% 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_264__5189078_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:06.800

% Could-be-implicit typings (51)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Pr80128425le_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_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,
    produc1556693961le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr1043548575le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1114386793le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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_Pr1145686105le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Pr2137209591e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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_Pr1430684246le_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__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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,
    produc867702393le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc1394898967e_indi : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    produc1787494048le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_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,
    produc1144330528le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Nat__Onat_J, type,
    produc1958338298lt_nat : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Pr1281515203e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_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_Pr1057697519le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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_Pr858239666le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Pr533560569e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr693134479le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc342768781e_indi : $tType).
thf(ty_n_t__Product____Type__Oprod_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,
    produc1134518969le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr346863910le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr1508209746le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1816647634le_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__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc821488067e_indi : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc518372441le_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2034271302le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1158092146le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Nat__Onat_J, type,
    produc107092996lt_nat : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc933147652le_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__Nat__Onat_J, type,
    produc1671307342lt_nat : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc136056654le_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__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Pr773120585e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr195493846le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Pr1205120524e_indi : $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__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc851024659e_indi : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1831632630le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc1873242156e_indi : $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__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    produc195853822e_indi : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Nat__Onat_J, type,
    produc1399759614di_nat : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc171651403le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J, type,
    produc1720672805lt_nat : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (110)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_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_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on1409615164le_alt : (arrow_1857593510le_alt > produc16571293le_alt) > set_Ar1665529862le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    inj_on528257168di_nat : (arrow_1429744205e_indi > nat) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Nat__Onat_J, type,
    inj_on2087578646lt_nat : (produc1394898967e_indi > produc1958338298lt_nat) > set_Pr2137209591e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J, type,
    inj_on1530862398lt_nat : (produc1873242156e_indi > produc1720672805lt_nat) > set_Pr1205120524e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_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_001t__Product____Type__Oprod_It__Nat__Onat_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,
    inj_on850269876le_alt : (produc867702393le_alt > produc1144330528le_alt) > set_Pr1145686105le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on1711456116le_alt : (produc1831632630le_alt > produc171651403le_alt) > set_Pr195493846le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Nat__Onat_J, type,
    inj_on1832254384di_nat : (produc851024659e_indi > produc1399759614di_nat) > set_Pr773120585e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    inj_on1612178390e_indi : (produc851024659e_indi > produc195853822e_indi) > set_Pr773120585e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    inj_on1635432290le_alt : (produc518372441le_alt > produc136056654le_alt) > set_Pr693134479le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_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__Nat__Onat_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    inj_on1188948002le_alt : (produc1134518969le_alt > produc933147652le_alt) > set_Pr1057697519le_alt > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Nat__Onat_J, type,
    inj_on48223910lt_nat : (produc821488067e_indi > produc1671307342lt_nat) > set_Pr533560569e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Nat__Onat_J, type,
    inj_on1689162448lt_nat : (produc342768781e_indi > produc107092996lt_nat) > set_Pr1281515203e_indi > $o).
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_Order__Relation_Ostrict__linear__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_257197092le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_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__Oalt_J, type,
    ord_le628013746le_alt : set_Ar1665529862le_alt > set_Ar1665529862le_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_Oord__class_Oless_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,
    ord_le1684089949le_alt : set_se2071012361le_alt > set_se2071012361le_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__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J, type,
    top_to701951606_alt_o : arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J, type,
    top_to516240647_alt_o : arrow_1857593510le_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_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_Eo_J, type,
    top_to1900088076_alt_o : set_Pr367596371le_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__Oalt_J, type,
    top_to958727510le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    top_to469035705le_alt : set_se2071012361le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    produc1316484634le_alt : arrow_1857593510le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1787494048le_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1724702748e_indi : arrow_1857593510le_alt > arrow_1429744205e_indi > produc1873242156e_indi).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1906488418le_alt : arrow_1857593510le_alt > produc16571293le_alt > produc1158092146le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc398768834le_alt : arrow_1857593510le_alt > set_Pr367596371le_alt > produc1816647634le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc245709870le_alt : arrow_1429744205e_indi > arrow_1857593510le_alt > produc1831632630le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1274704069e_indi : arrow_1429744205e_indi > arrow_1429744205e_indi > produc851024659e_indi).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc726962443le_alt : arrow_1429744205e_indi > produc16571293le_alt > produc518372441le_alt).
thf(sy_c_Product__Type_OPair_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,
    produc128414571le_alt : arrow_1429744205e_indi > set_Pr367596371le_alt > produc1134518969le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc283291649le_alt : produc16571293le_alt > (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc1556693961le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc78632318le_alt : produc16571293le_alt > arrow_1857593510le_alt > produc2034271302le_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1910909813e_indi : produc16571293le_alt > arrow_1429744205e_indi > produc821488067e_indi).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc268611099le_alt : produc16571293le_alt > set_Pr367596371le_alt > produc1114386793le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc2051668543e_indi : set_Pr367596371le_alt > arrow_1429744205e_indi > produc342768781e_indi).
thf(sy_c_Product__Type_OSigma_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1843003448e_indi : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1007576579e_indi) > set_Pr2137209591e_indi).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1598628137le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar809243995le_alt) > set_Pr1430684246le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2062971558le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Pr367596371le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc711907405e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Pr1205120524e_indi).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2023643283le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Pr367596371le_alt) > set_Pr1508209746le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1741626099le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_se2071012361le_alt) > set_Pr858239666le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc679053154le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar809243995le_alt) > set_Pr1145686105le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1380398175le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Pr195493846le_alt).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1762100436e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Pr773120585e_indi).
thf(sy_c_Product__Type_OSigma_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc124975386le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr693134479le_alt).
thf(sy_c_Product__Type_OSigma_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,
    produc442900346le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Pr1057697519le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1761277106le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr80128425le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc195787183le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar1665529862le_alt) > set_Pr346863910le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1308922756e_indi : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar1007576579e_indi) > set_Pr533560569e_indi).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc1360152522le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr448479039le_alt).
thf(sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1173532202le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr1043548575le_alt).
thf(sy_c_Product__Type_OSigma_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc218670670e_indi : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar1007576579e_indi) > set_Pr1281515203e_indi).
