%------------------------------------------------------------------------------
% File     : SCT171_2 : TPTP v8.2.0. Released v5.3.0.
% Domain   : Social Choice Theory
% Problem  : Arrow's Impossibility Theorem line 309, 500 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : arrow_500_tff_l309 [Bla11]

% Status   : Theorem
% Rating   : 0.00 v5.4.0, 0.33 v5.3.0
% Syntax   : Number of formulae    : 1442 ( 193 unt; 684 typ;   0 def)
%            Number of atoms       : 1861 ( 403 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives : 1389 ( 286   ~;  39   |;  54   &)
%                                         ( 179 <=>; 831  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :  253 ( 252 usr)
%            Number of type conns  :  558 ( 295   >; 263   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  431 ( 431 usr; 137 con; 0-3 aty)
%            Number of variables   : 1765 (1749   !;  16   ?;1765   :)
% SPC      : TF0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:41:23
%------------------------------------------------------------------------------
%----Should-be-implicit typings (252)
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tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_145,type,
    fun_Pr1055212137t_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_146,type,
    fun_Pr215145567t_unit: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_147,type,
    fun_Pr39488737i_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_148,type,
    fun_Pr359894313l_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_149,type,
    fun_Pr1907279903t_bool: $tType ).

tff(ty_ty_tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_150,type,
    fun_Pr1228236907l_bool: $tType ).

tff(ty_ty_tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__Arrow__,type,
    produc1840315303le_alt: $tType ).

%----Explicit typings (432)
tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_OIIA,type,
    arrow_888693696le_IIA: fun_fu1138137687l_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_OLin,type,
    arrow_915577424le_Lin: fun_fu1015689055l_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_OProf,type,
    arrow_1190054106e_Prof: fun_fu775006535l_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Oabove,type,
    arrow_1475523868_above: fun_fu699199419t_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Obelow,type,
    arrow_636638768_below: ( fun_Pr1055212137t_bool * arrow_931160158le_alt * arrow_931160158le_alt ) > fun_Pr1055212137t_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Odictator,type,
    arrow_1472924909ctator: fun_fu2127564915i_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Omkbot,type,
    arrow_592884904_mkbot: fun_fu1628463836t_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Omktop,type,
    arrow_741591990_mktop: fun_fu1628463836t_bool ).

tff(sy_c_Arrow__Order__Mirabelle__ctuiwsvqnm_Ounanimity,type,
    arrow_22284131nimity: fun_fu1138137687l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
    cOMBB_1015721476ol_nat: fun_bo1549164019l_bool > fun_fu2104074051l_bool ).

tff(sy_c_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,type,
    cOMBB_231886989e_indi: fun_bo462718181t_bool > fun_fu2115718429t_bool ).

tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__A,type,
    cOMBB_981137617e_indi: fun_nat_fun_nat_bool > fun_fu1845850437t_bool ).

tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__N,type,
    cOMBB_800536526ol_nat: fun_nat_fun_nat_bool > fun_fu717290361t_bool ).

tff(sy_c_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    cOMBB_1146692694ol_nat: fun_na1436237685l_bool > fun_fu1585362869l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__,type,
    cOMBB_1430402568le_alt: fun_fu709917073t_bool > fun_fu334859135t_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___151,type,
    cOMBB_1605735744le_alt: fun_fu1476972377l_bool > fun_fu960970567l_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    cOMBB_656639247e_indi: fun_fu699199419t_bool > fun_fu757621293t_bool ).

tff(sy_c_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___152,type,
    cOMBB_117136048e_indi: fun_fu1628463836t_bool > fun_fu1872020686t_bool ).

tff(sy_c_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_,type,
    cOMBB_480104238le_alt: fun_Pr1228236907l_bool > fun_fu1476972377l_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc,type,
    cOMBC_571858149l_bool: fun_fu709917073t_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc_153,type,
    cOMBC_1947566172t_bool: fun_fu1498496639t_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Arrow_,type,
    cOMBC_1505804284t_bool: fun_fu209106563t_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Arrow__154,type,
    cOMBC_18834461t_bool: fun_fu613599045t_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Nat__O,type,
    cOMBC_922322901t_bool: fun_fu954933197i_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_It,type,
    cOMBC_31215906l_bool: fun_fu1380565427i_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_It_155,type,
    cOMBC_1190055014t_bool: fun_fu51155629t_bool ).

tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_It_156,type,
    cOMBC_1490589522t_bool: fun_fu2117817733t_bool ).

tff(sy_c_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc_,type,
    cOMBC_1455277858l_bool: fun_fu1196098339l_bool ).

tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool,type,
    cOMBC_nat_nat_bool: fun_fu1733046955t_bool ).

tff(sy_c_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat,type,
    cOMBC_nat_nat_nat: fun_fu522653757at_nat ).

tff(sy_c_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__H,type,
    cOMBC_226598744l_bool: fun_fu80187629t_bool ).

tff(sy_c_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Type__Ounit_,type,
    cOMBC_2133163426l_bool: fun_fu363747255t_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_,type,
    cOMBC_941833506l_bool: fun_fu1444789715l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    cOMBC_1452216610l_bool: fun_fu1389232563l_bool ).

tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    cOMBC_437066390l_bool: fun_fu1697657963l_bool ).

tff(sy_c_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_,type,
    cOMBC_697226658l_bool: fun_fu528877839t_bool ).

tff(sy_c_COMBI_000tc__Nat__Onat,type,
    cOMBI_nat: fun_nat_nat ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    cOMBK_1820189998e_indi: fun_bo353189547i_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Nat__Onat,type,
    cOMBK_bool_nat: fun_bo1570548802t_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit,type,
    cOMBK_790042732t_unit: fun_bo1300789993t_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____ctui,type,
    cOMBK_670822686t_bool: fun_bo645734555l_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,type,
    cOMBK_759924014t_bool: fun_bo979888811l_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,type,
    cOMBK_1216274064t_bool: fun_bo96602657l_bool ).

tff(sy_c_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
    cOMBK_1566242880le_alt: fun_bo1116297149t_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_,type,
    cOMBK_854051296t_bool: fun_fu536674321i_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_Itc__Arrow__,type,
    cOMBK_1506144056le_alt: fun_fu1465670113l_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow____Order____,type,
    cOMBK_2091851729e_indi: fun_fu1692311659t_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Onat,type,
    cOMBK_583454926ol_nat: fun_fu429110920t_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    cOMBK_2140692976t_bool: fun_fu1355931153l_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
    cOMBK_1595020336e_indi: fun_fu279877163l_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_157,type,
    cOMBK_1446432t_bool: fun_fu16872987l_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    cOMBK_1522533360e_indi: fun_fu243393031t_bool ).

tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___158,type,
    cOMBK_382434616l_bool: fun_fu831091903t_bool ).

tff(sy_c_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_It,type,
    cOMBS_811328630t_bool: ( fun_Ar1519997101t_bool * fun_Ar500372357t_bool ) > fun_Ar1492469401t_bool ).

tff(sy_c_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_It_159,type,
    cOMBS_1921392482t_bool: ( fun_Ar1492469401t_bool * fun_Ar500372357t_bool ) > fun_Ar500372357t_bool ).

tff(sy_c_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool,type,
    cOMBS_nat_bool_bool: ( fun_na1469252690l_bool * fun_nat_bool ) > fun_nat_bool ).

tff(sy_c_Finite__Set_Ocard_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    finite783399747e_indi: fun_Ar552120407i_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__HOL__Obool,type,
    finite_card_bool: fun_bool_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
    finite_card_nat: fun_nat_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__Product____Type__Ounit,type,
    finite1949902593t_unit: fun_Pr1643180309t_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    finite1418900531t_bool: fun_fu775006535l_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,type,
    finite1445836347t_bool: fun_fu1015689055l_bool > nat ).

tff(sy_c_Finite__Set_Ocard_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,type,
    finite876838485le_alt: fun_Pr1055212137t_bool > nat ).

tff(sy_c_Finite__Set_Ofinite_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    finite1350902018e_indi: fun_fu1657302605l_bool ).

tff(sy_c_Finite__Set_Ofinite_000tc__HOL__Obool,type,
    finite_finite_bool: fun_fu1255657237l_bool ).

tff(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
    finite_finite_nat: fun_fu425979586l_bool ).

tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    finite1217814770t_bool: fun_fu614742333l_bool ).

tff(sy_c_Finite__Set_Ofinite_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle__,type,
    finite775027132t_bool: fun_fu705370401l_bool ).

tff(sy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    finite788329492le_alt: fun_fu1015689055l_bool ).

tff(sy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t,type,
    in_rel267123714le_alt: ( fun_Pr1055212137t_bool * arrow_931160158le_alt * arrow_931160158le_alt ) > bool ).

tff(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc_,type,
    inj_on886403158di_nat: fun_Ar1744566822di_nat > fun_fu1657302605l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__160,type,
    inj_on194063285t_bool: fun_Ar500372357t_bool > fun_fu1657302605l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle,type,
    inj_on2047198755le_alt: fun_bo1479727337le_alt > fun_fu1255657237l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__Nat__Onat_000tc__Nat__Onat,type,
    inj_on_nat_nat: fun_nat_nat > fun_fu425979586l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    inj_on937360581t_bool: fun_fu1595299477t_bool > fun_fu614742333l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    inj_on1048829645e_indi: fun_fu2016509975e_indi > fun_fu705370401l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw_161,type,
    inj_on456593853t_bool: fun_fu243393031t_bool > fun_fu705370401l_bool ).

tff(sy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
    inj_on899118883t_bool: fun_Pr1055212137t_bool > fun_fu1015689055l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__,type,
    pi_Arr159321468di_nat: ( fun_Ar552120407i_bool * fun_Ar2045874810t_bool ) > fun_fu192249448t_bool ).

tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc___162,type,
    pi_Arr1376550035t_bool: ( fun_Ar552120407i_bool * fun_Ar684516451l_bool ) > fun_fu1131021301l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc___163,type,
    pi_Arr353983907t_bool: ( fun_Ar552120407i_bool * fun_Ar1270429299l_bool ) > fun_fu1944573957l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc___164,type,
    pi_Arr487970267t_bool: ( fun_Ar552120407i_bool * fun_Ar1198543961l_bool ) > fun_fu775006535l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc___165,type,
    pi_Arr914482869le_alt: ( fun_Ar552120407i_bool * fun_Ar500372357t_bool ) > fun_fu2073792791t_bool ).

tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__Nat__Onat,type,
    pi_bool_nat: ( fun_bool_bool * fun_bo1570548802t_bool ) > fun_fu429484960t_bool ).

tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle__,type,
    pi_boo573599835t_bool: ( fun_bool_bool * fun_bo645734555l_bool ) > fun_fu1311768765l_bool ).

tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mi,type,
    pi_boo250534251t_bool: ( fun_bool_bool * fun_bo979888811l_bool ) > fun_fu497048781l_bool ).

tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____M,type,
    pi_boo98824211t_bool: ( fun_bool_bool * fun_bo96602657l_bool ) > fun_fu1337686655l_bool ).

tff(sy_c_FuncSet_OPi_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle_,type,
    pi_boo1374671485le_alt: ( fun_bool_bool * fun_bo1116297149t_bool ) > fun_fu853181919t_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    pi_nat1905227924e_indi: ( fun_nat_bool * fun_na457272970i_bool ) > fun_fu1470034170i_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__HOL__Obool,type,
    pi_nat_bool: ( fun_nat_bool * fun_na1469252690l_bool ) > fun_fu425979586l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Nat__Onat,type,
    pi_nat_nat: ( fun_nat_bool * fun_nat_fun_nat_bool ) > fun_fun_nat_nat_bool ).

tff(sy_c_FuncSet_OPi_000tc__Nat__Onat_000tc__Product____Type__Ounit,type,
    pi_nat_Product_unit: ( fun_nat_bool * fun_na1041622088t_bool ) > fun_fu1771765432t_bool ).

tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__Nat__Onat,type,
    pi_Product_unit_nat: ( fun_Pr1643180309t_bool * fun_Pr1029464120t_bool ) > fun_fu1108851754t_bool ).

tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__Arrow____Order___,type,
    pi_Pro1008448593t_bool: ( fun_Pr1643180309t_bool * fun_Pr1223320869l_bool ) > fun_fu176691123l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow___,type,
    pi_Pro1014195041t_bool: ( fun_Pr1643180309t_bool * fun_Pr1832937781l_bool ) > fun_fu38582723l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow__,type,
    pi_Pro278326941t_bool: ( fun_Pr1643180309t_bool * fun_Pr1510236951l_bool ) > fun_fu829220361l_bool ).

