @ (comp_n330120530e_indi @ F4 @ F) @ A) => (inj_on528257168di_nat @ F @ A))))). % inj_on_imageI2
thf(fact_132_inj__compose, axiom,
    ((![F : nat > nat, G : arrow_1429744205e_indi > nat]: ((inj_on_nat_nat @ F @ top_top_set_nat) => ((inj_on528257168di_nat @ G @ top_to1799531699e_indi) => (inj_on528257168di_nat @ (comp_n330120530e_indi @ F @ G) @ top_to1799531699e_indi)))))). % inj_compose
thf(fact_133_inj__compose, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((inj_on1663454827e_indi @ G @ top_to1799531699e_indi) => (inj_on528257168di_nat @ (comp_A2059482153e_indi @ F @ G) @ top_to1799531699e_indi)))))). % inj_compose
thf(fact_134_inj__compose, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : produc16571293le_alt > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((inj_on2029130011e_indi @ G @ top_to224369155le_alt) => (inj_on1748146656lt_nat @ (comp_A708674671le_alt @ F @ G) @ top_to224369155le_alt)))))). % inj_compose
thf(fact_135_inj__compose, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((inj_on1947401569e_indi @ G @ top_to685525675le_alt) => (inj_on598967066lt_nat @ (comp_A255443021le_alt @ F @ G) @ top_to685525675le_alt)))))). % inj_compose
thf(fact_136_inj__compose, axiom,
    ((![F : produc16571293le_alt > nat, G : arrow_1429744205e_indi > produc16571293le_alt]: ((inj_on1748146656lt_nat @ F @ top_to224369155le_alt) => ((inj_on845182641le_alt @ G @ top_to1799531699e_indi) => (inj_on528257168di_nat @ (comp_P498338521e_indi @ F @ G) @ top_to1799531699e_indi)))))). % inj_compose
thf(fact_137_inj__compose, axiom,
    ((![F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > nat, G : arrow_1429744205e_indi > arrow_1429744205e_indi > set_Pr367596371le_alt]: ((inj_on598967066lt_nat @ F @ top_to685525675le_alt) => ((inj_on783451275le_alt @ G @ top_to1799531699e_indi) => (inj_on528257168di_nat @ (comp_A1580130049e_indi @ F @ G) @ top_to1799531699e_indi)))))). % inj_compose
thf(fact_138_inv__o__cancel, axiom,
    ((![F : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => ((comp_n1073433769e_indi @ (hilber1586975467di_nat @ top_to1799531699e_indi @ F) @ F) = id_Arr152457500e_indi))))). % inv_o_cancel
thf(fact_139_inv__id, axiom,
    (((hilber700257104e_indi @ top_to1799531699e_indi @ id_Arr152457500e_indi) = id_Arr152457500e_indi))). % inv_id
thf(fact_140_inv__id, axiom,
    (((hilber790132294le_alt @ top_to224369155le_alt @ id_Pro1771394668le_alt) = id_Pro1771394668le_alt))). % inv_id
thf(fact_141_inv__id, axiom,
    (((hilber61073786le_alt @ top_to685525675le_alt @ id_Arr1104251884le_alt) = id_Arr1104251884le_alt))). % inv_id
thf(fact_142_inv__unique__comp, axiom,
    ((![F : arrow_1429744205e_indi > nat, G : nat > arrow_1429744205e_indi]: (((comp_A853618258at_nat @ F @ G) = id_nat) => (((comp_n1073433769e_indi @ G @ F) = id_Arr152457500e_indi) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F) = G)))))). % inv_unique_comp

% Conjectures (1)
thf(conj_0, conjecture,
    ((arrow_960434986ctator @ f @ (hilber1586975467di_nat @ top_to1799531699e_indi @ h @ n)))).