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_Oapfst_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,
    produc643774374le_alt : (arrow_1429744205e_indi > nat) > produc867702393le_alt > produc1144330528le_alt).
thf(sy_c_Product__Type_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1985979043le_alt : (arrow_1429744205e_indi > nat) > produc1831632630le_alt > produc171651403le_alt).
thf(sy_c_Product__Type_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc961456016e_indi : (arrow_1429744205e_indi > nat) > produc851024659e_indi > produc195853822e_indi).
thf(sy_c_Product__Type_Oapfst_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,
    produc424504278le_alt : (arrow_1429744205e_indi > nat) > produc518372441le_alt > produc136056654le_alt).
thf(sy_c_Product__Type_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc641180214le_alt : (arrow_1429744205e_indi > nat) > produc1134518969le_alt > produc933147652le_alt).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oapsnd_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,
    produc1195769064le_alt : (arrow_1429744205e_indi > nat) > produc1394898967e_indi > produc1958338298lt_nat).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc86521573le_alt : (arrow_1429744205e_indi > nat) > produc1873242156e_indi > produc1720672805lt_nat).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    produc1894589390e_indi : (arrow_1429744205e_indi > nat) > produc851024659e_indi > produc1399759614di_nat).
thf(sy_c_Product__Type_Oapsnd_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,
    produc489426964le_alt : (arrow_1429744205e_indi > nat) > produc821488067e_indi > produc1671307342lt_nat).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1828081268le_alt : (arrow_1429744205e_indi > nat) > produc342768781e_indi > produc107092996lt_nat).
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__Oalt, type,
    collec1364151825le_alt : (arrow_1857593510le_alt > $o) > set_Ar1665529862le_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_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_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__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_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,
    member960954167le_alt : produc1787494048le_alt > set_Pr1430684246le_alt > $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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    member2031612117e_indi : produc1873242156e_indi > set_Pr1205120524e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1000073755le_alt : produc1158092146le_alt > set_Pr1508209746le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1361938555le_alt : produc1816647634le_alt > set_Pr858239666le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member1990002591le_alt : produc1831632630le_alt > set_Pr195493846le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    member236207274e_indi : produc851024659e_indi > set_Pr773120585e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member573510128le_alt : produc518372441le_alt > set_Pr693134479le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_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,
    member1221516368le_alt : produc1134518969le_alt > set_Pr1057697519le_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_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,
    member1263449330le_alt : produc1556693961le_alt > set_Pr80128425le_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__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member1876252911le_alt : produc2034271302le_alt > set_Pr346863910le_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    member876625754e_indi : produc821488067e_indi > set_Pr533560569e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1923768064le_alt : produc1114386793le_alt > set_Pr1043548575le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    member429766180e_indi : produc342768781e_indi > set_Pr1281515203e_indi > $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_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_n, type,
    n : nat).

% Relevant facts (246)
thf(fact_0__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_1__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_2_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_3_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_4_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_5_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_6_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_7_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_8_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_9_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_10_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_11_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_12_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_13_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_14_top_Oextremum__strict, axiom,
    ((![A : set_Pr367596371le_alt]: (~ ((ord_le1510239143le_alt @ top_to224369155le_alt @ A)))))). % top.extremum_strict
thf(fact_15_top_Oextremum__strict, axiom,
    ((![A : set_se2071012361le_alt]: (~ ((ord_le1684089949le_alt @ top_to469035705le_alt @ A)))))). % top.extremum_strict
thf(fact_16_top_Oextremum__strict, axiom,
    ((![A : set_Ar809243995le_alt]: (~ ((ord_le875007495le_alt @ top_to685525675le_alt @ A)))))). % top.extremum_strict
thf(fact_17_top_Oextremum__strict, axiom,
    ((![A : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ top_to1799531699e_indi @ A)))))). % top.extremum_strict
thf(fact_18_top_Oextremum__strict, axiom,
    ((![A : set_Ar1665529862le_alt]: (~ ((ord_le628013746le_alt @ top_to958727510le_alt @ A)))))). % top.extremum_strict
thf(fact_19_top_Onot__eq__extremum, axiom,
    ((![A : set_Pr367596371le_alt]: ((~ ((A = top_to224369155le_alt))) = (ord_le1510239143le_alt @ A @ top_to224369155le_alt))))). % top.not_eq_extremum
thf(fact_20_top_Onot__eq__extremum, axiom,
    ((![A : set_se2071012361le_alt]: ((~ ((A = top_to469035705le_alt))) = (ord_le1684089949le_alt @ A @ top_to469035705le_alt))))). % top.not_eq_extremum
thf(fact_21_top_Onot__eq__extremum, axiom,
    ((![A : set_Ar809243995le_alt]: ((~ ((A = top_to685525675le_alt))) = (ord_le875007495le_alt @ A @ top_to685525675le_alt))))). % top.not_eq_extremum
thf(fact_22_top_Onot__eq__extremum, axiom,