tff(sy_c_FuncSet_OPi_000tc__Product____Type__Ounit_000tc__prod_Itc__Arrow____Order__,type,
    pi_Pro1041002611le_alt: ( fun_Pr1643180309t_bool * fun_Pr1572389447t_bool ) > fun_fu209254101t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oind,type,
    pi_fun64467091e_indi: ( fun_fu775006535l_bool * fun_fu1765260675i_bool ) > fun_fu887487221i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oind_166,type,
    pi_fun1624909403l_bool: ( fun_fu775006535l_bool * fun_fu1471766731l_bool ) > fun_fu614742333l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oind_167,type,
    pi_fun1455727697t_unit: ( fun_fu775006535l_bool * fun_fu587068865t_bool ) > fun_fu1386428467t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oind_168,type,
    pi_fun530160875t_bool: ( fun_fu775006535l_bool * fun_fu787660105l_bool ) > fun_fu1138137687l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    pi_fun1073350051e_indi: ( fun_fu1138137687l_bool * fun_fu2127564915i_bool ) > fun_fu1480005125i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsv_169,type,
    pi_fun351900523l_bool: ( fun_fu1138137687l_bool * fun_fu1460706235l_bool ) > fun_fu1378577485l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsv_170,type,
    pi_fun1254023521t_unit: ( fun_fu1138137687l_bool * fun_fu327311537t_bool ) > fun_fu829635395t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    pi_fun1342736627e_indi: ( fun_fu1015689055l_bool * fun_fu1766473067i_bool ) > fun_fu790078681i_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiws_171,type,
    pi_fun1412468411l_bool: ( fun_fu1015689055l_bool * fun_fu44268723l_bool ) > fun_fu705370401l_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiws_172,type,
    pi_fun116255921t_unit: ( fun_fu1015689055l_bool * fun_fu105994665t_bool ) > fun_fu545713175t_bool ).

tff(sy_c_FuncSet_OPi_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiws_173,type,
    pi_fun49394147t_bool: ( fun_fu1015689055l_bool * fun_fu1583538011l_bool ) > fun_fu1916585161l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal,type,
    pi_Pro1592011445e_indi: ( fun_Pr1055212137t_bool * fun_Pr39488737i_bool ) > fun_fu83070487i_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_174,type,
    pi_Pro226591613t_bool: ( fun_Pr1055212137t_bool * fun_Pr359894313l_bool ) > fun_fu1015689055l_bool ).

tff(sy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_175,type,
    pi_Pro185129843t_unit: ( fun_Pr1055212137t_bool * fun_Pr1907279903t_bool ) > fun_fu1367017557t_bool ).

tff(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
    one_one_nat: nat ).

tff(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
    plus_plus_nat: fun_nat_fun_nat_nat ).

tff(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
    zero_zero_nat: nat ).

tff(sy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    hilber506087739di_nat: ( fun_Ar552120407i_bool * fun_Ar1744566822di_nat ) > fun_na1392860600e_indi ).

tff(sy_c_Hilbert__Choice_Oinv__into_000tc__Nat__Onat_000tc__Nat__Onat,type,
    hilber195283148at_nat: ( fun_nat_bool * fun_nat_nat ) > fun_nat_nat ).

tff(sy_c_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal,type,
    if_fun1658569689t_bool: fun_bo462718181t_bool ).

tff(sy_c_Nat_OSuc,type,
    suc: fun_nat_nat ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__HOL__Obool,type,
    ord_less_bool: fun_bo1549164019l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Arrow____Order____Mirabelle____,type,
    ord_le1115695277i_bool: fun_fu1310412861l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    ord_le197158773l_bool: fun_fu1393819981l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    ord_le382113706t_bool: fun_fu1217155507l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL,type,
    ord_le1976645739t_bool: fun_fu43485241l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,type,
    ord_le583255965l_bool: fun_fu1420978973l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,type,
    ord_le1306091181l_bool: fun_fu385975869l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,type,
    ord_le2104736649l_bool: fun_fu1216534899l_bool ).

tff(sy_c_Orderings_Oord__class_Oless_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,type,
    ord_le466311871t_bool: fun_fu1515494241l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__HOL__Obool,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle,type,
    ord_le1254553345t_bool: fun_fu304639347l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Arrow____Order____Mirabelle_176,type,
    ord_le351904673i_bool: fun_fu1310412861l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
    ord_le742797417l_bool: fun_fu1393819981l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    ord_le1568362934t_bool: fun_fu1217155507l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__Product____Type__Ounit_Mtc_,type,
    ord_le1874503007t_bool: fun_fu43485241l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__Arrow____Order____,type,
    ord_le1871091345l_bool: fun_fu1420978973l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____,type,
    ord_le161055137l_bool: fun_fu385975869l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow___,type,
    ord_le1923264405l_bool: fun_fu1216534899l_bool ).

tff(sy_c_Orderings_Oord__class_Oless__eq_000tc__fun_Itc__prod_Itc__Arrow____Order___,type,
    ord_le565024179t_bool: fun_fu1515494241l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,type,
    top_top_bool: bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____c,type,
    top_to1678393681i_bool: fun_Ar552120407i_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    top_to1647826457l_bool: fun_bool_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    top_top_fun_nat_bool: fun_nat_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL_,type,
    top_to1257323279t_bool: fun_Pr1643180309t_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirab,type,
    top_to1324311617l_bool: fun_fu775006535l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order,type,
    top_to2013953873l_bool: fun_fu1138137687l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Orde,type,
    top_to1690334693l_bool: fun_fu1015689055l_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mira,type,
    top_to126038883t_bool: fun_Pr1055212137t_bool ).

tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_,type,
    produc362059031le_alt: fun_Ar2049444117le_alt ).

tff(sy_c_SetInterval_Oord__class_OatLeastLessThan_000tc__Nat__Onat,type,
    ord_at4362885an_nat: nat > fun_nat_fun_nat_bool ).

tff(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    collec708328256e_indi: fun_Ar552120407i_bool > fun_Ar552120407i_bool ).

tff(sy_c_Set_OCollect_000tc__Nat__Onat,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

tff(sy_c_Set_OCollect_000tc__Product____Type__Ounit,type,
    collect_Product_unit: fun_Pr1643180309t_bool > fun_Pr1643180309t_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    collec1461897520t_bool: fun_fu775006535l_bool > fun_fu775006535l_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    collec1699798848t_bool: fun_fu1138137687l_bool > fun_fu1138137687l_bool ).

tff(sy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    collec1113178622t_bool: fun_fu1015689055l_bool > fun_fu1015689055l_bool ).