    ((![A : set_Ar1007576579e_indi]: ((~ ((A = top_to1799531699e_indi))) = (ord_le1187139159e_indi @ A @ top_to1799531699e_indi))))). % top.not_eq_extremum
thf(fact_23_top_Onot__eq__extremum, axiom,
    ((![A : set_Ar1665529862le_alt]: ((~ ((A = top_to958727510le_alt))) = (ord_le628013746le_alt @ A @ top_to958727510le_alt))))). % top.not_eq_extremum
thf(fact_24_UNIV__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ (^[X2 : produc16571293le_alt]: $true))))). % UNIV_def
thf(fact_25_UNIV__def, axiom,
    ((top_to685525675le_alt = (collec1559089382le_alt @ (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_26_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X2 : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_27_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X2 : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_28_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X2 : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_29_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L2 @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_30_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L2 @ X @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_31_mkbot__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L2 @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_32_mktop__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L2 @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_33_UNIV__eq__I, axiom,
    ((![A2 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A2)) => (top_to1799531699e_indi = A2))))). % UNIV_eq_I
thf(fact_34_UNIV__eq__I, axiom,
    ((![A2 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A2)) => (top_to958727510le_alt = A2))))). % UNIV_eq_I
thf(fact_35_UNIV__eq__I, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A2)) => (top_to224369155le_alt = A2))))). % UNIV_eq_I
thf(fact_36_UNIV__eq__I, axiom,
    ((![A2 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A2)) => (top_to469035705le_alt = A2))))). % UNIV_eq_I
thf(fact_37_UNIV__eq__I, axiom,
    ((![A2 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A2)) => (top_to685525675le_alt = A2))))). % UNIV_eq_I
thf(fact_38_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_39_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_40_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_41_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_42_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_43_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_44_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_45_top__set__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ top_to1074038850_alt_o)))). % top_set_def
thf(fact_46_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_47_top__set__def, axiom,
    ((top_to685525675le_alt = (collec1559089382le_alt @ top_to1344581618_alt_o)))). % top_set_def
thf(fact_48_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_49_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : set_Ar1665529862le_alt, A : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_50_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : set_Ar1007576579e_indi, A : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_51_order_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_52_order_Ostrict__implies__not__eq, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_53_order_Ostrict__implies__not__eq, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_54_not__less__iff__gr__or__eq, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) = (((ord_less_nat @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_55_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_nat @ B @ A) => ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))))). % dual_order.strict_trans
thf(fact_56_dual__order_Ostrict__trans, axiom,
    ((![B : set_Ar1665529862le_alt, A : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ B @ A) => ((ord_le628013746le_alt @ C @ B) => (ord_le628013746le_alt @ C @ A)))))). % dual_order.strict_trans
thf(fact_57_dual__order_Ostrict__trans, axiom,
    ((![B : set_Ar1007576579e_indi, A : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ B @ A) => ((ord_le1187139159e_indi @ C @ B) => (ord_le1187139159e_indi @ C @ A)))))). % dual_order.strict_trans
thf(fact_58_linorder__less__wlog, axiom,
    ((![P : nat > nat > $o, A : 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 @ A @ B))))))). % linorder_less_wlog
thf(fact_59_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_60_less__imp__not__less, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_imp_not_less
thf(fact_61_less__imp__not__less, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((ord_le628013746le_alt @ Y @ X))))))). % less_imp_not_less
thf(fact_62_less__imp__not__less, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((ord_le1187139159e_indi @ Y @ X))))))). % less_imp_not_less
thf(fact_63_order_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % order.strict_trans
thf(fact_64_order_Ostrict__trans, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => ((ord_le628013746le_alt @ B @ C) => (ord_le628013746le_alt @ A @ C)))))). % order.strict_trans
thf(fact_65_order_Ostrict__trans, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => ((ord_le1187139159e_indi @ B @ C) => (ord_le1187139159e_indi @ A @ C)))))). % order.strict_trans
thf(fact_66_dual__order_Oirrefl, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % dual_order.irrefl
thf(fact_67_dual__order_Oirrefl, axiom,
    ((![A : set_Ar1665529862le_alt]: (~ ((ord_le628013746le_alt @ A @ A)))))). % dual_order.irrefl
thf(fact_68_dual__order_Oirrefl, axiom,
    ((![A : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ A @ A)))))). % dual_order.irrefl
thf(fact_69_linorder__cases, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) => ((~ ((X = Y))) => (ord_less_nat @ Y @ X)))))). % linorder_cases
thf(fact_70_less__imp__triv, axiom,
    ((![X : nat, Y : nat, P : $o]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ X) => P))))). % less_imp_triv
thf(fact_71_less__imp__triv, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt, P : $o]: ((ord_le628013746le_alt @ X @ Y) => ((ord_le628013746le_alt @ Y @ X) => P))))). % less_imp_triv
thf(fact_72_less__imp__triv, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi, P : $o]: ((ord_le1187139159e_indi @ X @ Y) => ((ord_le1187139159e_indi @ Y @ X) => P))))). % less_imp_triv