tff(sy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
    collec1209019986le_alt: fun_Pr1055212137t_bool > fun_Pr1055212137t_bool ).

tff(sy_c_Set_Oimage_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__N,type,
    image_391852738di_nat: ( fun_Ar1744566822di_nat * fun_Ar552120407i_bool ) > fun_nat_bool ).

tff(sy_c_fFalse,type,
    fFalse: bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fconj,type,
    fconj: fun_bo1549164019l_bool ).

tff(sy_c_fequal_000tc__Nat__Onat,type,
    fequal_nat: fun_nat_fun_nat_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__HOL__Obo,type,
    hAPP_A674791462t_bool: ( fun_Ar1091019988t_bool * arrow_931160158le_alt ) > bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc_,type,
    hAPP_A1858212765t_bool: ( fun_Ar1414184139t_bool * arrow_931160158le_alt ) > fun_Ar1091019988t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__177,type,
    hAPP_A1256181151l_bool: ( fun_Ar1689125069l_bool * arrow_931160158le_alt ) > fun_Ar1026121174l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__178,type,
    hAPP_A501825983t_bool: ( fun_Ar1164786343t_bool * arrow_931160158le_alt ) > fun_Ar1275715144t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__179,type,
    hAPP_A1485971815le_alt: ( fun_Ar2049444117le_alt * arrow_931160158le_alt ) > fun_Ar836847646le_alt ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__180,type,
    hAPP_A102926893t_bool: ( fun_Ar2078312923t_bool * arrow_931160158le_alt ) > fun_Ar698916836t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__181,type,
    hAPP_A658738638t_bool: ( fun_Ar421919996t_bool * arrow_931160158le_alt ) > fun_Ar500372357t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__182,type,
    hAPP_A1787768616l_bool: ( fun_Ar1026121174l_bool * arrow_931160158le_alt ) > fun_fu1015689055l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__183,type,
    hAPP_A1770325791t_bool: ( fun_Ar1364097613t_bool * arrow_931160158le_alt ) > fun_fu1540265814t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__184,type,
    hAPP_A606737888t_bool: ( fun_Ar1275715144t_bool * arrow_931160158le_alt ) > fun_Pr1055212137t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__prod_Itc,type,
    hAPP_A1313367280le_alt: ( fun_Ar836847646le_alt * arrow_931160158le_alt ) > produc1840315303le_alt ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__HOL__Ob,type,
    hAPP_A1888055029i_bool: ( fun_Ar552120407i_bool * arrow_2115524757e_indi ) > bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Nat__On,type,
    hAPP_A1450069362di_nat: ( fun_Ar1744566822di_nat * arrow_2115524757e_indi ) > nat ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc,type,
    hAPP_A131904271t_bool: ( fun_Ar1583656131t_bool * arrow_2115524757e_indi ) > fun_Ar1164786343t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_185,type,
    hAPP_A1020253872t_bool: ( fun_Ar698916836t_bool * arrow_2115524757e_indi ) > fun_Ar1275715144t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_186,type,
    hAPP_A1458779421t_bool: ( fun_Ar687924991t_bool * arrow_2115524757e_indi ) > fun_Ar500372357t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_187,type,
    hAPP_A981395480t_bool: ( fun_Ar2045874810t_bool * arrow_2115524757e_indi ) > fun_nat_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_188,type,
    hAPP_A605074405l_bool: ( fun_Ar1380772935l_bool * arrow_2115524757e_indi ) > fun_fu1657302605l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_189,type,
    hAPP_A182831535l_bool: ( fun_Ar684516451l_bool * arrow_2115524757e_indi ) > fun_fu775006535l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_190,type,
    hAPP_A1044336685t_bool: ( fun_Ar1939863823t_bool * arrow_2115524757e_indi ) > fun_fu1595299477t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_191,type,
    hAPP_A1538515647l_bool: ( fun_Ar1270429299l_bool * arrow_2115524757e_indi ) > fun_fu1138137687l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_192,type,
    hAPP_A1279849719l_bool: ( fun_Ar1198543961l_bool * arrow_2115524757e_indi ) > fun_fu1015689055l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_193,type,
    hAPP_A594708985t_bool: ( fun_Ar1519997101t_bool * arrow_2115524757e_indi ) > fun_fu1324073361t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_194,type,
    hAPP_A892860133t_bool: ( fun_Ar1492469401t_bool * arrow_2115524757e_indi ) > fun_fu962221693t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_195,type,
    hAPP_A1174518481t_bool: ( fun_Ar500372357t_bool * arrow_2115524757e_indi ) > fun_Pr1055212137t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__prod_It,type,
    hAPP_A353813823le_alt: ( fun_Ar369661729le_alt * arrow_2115524757e_indi ) > produc1840315303le_alt ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,type,
    hAPP_bool_bool: ( fun_bool_bool * bool ) > bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__Nat__Onat,type,
    hAPP_bool_nat: ( fun_bool_nat * bool ) > nat ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    hAPP_b1439777783i_bool: ( fun_bo353189547i_bool * bool ) > fun_Ar552120407i_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiw_196,type,
    hAPP_b715352037t_bool: ( fun_bo266809543t_bool * bool ) > fun_Ar500372357t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_b589554111l_bool: ( fun_bo1549164019l_bool * bool ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    hAPP_b1013836512t_bool: ( fun_bo1570548802t_bool * bool ) > fun_nat_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo,type,
    hAPP_b1096750261t_bool: ( fun_bo1300789993t_bool * bool ) > fun_Pr1643180309t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
    hAPP_b1849744615l_bool: ( fun_bo645734555l_bool * bool ) > fun_fu775006535l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_197,type,
    hAPP_b510135029t_bool: ( fun_bo2027801303t_bool * bool ) > fun_fu1595299477t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_,type,
    hAPP_b1787118453l_bool: ( fun_bo492988759l_bool * bool ) > fun_fu1255657237l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____,type,
    hAPP_b816606711l_bool: ( fun_bo979888811l_bool * bool ) > fun_fu1138137687l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order___,type,
    hAPP_b1650070463l_bool: ( fun_bo96602657l_bool * bool ) > fun_fu1015689055l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____198,type,
    hAPP_b1061655857t_bool: ( fun_bo462718181t_bool * bool ) > fun_fu1324073361t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,type,
    hAPP_b1263785481t_bool: ( fun_bo1116297149t_bool * bool ) > fun_Pr1055212137t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____ctui,type,
    hAPP_b1314516999le_alt: ( fun_bo1479727337le_alt * bool ) > produc1840315303le_alt ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    hAPP_n1048492170e_indi: ( fun_na1392860600e_indi * nat ) > arrow_2115524757e_indi ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,type,
    hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Nat__Onat,type,
    hAPP_nat_nat: ( fun_nat_nat * nat ) > nat ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__Product____Type__Ounit,type,
    hAPP_n633340360t_unit: ( fun_nat_Product_unit * nat ) > product_unit ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    hAPP_n924210722i_bool: ( fun_na457272970i_bool * nat ) > fun_Ar552120407i_bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_n1006566506l_bool: ( fun_na1469252690l_bool * nat ) > fun_bool_bool ).

tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).

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tff(sy_c_member_000tc__Nat__Onat,type,
    member_nat: fun_na1436237685l_bool ).

tff(sy_c_member_000tc__Product____Type__Ounit,type,
    member_Product_unit: fun_Pr1863373635l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc,type,
    member428554515di_nat: fun_fu85234537l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_304,type,
    member1188420050t_bool: fun_fu1591782325l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_305,type,
    member291481314t_bool: fun_fu1816256693l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_306,type,
    member1159072754t_bool: fun_fu1291054887l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_307,type,
    member418553588le_alt: fun_fu1338365749l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J,type,
    member_fun_bool_nat: fun_fu1531935961l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mirabelle,type,
    member1283254298t_bool: fun_fu1395443509l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Order____,type,
    member1103019306t_bool: fun_fu752049205l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____Order___,type,
    member818572202t_bool: fun_fu572324631l_bool ).

tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____Mirabell,type,
    member481633596le_alt: fun_fu1156700085l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle____ctuiws,type,
    member76848293e_indi: fun_fu1500933005l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
    member_fun_nat_bool: fun_fu1436348701l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J,type,
    member_fun_nat_nat: fun_fu1988302005l_bool ).

tff(sy_c_member_000tc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J,type,
    member1024687843t_unit: fun_fu1028680969l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J,type,
    member87760213it_nat: fun_fu486305773l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow____Order_,type,
    member1302538000t_bool: fun_fu166516917l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc__Arrow_,type,
    member1948336672t_bool: fun_fu1208702901l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_Itc__Arrow,type,
    member488877876t_bool: fun_fu1969848875l_bool ).

tff(sy_c_member_000tc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow____Order,type,
    member666484274le_alt: fun_fu662844725l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    member1408848082e_indi: fun_fu1227713461l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___308,type,
    member1791451290l_bool: fun_fu81176373l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___309,type,
    member1814595472t_unit: fun_fu1166948533l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___310,type,
    member1801442306t_bool: fun_fu446267975l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,type,
    member2095441122e_indi: fun_fu1739677877l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_311,type,
    member213355690l_bool: fun_fu413400117l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_312,type,
    member1805026208t_unit: fun_fu804386741l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,type,
    member527726724e_indi: fun_fu1041166411l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_313,type,
    member717964108l_bool: fun_fu830715227l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_314,type,
    member1667929154t_unit: fun_fu978460487l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_315,type,
    member449535860t_bool: fun_fu675160875l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    member1747786740e_indi: fun_fu1286543157l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__316,type,
    member57118396t_bool: fun_fu1556412341l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__317,type,
    member1142067122t_unit: fun_fu638047541l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc,type,
    member553230100le_alt: fun_Pr1228236907l_bool ).

tff(sy_v_F,type,
    f: fun_fu1595299477t_bool ).

tff(sy_v_Lab____,type,
    lab: fun_Pr1055212137t_bool ).

tff(sy_v_Lba____,type,
    lba: fun_Pr1055212137t_bool ).

tff(sy_v_P____,type,
    p: fun_Ar500372357t_bool ).

tff(sy_v_a____,type,
    a: arrow_931160158le_alt ).

tff(sy_v_b____,type,
    b: arrow_931160158le_alt ).

tff(sy_v_c____,type,
    c: arrow_931160158le_alt ).

tff(sy_v_d____,type,
    d: arrow_931160158le_alt ).

tff(sy_v_e____,type,
    e: arrow_931160158le_alt ).

tff(sy_v_h____,type,
    h: fun_Ar1744566822di_nat ).

tff(sy_v_n____,type,
    n: nat ).

%----Relevant facts (700)
tff(fact_0_assms_I3_J,axiom,
    hBOOL(hAPP_f611501301l_bool(arrow_888693696le_IIA,f)) ).

tff(fact_1_u,axiom,
    hBOOL(hAPP_f611501301l_bool(arrow_22284131nimity,f)) ).

tff(fact_2__096c_A_126_061_Ad_096,axiom,
    c != d ).

tff(fact_3__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,p),arrow_1190054106e_Prof)) ).

tff(fact_4_in__mkbot,axiom,
    ! [X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool,Z_1: arrow_931160158le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_592884904_mkbot,L_3),Z_1)))
    <=> ( ( Y_2 != Z_1 )
        & ( ( X_2 = Z_1 )
         => ( X_2 != Y_2 ) )
        & ( ( X_2 != Z_1 )
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),L_3)) ) ) ) ).

tff(fact_5_in__mktop,axiom,
    ! [X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool,Z_1: arrow_931160158le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_741591990_mktop,L_3),Z_1)))
    <=> ( ( X_2 != Z_1 )
        & ( ( Y_2 = Z_1 )
         => ( X_2 != Y_2 ) )
        & ( ( Y_2 != Z_1 )
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),L_3)) ) ) ) ).

tff(fact_6__C2_C,axiom,
    ! [P_1: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,A_34: arrow_931160158le_alt,B_32: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( ( Aa != B_32 )
         => ( ( Ba != A_34 )
           => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
             => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_1),arrow_1190054106e_Prof))
               => ( ! [I_2: arrow_2115524757e_indi] :
                      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_A1174518481t_bool(Pa,I_2)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_A1174518481t_bool(P_1,I_2))) )
                 => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_f792184801t_bool(f,Pa)))
                  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_f792184801t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).

tff(fact_7__C1_C,axiom,
    ! [P_1: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,A_34: arrow_931160158le_alt,B_32: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( ( Aa != B_32 )
         => ( ( Ba != A_34 )
           => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
             => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_1),arrow_1190054106e_Prof))
               => ( ! [I_2: arrow_2115524757e_indi] :
                      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_A1174518481t_bool(Pa,I_2)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_A1174518481t_bool(P_1,I_2))) )
                 => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_f792184801t_bool(f,Pa)))
                   => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_f792184801t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).