thf(fact_73_less__imp__not__eq2, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_74_less__imp__not__eq2, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_75_less__imp__not__eq2, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_76_antisym__conv3, axiom,
    ((![Y : nat, X : nat]: ((~ ((ord_less_nat @ Y @ X))) => ((~ ((ord_less_nat @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_77_less__induct, axiom,
    ((![P : nat > $o, A : nat]: ((![X3 : nat]: ((![Y2 : nat]: ((ord_less_nat @ Y2 @ X3) => (P @ Y2))) => (P @ X3))) => (P @ A))))). % less_induct
thf(fact_78_less__not__sym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_not_sym
thf(fact_79_less__not__sym, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((ord_le628013746le_alt @ Y @ X))))))). % less_not_sym
thf(fact_80_less__not__sym, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((ord_le1187139159e_indi @ Y @ X))))))). % less_not_sym
thf(fact_81_less__imp__not__eq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_82_less__imp__not__eq, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_83_less__imp__not__eq, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_84_dual__order_Oasym, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((ord_less_nat @ A @ B))))))). % dual_order.asym
thf(fact_85_dual__order_Oasym, axiom,
    ((![B : set_Ar1665529862le_alt, A : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ B @ A) => (~ ((ord_le628013746le_alt @ A @ B))))))). % dual_order.asym
thf(fact_86_dual__order_Oasym, axiom,
    ((![B : set_Ar1007576579e_indi, A : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ B @ A) => (~ ((ord_le1187139159e_indi @ A @ B))))))). % dual_order.asym
thf(fact_87_ord__less__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C)))))). % ord_less_eq_trans
thf(fact_88_ord__less__eq__trans, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => ((B = C) => (ord_le628013746le_alt @ A @ C)))))). % ord_less_eq_trans
thf(fact_89_ord__less__eq__trans, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => ((B = C) => (ord_le1187139159e_indi @ A @ C)))))). % ord_less_eq_trans
thf(fact_90_ord__eq__less__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))))). % ord_eq_less_trans
thf(fact_91_ord__eq__less__trans, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((A = B) => ((ord_le628013746le_alt @ B @ C) => (ord_le628013746le_alt @ A @ C)))))). % ord_eq_less_trans
thf(fact_92_ord__eq__less__trans, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((A = B) => ((ord_le1187139159e_indi @ B @ C) => (ord_le1187139159e_indi @ A @ C)))))). % ord_eq_less_trans
thf(fact_93_less__irrefl, axiom,
    ((![X : nat]: (~ ((ord_less_nat @ X @ X)))))). % less_irrefl
thf(fact_94_less__irrefl, axiom,
    ((![X : set_Ar1665529862le_alt]: (~ ((ord_le628013746le_alt @ X @ X)))))). % less_irrefl
thf(fact_95_less__irrefl, axiom,
    ((![X : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ X @ X)))))). % less_irrefl
thf(fact_96_less__linear, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) | ((X = Y) | (ord_less_nat @ Y @ X)))))). % less_linear
thf(fact_97_less__trans, axiom,
    ((![X : nat, Y : nat, Z : nat]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ Z) => (ord_less_nat @ X @ Z)))))). % less_trans
thf(fact_98_less__trans, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt, Z : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => ((ord_le628013746le_alt @ Y @ Z) => (ord_le628013746le_alt @ X @ Z)))))). % less_trans
thf(fact_99_less__trans, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi, Z : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => ((ord_le1187139159e_indi @ Y @ Z) => (ord_le1187139159e_indi @ X @ Z)))))). % less_trans
thf(fact_100_less__asym_H, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % less_asym'
thf(fact_101_less__asym_H, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => (~ ((ord_le628013746le_alt @ B @ A))))))). % less_asym'
thf(fact_102_less__asym_H, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => (~ ((ord_le1187139159e_indi @ B @ A))))))). % less_asym'
thf(fact_103_less__asym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_asym
thf(fact_104_less__asym, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((ord_le628013746le_alt @ Y @ X))))))). % less_asym
thf(fact_105_less__asym, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((ord_le1187139159e_indi @ Y @ X))))))). % less_asym
thf(fact_106_less__imp__neq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_107_less__imp__neq, axiom,
    ((![X : set_Ar1665529862le_alt, Y : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_108_less__imp__neq, axiom,
    ((![X : set_Ar1007576579e_indi, Y : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_109_order_Oasym, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % order.asym
thf(fact_110_order_Oasym, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => (~ ((ord_le628013746le_alt @ B @ A))))))). % order.asym
thf(fact_111_order_Oasym, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => (~ ((ord_le1187139159e_indi @ B @ A))))))). % order.asym
thf(fact_112_neq__iff, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) = (((ord_less_nat @ X @ Y)) | ((ord_less_nat @ Y @ X))))))). % neq_iff
thf(fact_113_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_114_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_115_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_116_mem__Collect__eq, axiom,
    ((![A : arrow_1857593510le_alt, P : arrow_1857593510le_alt > $o]: ((member519365071le_alt @ A @ (collec1364151825le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_117_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi, P : arrow_1429744205e_indi > $o]: ((member1966420836e_indi @ A @ (collec1169676194e_indi @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_118_Collect__mem__eq, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_119_Collect__mem__eq, axiom,
    ((![A2 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_120_Collect__mem__eq, axiom,
    ((![A2 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_121_Collect__mem__eq, axiom,
    ((![A2 : set_Ar1665529862le_alt]: ((collec1364151825le_alt @ (^[X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_122_Collect__mem__eq, axiom,
    ((![A2 : set_Ar1007576579e_indi]: ((collec1169676194e_indi @ (^[X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_123_Collect__cong, axiom,