tff(fact_8__C4_C,axiom,
    ! [P_1: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,Ca: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( Ba != Ca )
       => ( ( Aa != Ca )
         => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
           => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_1),arrow_1190054106e_Prof))
             => ( ! [I_2: arrow_2115524757e_indi] :
                    ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_A1174518481t_bool(Pa,I_2)))
                  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Ca)),hAPP_A1174518481t_bool(P_1,I_2))) )
               => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_f792184801t_bool(f,Pa)))
                <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Ca)),hAPP_f792184801t_bool(f,P_1))) ) ) ) ) ) ) ) ).

tff(fact_9_pairwise__neutrality,axiom,
    ! [P_1: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,A_34: arrow_931160158le_alt,B_32: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( A_34 != B_32 )
       => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
         => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_1),arrow_1190054106e_Prof))
           => ( ! [I_2: arrow_2115524757e_indi] :
                  ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_A1174518481t_bool(Pa,I_2)))
                <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_A1174518481t_bool(P_1,I_2))) )
             => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_f792184801t_bool(f,Pa)))
              <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32)),hAPP_f792184801t_bool(f,P_1))) ) ) ) ) ) ) ).

tff(fact_10__C3_C,axiom,
    ! [P_1: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
       => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_1),arrow_1190054106e_Prof))
         => ( ! [I_2: arrow_2115524757e_indi] :
                ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_A1174518481t_bool(Pa,I_2)))
              <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Aa)),hAPP_A1174518481t_bool(P_1,I_2))) )
           => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),hAPP_f792184801t_bool(f,Pa)))
            <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Aa)),hAPP_f792184801t_bool(f,P_1))) ) ) ) ) ) ).

tff(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
    ! [I_2: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_A1174518481t_bool(p,I_2)))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_741591990_mktop,hAPP_A1174518481t_bool(p,I_2)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => ( ( ( hAPP_A1450069362di_nat(h,I_2) = n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_1475523868_above,hAPP_A1174518481t_bool(p,I_2)),c),e))) )
            & ( ( hAPP_A1450069362di_nat(h,I_2) != n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_592884904_mkbot,hAPP_A1174518481t_bool(p,I_2)),e))) ) ) ) ) ) ).

tff(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_A1174518481t_bool(p,hAPP_n1048492170e_indi(hilber506087739di_nat(top_to1678393681i_bool,h),n)))) ).

tff(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) ).

tff(fact_14_PW,axiom,
    ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p)))
  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) ) ).

tff(fact_15_split__paired__All,axiom,
    ! [Pa: fun_Pr1055212137t_bool] :
      ( ! [X1: produc1840315303le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,X1))
    <=> ! [A_1: arrow_931160158le_alt,B_25: arrow_931160158le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25))) ) ).

tff(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))),arrow_1190054106e_Prof)) ).

tff(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),e)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) ).

tff(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,e),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e)))))) ).

tff(fact_19_n_I1_J,axiom,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite783399747e_indi(top_to1678393681i_bool))) ).

tff(fact_20_injh,axiom,
    hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(h),top_to1678393681i_bool)) ).

tff(fact_21_Pair__inject,axiom,
    ! [A_36: arrow_931160158le_alt,B_34: arrow_931160158le_alt,A_35: arrow_931160158le_alt,B_33: arrow_931160158le_alt] :
      ( ( hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_36),B_34) = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_35),B_33) )
     => ~ ( ( A_36 = A_35 )
         => ( B_34 != B_33 ) ) ) ).

tff(fact_22_Pair__eq,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt,A_34: arrow_931160158le_alt,B_32: arrow_931160158le_alt] :
      ( ( hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba) = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_34),B_32) )
    <=> ( ( Aa = A_34 )
        & ( Ba = B_32 ) ) ) ).

tff(fact_23_IIA__def,axiom,
    ! [Fa: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(arrow_888693696le_IIA,Fa))
    <=> ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),arrow_1190054106e_Prof))
         => ! [Xa: fun_Ar500372357t_bool] :
              ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Xa),arrow_1190054106e_Prof))
             => ! [A_1: arrow_931160158le_alt,B_25: arrow_931160158le_alt] :
                  ( ! [I_2: arrow_2115524757e_indi] :
                      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_A1174518481t_bool(X_1,I_2)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_A1174518481t_bool(Xa,I_2))) )
                 => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_f792184801t_bool(Fa,X_1)))
                  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_f792184801t_bool(Fa,Xa))) ) ) ) ) ) ).

tff(fact_24_unanimity__def,axiom,
    ! [Fa: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(arrow_22284131nimity,Fa))
    <=> ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),arrow_1190054106e_Prof))
         => ! [A_1: arrow_931160158le_alt,B_25: arrow_931160158le_alt] :
              ( ! [I_2: arrow_2115524757e_indi] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_A1174518481t_bool(X_1,I_2)))
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_f792184801t_bool(Fa,X_1))) ) ) ) ).

tff(fact_25_top1I,axiom,
    ! [X_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f429946033l_bool(top_to1690334693l_bool,X_2)) ).

tff(fact_26_top1I,axiom,
    ! [X_2: fun_Ar500372357t_bool] : hBOOL(hAPP_f1766661605l_bool(top_to1324311617l_bool,X_2)) ).

tff(fact_27_top1I,axiom,
    ! [X_2: fun_fu1595299477t_bool] : hBOOL(hAPP_f611501301l_bool(top_to2013953873l_bool,X_2)) ).

tff(fact_28_top1I,axiom,
    ! [X_2: produc1840315303le_alt] : hBOOL(hAPP_P166437127t_bool(top_to126038883t_bool,X_2)) ).

tff(fact_29_top1I,axiom,
    ! [X_2: arrow_2115524757e_indi] : hBOOL(hAPP_A1888055029i_bool(top_to1678393681i_bool,X_2)) ).

tff(fact_30_top1I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2)) ).

tff(fact_31_top1I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2)) ).

tff(fact_32_UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_33_UNIV__I,axiom,
    ! [X_2: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),top_to1678393681i_bool)) ).

tff(fact_34_UNIV__I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).

tff(fact_35_UNIV__I,axiom,
    ! [X_2: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),top_to126038883t_bool)) ).

tff(fact_36_UNIV__I,axiom,
    ! [X_2: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),top_to1324311617l_bool)) ).

tff(fact_37_UNIV__I,axiom,
    ! [X_2: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),top_to2013953873l_bool)) ).

tff(fact_38_UNIV__I,axiom,
    ! [X_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),top_to1690334693l_bool)) ).

tff(fact_39_UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_40_iso__tuple__UNIV__I,axiom,
    ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_41_iso__tuple__UNIV__I,axiom,
    ! [X_2: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),top_to1678393681i_bool)) ).

tff(fact_42_iso__tuple__UNIV__I,axiom,
    ! [X_2: product_unit] : hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),top_to1257323279t_bool)) ).

tff(fact_43_iso__tuple__UNIV__I,axiom,
    ! [X_2: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),top_to126038883t_bool)) ).

tff(fact_44_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),top_to1324311617l_bool)) ).

tff(fact_45_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),top_to2013953873l_bool)) ).

tff(fact_46_iso__tuple__UNIV__I,axiom,
    ! [X_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),top_to1690334693l_bool)) ).

tff(fact_47_iso__tuple__UNIV__I,axiom,
    ! [X_2: nat] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),top_top_fun_nat_bool)) ).

tff(fact_48_top__apply,axiom,
    ! [X_2: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(top_to1690334693l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_49_top__apply,axiom,
    ! [X_2: fun_Ar500372357t_bool] :
      ( hBOOL(hAPP_f1766661605l_bool(top_to1324311617l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_50_top__apply,axiom,
    ! [X_2: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(top_to2013953873l_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_51_top__apply,axiom,
    ! [X_2: produc1840315303le_alt] :
      ( hBOOL(hAPP_P166437127t_bool(top_to126038883t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_52_top__apply,axiom,
    ! [X_2: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_A1888055029i_bool(top_to1678393681i_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_53_top__apply,axiom,
    ! [X_2: product_unit] :
      ( hBOOL(hAPP_P1676879539t_bool(top_to1257323279t_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_54_top__apply,axiom,
    ! [X_2: nat] :
      ( hBOOL(hAPP_nat_bool(top_top_fun_nat_bool,X_2))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_55_not__top__less,axiom,
    ! [Aa: fun_fu1015689055l_bool] : ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le2104736649l_bool,top_to1690334693l_bool),Aa)) ).

tff(fact_56_not__top__less,axiom,
    ! [Aa: fun_fu775006535l_bool] : ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le583255965l_bool,top_to1324311617l_bool),Aa)) ).

tff(fact_57_not__top__less,axiom,
    ! [Aa: fun_fu1138137687l_bool] : ~ hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le1306091181l_bool,top_to2013953873l_bool),Aa)) ).

tff(fact_58_not__top__less,axiom,
    ! [Aa: bool] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)) ).

tff(fact_59_not__top__less,axiom,
    ! [Aa: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le466311871t_bool,top_to126038883t_bool),Aa)) ).

tff(fact_60_not__top__less,axiom,
    ! [Aa: fun_Ar552120407i_bool] : ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,top_to1678393681i_bool),Aa)) ).

tff(fact_61_not__top__less,axiom,
    ! [Aa: fun_Pr1643180309t_bool] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,top_to1257323279t_bool),Aa)) ).

tff(fact_62_not__top__less,axiom,
    ! [Aa: fun_nat_bool] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,top_top_fun_nat_bool),Aa)) ).

tff(fact_63_less__top,axiom,
    ! [Aa: fun_fu1015689055l_bool] :
      ( ( Aa != top_to1690334693l_bool )
    <=> hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le2104736649l_bool,Aa),top_to1690334693l_bool)) ) ).

tff(fact_64_less__top,axiom,
    ! [Aa: fun_fu775006535l_bool] :
      ( ( Aa != top_to1324311617l_bool )
    <=> hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le583255965l_bool,Aa),top_to1324311617l_bool)) ) ).

tff(fact_65_less__top,axiom,
    ! [Aa: fun_fu1138137687l_bool] :
      ( ( Aa != top_to2013953873l_bool )
    <=> hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le1306091181l_bool,Aa),top_to2013953873l_bool)) ) ).

tff(fact_66_less__top,axiom,
    ! [Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(top_top_bool) )
    <=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ) ).

tff(fact_67_less__top,axiom,
    ! [Aa: fun_Pr1055212137t_bool] :
      ( ( Aa != top_to126038883t_bool )
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le466311871t_bool,Aa),top_to126038883t_bool)) ) ).

tff(fact_68_less__top,axiom,
    ! [Aa: fun_Ar552120407i_bool] :
      ( ( Aa != top_to1678393681i_bool )
    <=> hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),top_to1678393681i_bool)) ) ).

tff(fact_69_less__top,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( ( Aa != top_to1257323279t_bool )
    <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),top_to1257323279t_bool)) ) ).

tff(fact_70_less__top,axiom,
    ! [Aa: fun_nat_bool] :
      ( ( Aa != top_top_fun_nat_bool )
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),top_top_fun_nat_bool)) ) ).

tff(fact_71_assms_I1_J,axiom,
    hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,f),pi_fun530160875t_bool(arrow_1190054106e_Prof,hAPP_f422714471l_bool(cOMBK_1446432t_bool,arrow_915577424le_Lin)))) ).

tff(fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,e),d)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n))),lab)),lba)))) ) ).

tff(fact_73__096Lab_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,lab),arrow_915577424le_Lin)) ).

tff(fact_74__096Lba_A_058_ALin_096,axiom,
    hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,lba),arrow_915577424le_Lin)) ).

tff(fact_75__096a_A_126_061_Ab_096,axiom,
    a != b ).

tff(fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),lab)) ).

tff(fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),lba)) ).

tff(fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
    ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),lba)) ).

tff(fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
    ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),lab)) ).

tff(fact_80_PiProf,axiom,
    ! [Na: nat] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),Na))),lab)),lba)),arrow_1190054106e_Prof)) ).

tff(fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_,axiom,
    ~ ! [Lab: fun_Pr1055212137t_bool] :
        ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),Lab))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Lab),arrow_915577424le_Lin)) ) ).

tff(fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_,axiom,
    ~ ! [Lba: fun_Pr1055212137t_bool] :
        ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),Lba))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Lba),arrow_915577424le_Lin)) ) ).

tff(fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk,axiom,
    ! [I_2: arrow_2115524757e_indi] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,e),d)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_741591990_mktop,hAPP_A1174518481t_bool(p,I_2)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => ( ( ( hAPP_A1450069362di_nat(h,I_2) = n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,e),d)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_1475523868_above,hAPP_A1174518481t_bool(p,I_2)),c),e))) )
            & ( ( hAPP_A1450069362di_nat(h,I_2) != n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,e),d)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_592884904_mkbot,hAPP_A1174518481t_bool(p,I_2)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),lba)) ) ) ) ).