    ((![P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o, Q : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1559089382le_alt @ P) = (collec1559089382le_alt @ Q)))))). % Collect_cong
thf(fact_124_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_125_Collect__cong, axiom,
    ((![P : arrow_1857593510le_alt > $o, Q : arrow_1857593510le_alt > $o]: ((![X3 : arrow_1857593510le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1364151825le_alt @ P) = (collec1364151825le_alt @ Q)))))). % Collect_cong
thf(fact_126_Collect__cong, axiom,
    ((![P : arrow_1429744205e_indi > $o, Q : arrow_1429744205e_indi > $o]: ((![X3 : arrow_1429744205e_indi]: ((P @ X3) = (Q @ X3))) => ((collec1169676194e_indi @ P) = (collec1169676194e_indi @ Q)))))). % Collect_cong
thf(fact_127_neqE, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % neqE
thf(fact_128_gt__ex, axiom,
    ((![X : nat]: (?[X_1 : nat]: (ord_less_nat @ X @ X_1))))). % gt_ex
thf(fact_129_order__less__subst2, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (F @ B) @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_130_order__less__subst2, axiom,
    ((![A : nat, B : nat, F : nat > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_less_nat @ A @ B) => ((ord_le628013746le_alt @ (F @ B) @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_131_order__less__subst2, axiom,
    ((![A : nat, B : nat, F : nat > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_less_nat @ A @ B) => ((ord_le1187139159e_indi @ (F @ B) @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_132_order__less__subst2, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > nat, C : nat]: ((ord_le628013746le_alt @ A @ B) => ((ord_less_nat @ (F @ B) @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_133_order__less__subst2, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => ((ord_le628013746le_alt @ (F @ B) @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_134_order__less__subst2, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le628013746le_alt @ A @ B) => ((ord_le1187139159e_indi @ (F @ B) @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_135_order__less__subst2, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > nat, C : nat]: ((ord_le1187139159e_indi @ A @ B) => ((ord_less_nat @ (F @ B) @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_136_order__less__subst2, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le1187139159e_indi @ A @ B) => ((ord_le628013746le_alt @ (F @ B) @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_137_order__less__subst2, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => ((ord_le1187139159e_indi @ (F @ B) @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_138_order__less__subst1, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((ord_less_nat @ A @ (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_139_order__less__subst1, axiom,
    ((![A : nat, F : set_Ar1665529862le_alt > nat, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_less_nat @ A @ (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_140_order__less__subst1, axiom,
    ((![A : nat, F : set_Ar1007576579e_indi > nat, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_less_nat @ A @ (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_141_order__less__subst1, axiom,
    ((![A : set_Ar1665529862le_alt, F : nat > set_Ar1665529862le_alt, B : nat, C : nat]: ((ord_le628013746le_alt @ A @ (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_142_order__less__subst1, axiom,
    ((![A : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_143_order__less__subst1, axiom,
    ((![A : set_Ar1665529862le_alt, F : set_Ar1007576579e_indi > set_Ar1665529862le_alt, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le628013746le_alt @ A @ (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_144_order__less__subst1, axiom,
    ((![A : set_Ar1007576579e_indi, F : nat > set_Ar1007576579e_indi, B : nat, C : nat]: ((ord_le1187139159e_indi @ A @ (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_145_order__less__subst1, axiom,
    ((![A : set_Ar1007576579e_indi, F : set_Ar1665529862le_alt > set_Ar1007576579e_indi, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le1187139159e_indi @ A @ (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_146_order__less__subst1, axiom,
    ((![A : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_147_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > nat, C : nat]: ((ord_less_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_148_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_less_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_149_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F : nat > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_less_nat @ A @ B) => (((F @ B) = C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_150_ord__less__eq__subst, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > nat, C : nat]: ((ord_le628013746le_alt @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_151_ord__less__eq__subst, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_152_ord__less__eq__subst, axiom,
    ((![A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le628013746le_alt @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_153_ord__less__eq__subst, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > nat, C : nat]: ((ord_le1187139159e_indi @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_154_ord__less__eq__subst, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((ord_le1187139159e_indi @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_155_ord__less__eq__subst, axiom,
    ((![A : set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ A @ B) => (((F @ B) = C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_156_ord__eq__less__subst, axiom,
    ((![A : nat, F : nat > nat, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_157_ord__eq__less__subst, axiom,
    ((![A : set_Ar1665529862le_alt, F : nat > set_Ar1665529862le_alt, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_158_ord__eq__less__subst, axiom,
    ((![A : set_Ar1007576579e_indi, F : nat > set_Ar1007576579e_indi, B : nat, C : nat]: ((A = (F @ B)) => ((ord_less_nat @ B @ C) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_159_ord__eq__less__subst, axiom,
    ((![A : nat, F : set_Ar1665529862le_alt > nat, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((A = (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_160_ord__eq__less__subst, axiom,
    ((![A : set_Ar1665529862le_alt, F : set_Ar1665529862le_alt > set_Ar1665529862le_alt, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((A = (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_161_ord__eq__less__subst, axiom,
    ((![A : set_Ar1007576579e_indi, F : set_Ar1665529862le_alt > set_Ar1007576579e_indi, B : set_Ar1665529862le_alt, C : set_Ar1665529862le_alt]: ((A = (F @ B)) => ((ord_le628013746le_alt @ B @ C) => ((![X3 : set_Ar1665529862le_alt, Y3 : set_Ar1665529862le_alt]: ((ord_le628013746le_alt @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_162_ord__eq__less__subst, axiom,
    ((![A : nat, F : set_Ar1007576579e_indi > nat, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((A = (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_less_nat @ (F @ X3) @ (F @ Y3)))) => (ord_less_nat @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_163_ord__eq__less__subst, axiom,
    ((![A : set_Ar1665529862le_alt, F : set_Ar1007576579e_indi > set_Ar1665529862le_alt, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((A = (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le628013746le_alt @ (F @ X3) @ (F @ Y3)))) => (ord_le628013746le_alt @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_164_ord__eq__less__subst, axiom,
    ((![A : set_Ar1007576579e_indi, F : set_Ar1007576579e_indi > set_Ar1007576579e_indi, B : set_Ar1007576579e_indi, C : set_Ar1007576579e_indi]: ((A = (F @ B)) => ((ord_le1187139159e_indi @ B @ C) => ((![X3 : set_Ar1007576579e_indi, Y3 : set_Ar1007576579e_indi]: ((ord_le1187139159e_indi @ X3 @ Y3) => (ord_le1187139159e_indi @ (F @ X3) @ (F @ Y3)))) => (ord_le1187139159e_indi @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_165_inj__def, axiom,
    ((![F : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) = (![X2 : arrow_1429744205e_indi]: (![Y4 : arrow_1429744205e_indi]: ((((F @ X2) = (F @ Y4))) => ((X2 = Y4))))))))). % inj_def
thf(fact_166_inj__eq, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = (F @ Y)) = (X = Y)))))). % inj_eq
thf(fact_167_injI, axiom,
    ((![F : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: (((F @ X3) = (F @ Y3)) => (X3 = Y3))) => (inj_on528257168di_nat @ F @ top_to1799531699e_indi))))). % injI
thf(fact_168_injD, axiom,
    ((![F : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ top_to1799531699e_indi) => (((F @ X) = (F @ Y)) => (X = Y)))))). % injD
thf(fact_169_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_170_inj__onD, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A2) => (((F @ X) = (F @ Y)) => ((member1966420836e_indi @ X @ A2) => ((member1966420836e_indi @ Y @ A2) => (X = Y)))))))). % inj_onD
thf(fact_171_inj__on__inverseI, axiom,
    ((![A2 : set_Ar1007576579e_indi, G : nat > arrow_1429744205e_indi, F : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A2) => ((G @ (F @ X3)) = X3))) => (inj_on528257168di_nat @ F @ A2))))). % inj_on_inverseI
thf(fact_172_inj__on__contraD, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A2) => ((~ ((X = Y))) => ((member1966420836e_indi @ X @ A2) => ((member1966420836e_indi @ Y @ A2) => (~ (((F @ X) = (F @ Y))))))))))). % inj_on_contraD
thf(fact_173_inj__on__eq__iff, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F @ A2) => ((member1966420836e_indi @ X @ A2) => ((member1966420836e_indi @ Y @ A2) => (((F @ X) = (F @ Y)) = (X = Y)))))))). % inj_on_eq_iff
thf(fact_174_inj__on__cong, axiom,
    ((![A2 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > nat]: ((![A3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ A3 @ A2) => ((F @ A3) = (G @ A3)))) => ((inj_on528257168di_nat @ F @ A2) = (inj_on528257168di_nat @ G @ A2)))))). % inj_on_cong
thf(fact_175_inj__on__def, axiom,
    ((inj_on528257168di_nat = (^[F2 : arrow_1429744205e_indi > nat]: (^[A4 : set_Ar1007576579e_indi]: (![X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ A4)) => ((![Y4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ Y4 @ A4)) => (((((F2 @ X2) = (F2 @ Y4))) => ((X2 = Y4)))))))))))))). % inj_on_def
thf(fact_176_inj__onI, axiom,
    ((![A2 : set_Ar1007576579e_indi, F : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A2) => ((member1966420836e_indi @ Y3 @ A2) => (((F @ X3) = (F @ Y3)) => (X3 = Y3))))) => (inj_on528257168di_nat @ F @ A2))))). % inj_onI
thf(fact_177_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_178_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_179_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_180_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_181_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_182_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_183_less__not__refl, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_not_refl
thf(fact_184_linorder__neqE__nat, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % linorder_neqE_nat
thf(fact_185_infinite__descent, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N3 : nat]: ((~ ((P @ N3))) => (?[M3 : nat]: ((ord_less_nat @ M3 @ N3) & (~ ((P @ M3))))))) => (P @ N2))))). % infinite_descent
thf(fact_186_nat__less__induct, axiom,
    ((![P : nat > $o, N2 : nat]: ((![N3 : nat]: ((![M3 : nat]: ((ord_less_nat @ M3 @ N3) => (P @ M3))) => (P @ N3))) => (P @ N2))))). % nat_less_induct
thf(fact_187_less__irrefl__nat, axiom,
    ((![N2 : nat]: (~ ((ord_less_nat @ N2 @ N2)))))). % less_irrefl_nat
thf(fact_188_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_189_less__not__refl2, axiom,
    ((![N2 : nat, M2 : nat]: ((ord_less_nat @ N2 @ M2) => (~ ((M2 = N2))))))). % less_not_refl2
thf(fact_190_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L2 @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L2)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L2)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))))))))). % in_below
thf(fact_191_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L2 @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L2)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L2)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))))))))). % in_above
thf(fact_192_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X2 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y4) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_193_inj__on__convol__ident, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X5 : set_Ar1665529862le_alt]: (inj_on1409615164le_alt @ (^[X2 : arrow_1857593510le_alt]: (produc1494124311le_alt @ X2 @ (F @ X2))) @ X5)))). % inj_on_convol_ident
thf(fact_194_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: (((^[X2 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y4) @ R))) = (^[X2 : arrow_1857593510le_alt]: (^[Y4 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y4) @ S2)))) = (R = S2))))). % pred_equals_eq2
thf(fact_195_notin__Lin__iff, axiom,
    ((![L2 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L2))))))). % notin_Lin_iff
thf(fact_196_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_197_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_198_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L2 @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))). % in_mktop
thf(fact_199_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L2 @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L2))))))))))). % in_mkbot
thf(fact_200__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_201__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_202_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A5 @ B3)) = (((A = A5)) & ((B = B3))))))). % old.prod.inject
thf(fact_203__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_204_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_205__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_206__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_207__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_208__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_209_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_210_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B2))) => (P @ P4))))). % prod_cases
thf(fact_211_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A5 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A5 @ B3)) => (~ (((A = A5) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_212_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B2)))))))))). % old.prod.exhaust
thf(fact_213_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_214_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ (F @ X) @ Y))))). % apfst_conv
thf(fact_215_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ X @ (F @ Y)))))). % apsnd_conv
thf(fact_216_inj__on__apsnd, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1832254384di_nat @ (produc1894589390e_indi @ F) @ (produc1762100436e_indi @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: A2))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apsnd
thf(fact_217_inj__on__apsnd, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1530862398lt_nat @ (produc86521573le_alt @ F) @ (produc711907405e_indi @ top_to958727510le_alt @ (^[Uu : arrow_1857593510le_alt]: A2))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apsnd
thf(fact_218_inj__on__apsnd, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on48223910lt_nat @ (produc489426964le_alt @ F) @ (produc1308922756e_indi @ top_to224369155le_alt @ (^[Uu : produc16571293le_alt]: A2))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apsnd
thf(fact_219_inj__on__apsnd, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1689162448lt_nat @ (produc1828081268le_alt @ F) @ (produc218670670e_indi @ top_to469035705le_alt @ (^[Uu : set_Pr367596371le_alt]: A2))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apsnd
thf(fact_220_inj__on__apsnd, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on2087578646lt_nat @ (produc1195769064le_alt @ F) @ (produc1843003448e_indi @ top_to685525675le_alt @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: A2))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apsnd
thf(fact_221_inj__on__apfst, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1612178390e_indi @ (produc961456016e_indi @ F) @ (produc1762100436e_indi @ A2 @ (^[Uu : arrow_1429744205e_indi]: top_to1799531699e_indi))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apfst
thf(fact_222_inj__on__apfst, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1711456116le_alt @ (produc1985979043le_alt @ F) @ (produc1380398175le_alt @ A2 @ (^[Uu : arrow_1429744205e_indi]: top_to958727510le_alt))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apfst
thf(fact_223_inj__on__apfst, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1635432290le_alt @ (produc424504278le_alt @ F) @ (produc124975386le_alt @ A2 @ (^[Uu : arrow_1429744205e_indi]: top_to224369155le_alt))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apfst
thf(fact_224_inj__on__apfst, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on1188948002le_alt @ (produc641180214le_alt @ F) @ (produc442900346le_alt @ A2 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apfst
thf(fact_225_inj__on__apfst, axiom,
    ((![F : arrow_1429744205e_indi > nat, A2 : set_Ar1007576579e_indi]: ((inj_on850269876le_alt @ (produc643774374le_alt @ F) @ (produc679053154le_alt @ A2 @ (^[Uu : arrow_1429744205e_indi]: top_to685525675le_alt))) = (inj_on528257168di_nat @ F @ A2))))). % inj_on_apfst
thf(fact_226_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi, B : arrow_1429744205e_indi, A2 : set_Ar1007576579e_indi, B4 : arrow_1429744205e_indi > set_Ar1007576579e_indi]: ((member236207274e_indi @ (produc1274704069e_indi @ A @ B) @ (produc1762100436e_indi @ A2 @ B4)) = (((member1966420836e_indi @ A @ A2)) & ((member1966420836e_indi @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_227_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi, B : arrow_1857593510le_alt, A2 : set_Ar1007576579e_indi, B4 : arrow_1429744205e_indi > set_Ar1665529862le_alt]: ((member1990002591le_alt @ (produc245709870le_alt @ A @ B) @ (produc1380398175le_alt @ A2 @ B4)) = (((member1966420836e_indi @ A @ A2)) & ((member519365071le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_228_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1429744205e_indi, A2 : set_Ar1665529862le_alt, B4 : arrow_1857593510le_alt > set_Ar1007576579e_indi]: ((member2031612117e_indi @ (produc1724702748e_indi @ A @ B) @ (produc711907405e_indi @ A2 @ B4)) = (((member519365071le_alt @ A @ A2)) & ((member1966420836e_indi @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_229_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B4 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A2 @ B4)) = (((member519365071le_alt @ A @ A2)) & ((member519365071le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_230_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi, B : produc16571293le_alt, A2 : set_Ar1007576579e_indi, B4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member573510128le_alt @ (produc726962443le_alt @ A @ B) @ (produc124975386le_alt @ A2 @ B4)) = (((member1966420836e_indi @ A @ A2)) & ((member2048039092le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_231_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1429744205e_indi, A2 : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Ar1007576579e_indi]: ((member876625754e_indi @ (produc1910909813e_indi @ A @ B) @ (produc1308922756e_indi @ A2 @ B4)) = (((member2048039092le_alt @ A @ A2)) & ((member1966420836e_indi @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_232_mem__Sigma__iff, axiom,
    ((![A : produc16571293le_alt, B : arrow_1857593510le_alt, A2 : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member1876252911le_alt @ (produc78632318le_alt @ A @ B) @ (produc195787183le_alt @ A2 @ B4)) = (((member2048039092le_alt @ A @ A2)) & ((member519365071le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_233_mem__Sigma__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : produc16571293le_alt, A2 : set_Ar1665529862le_alt, B4 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member1000073755le_alt @ (produc1906488418le_alt @ A @ B) @ (produc2023643283le_alt @ A2 @ B4)) = (((member519365071le_alt @ A @ A2)) & ((member2048039092le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_234_mem__Sigma__iff, axiom,
    ((![A : arrow_1429744205e_indi, B : set_Pr367596371le_alt, A2 : set_Ar1007576579e_indi, B4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member1221516368le_alt @ (produc128414571le_alt @ A @ B) @ (produc442900346le_alt @ A2 @ B4)) = (((member1966420836e_indi @ A @ A2)) & ((member1334244458le_alt @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_235_mem__Sigma__iff, axiom,
    ((![A : set_Pr367596371le_alt, B : arrow_1429744205e_indi, A2 : set_se2071012361le_alt, B4 : set_Pr367596371le_alt > set_Ar1007576579e_indi]: ((member429766180e_indi @ (produc2051668543e_indi @ A @ B) @ (produc218670670e_indi @ A2 @ B4)) = (((member1334244458le_alt @ A @ A2)) & ((member1966420836e_indi @ B @ (B4 @ A)))))))). % mem_Sigma_iff
thf(fact_236_SigmaI, axiom,
    ((![A : produc16571293le_alt, A2 : set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : produc16571293le_alt > set_Ar809243995le_alt]: ((member2048039092le_alt @ A @ A2) => ((member684274596le_alt @ B @ (B4 @ A)) => (member1263449330le_alt @ (produc283291649le_alt @ A @ B) @ (produc1761277106le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_237_SigmaI, axiom,
    ((![A : produc16571293le_alt, A2 : set_Pr367596371le_alt, B : arrow_1429744205e_indi, B4 : produc16571293le_alt > set_Ar1007576579e_indi]: ((member2048039092le_alt @ A @ A2) => ((member1966420836e_indi @ B @ (B4 @ A)) => (member876625754e_indi @ (produc1910909813e_indi @ A @ B) @ (produc1308922756e_indi @ A2 @ B4))))))). % SigmaI
thf(fact_238_SigmaI, axiom,
    ((![A : produc16571293le_alt, A2 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, B4 : produc16571293le_alt > set_se2071012361le_alt]: ((member2048039092le_alt @ A @ A2) => ((member1334244458le_alt @ B @ (B4 @ A)) => (member1923768064le_alt @ (produc268611099le_alt @ A @ B) @ (produc1173532202le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_239_SigmaI, axiom,
    ((![A : produc16571293le_alt, A2 : set_Pr367596371le_alt, B : produc16571293le_alt, B4 : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A2) => ((member2048039092le_alt @ B @ (B4 @ A)) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (produc1360152522le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_240_SigmaI, axiom,
    ((![A : produc16571293le_alt, A2 : set_Pr367596371le_alt, B : arrow_1857593510le_alt, B4 : produc16571293le_alt > set_Ar1665529862le_alt]: ((member2048039092le_alt @ A @ A2) => ((member519365071le_alt @ B @ (B4 @ A)) => (member1876252911le_alt @ (produc78632318le_alt @ A @ B) @ (produc195787183le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_241_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B : arrow_1429744205e_indi > set_Pr367596371le_alt, B4 : arrow_1857593510le_alt > set_Ar809243995le_alt]: ((member519365071le_alt @ A @ A2) => ((member684274596le_alt @ B @ (B4 @ A)) => (member960954167le_alt @ (produc1316484634le_alt @ A @ B) @ (produc1598628137le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_242_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B : arrow_1429744205e_indi, B4 : arrow_1857593510le_alt > set_Ar1007576579e_indi]: ((member519365071le_alt @ A @ A2) => ((member1966420836e_indi @ B @ (B4 @ A)) => (member2031612117e_indi @ (produc1724702748e_indi @ A @ B) @ (produc711907405e_indi @ A2 @ B4))))))). % SigmaI
thf(fact_243_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B : set_Pr367596371le_alt, B4 : arrow_1857593510le_alt > set_se2071012361le_alt]: ((member519365071le_alt @ A @ A2) => ((member1334244458le_alt @ B @ (B4 @ A)) => (member1361938555le_alt @ (produc398768834le_alt @ A @ B) @ (produc1741626099le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_244_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B : produc16571293le_alt, B4 : arrow_1857593510le_alt > set_Pr367596371le_alt]: ((member519365071le_alt @ A @ A2) => ((member2048039092le_alt @ B @ (B4 @ A)) => (member1000073755le_alt @ (produc1906488418le_alt @ A @ B) @ (produc2023643283le_alt @ A2 @ B4))))))). % SigmaI
thf(fact_245_SigmaI, axiom,
    ((![A : arrow_1857593510le_alt, A2 : set_Ar1665529862le_alt, B : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt > set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A2) => ((member519365071le_alt @ B @ (B4 @ A)) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (produc2062971558le_alt @ A2 @ B4))))))). % SigmaI

% 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,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $false @ X @ Y) = Y)))).
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,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ n) @ lab @ lba)) @ (collec1559089382le_alt @ (^[F2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (![X2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X2 @ top_to1799531699e_indi)) => ((member1334244458le_alt @ (F2 @ X2) @ arrow_1848678355le_Lin))))))))).