tff(fact_84_n_I2_J,axiom,
    ! [M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),n))
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),M))),lab)),lba)))) ) ).

tff(fact_85_notin__Lin__iff,axiom,
    ! [X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
     => ( ( X_2 != Y_2 )
       => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),L_3))
        <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Y_2),X_2)),L_3)) ) ) ) ).

tff(fact_86_Lin__irrefl,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),L_3))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Aa)),L_3)) ) ) ).

tff(fact_87_mktop__Lin,axiom,
    ! [X_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_741591990_mktop,L_3),X_2)),arrow_915577424le_Lin)) ) ).

tff(fact_88_mkbot__Lin,axiom,
    ! [X_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_592884904_mkbot,L_3),X_2)),arrow_915577424le_Lin)) ) ).

tff(fact_89_above__Lin,axiom,
    ! [L_3: fun_Pr1055212137t_bool,X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_1475523868_above,L_3),X_2),Y_2)),arrow_915577424le_Lin)) ) ) ).

tff(fact_90_const__Lin__Prof,axiom,
    ! [L_3: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_f311418073t_bool(cOMBK_1522533360e_indi,L_3)),arrow_1190054106e_Prof)) ) ).

tff(fact_91_linorder__cases,axiom,
    ! [X_32: nat,Y_30: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_32),Y_30))
     => ( ( X_32 != Y_30 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_30),X_32)) ) ) ).

tff(fact_92_order__less__asym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_93_order__less__asym,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_94_order__less__asym,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2)) ) ).

tff(fact_95_order__less__asym,axiom,
    ! [X_31: nat,Y_29: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_31),Y_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_29),X_31)) ) ).

tff(fact_96_xt1_I10_J,axiom,
    ! [Z_1: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).

tff(fact_97_xt1_I10_J,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).

tff(fact_98_xt1_I10_J,axiom,
    ! [Z_1: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Z_1),X_2)) ) ) ).

tff(fact_99_xt1_I10_J,axiom,
    ! [Z_9: nat,Y_28: nat,X_30: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_28),X_30))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),Y_28))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_9),X_30)) ) ) ).

tff(fact_100_order__less__trans,axiom,
    ! [Z_1: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).

tff(fact_101_order__less__trans,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).

tff(fact_102_order__less__trans,axiom,
    ! [Z_1: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Z_1)) ) ) ).

tff(fact_103_order__less__trans,axiom,
    ! [Z_8: nat,X_29: nat,Y_27: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Y_27))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_27),Z_8))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_29),Z_8)) ) ) ).

tff(fact_104_xt1_I2_J,axiom,
    ! [Ca: fun_nat_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).

tff(fact_105_xt1_I2_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).

tff(fact_106_xt1_I2_J,axiom,
    ! [Ca: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ca),Aa)) ) ) ).

tff(fact_107_xt1_I2_J,axiom,
    ! [C_24: nat,B_31: nat,A_33: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_31),A_33))
     => ( ( B_31 = C_24 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_24),A_33)) ) ) ).

tff(fact_108_ord__less__eq__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).

tff(fact_109_ord__less__eq__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).

tff(fact_110_ord__less__eq__trans,axiom,
    ! [Ca: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ca)) ) ) ).

tff(fact_111_ord__less__eq__trans,axiom,
    ! [C_23: nat,A_32: nat,B_30: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),B_30))
     => ( ( B_30 = C_23 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_32),C_23)) ) ) ).

tff(fact_112_xt1_I1_J,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ca),Aa)) ) ) ).

tff(fact_113_xt1_I1_J,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ca),Aa)) ) ) ).

tff(fact_114_xt1_I1_J,axiom,
    ! [Ca: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ca),Ba))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ca),Aa)) ) ) ).

tff(fact_115_xt1_I1_J,axiom,
    ! [C_22: nat,A_31: nat,B_29: nat] :
      ( ( A_31 = B_29 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),B_29))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_22),A_31)) ) ) ).

tff(fact_116_ord__eq__less__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ca)) ) ) ).

tff(fact_117_ord__eq__less__trans,axiom,
    ! [Ca: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Ca))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ca)) ) ) ).

tff(fact_118_ord__eq__less__trans,axiom,
    ! [Ca: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Ca))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ca)) ) ) ).

tff(fact_119_ord__eq__less__trans,axiom,
    ! [C_21: nat,A_30: nat,B_28: nat] :
      ( ( A_30 = B_28 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_28),C_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_30),C_21)) ) ) ).

tff(fact_120_xt1_I9_J,axiom,
    ! [Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ).

tff(fact_121_xt1_I9_J,axiom,
    ! [Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ).

tff(fact_122_xt1_I9_J,axiom,
    ! [Ba: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Aa))
     => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ba)) ) ).

tff(fact_123_xt1_I9_J,axiom,
    ! [B_27: nat,A_29: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_27),A_29))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_29),B_27)) ) ).

tff(fact_124_order__less__asym_H,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ).

tff(fact_125_order__less__asym_H,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ).

tff(fact_126_order__less__asym_H,axiom,
    ! [Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ba))
     => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Aa)) ) ).

tff(fact_127_order__less__asym_H,axiom,
    ! [A_28: nat,B_26: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_28),B_26))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_26),A_28)) ) ).

tff(fact_128_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_129_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_130_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_131_order__less__imp__triv,axiom,
    ! [Pa: bool,X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
       => hBOOL(Pa) ) ) ).

tff(fact_132_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_133_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_134_order__less__imp__not__eq2,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( Y_2 != X_2 ) ) ).

tff(fact_135_order__less__imp__not__eq2,axiom,
    ! [X_28: nat,Y_26: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_28),Y_26))
     => ( Y_26 != X_28 ) ) ).

tff(fact_136_order__less__imp__not__eq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_137_order__less__imp__not__eq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_138_order__less__imp__not__eq,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_139_order__less__imp__not__eq,axiom,
    ! [X_27: nat,Y_25: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_27),Y_25))
     => ( X_27 != Y_25 ) ) ).

tff(fact_140_order__less__imp__not__less,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_141_order__less__imp__not__less,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_142_order__less__imp__not__less,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2)) ) ).

tff(fact_143_order__less__imp__not__less,axiom,
    ! [X_26: nat,Y_24: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_26),Y_24))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_24),X_26)) ) ).

tff(fact_144_order__less__not__sym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2)) ) ).

tff(fact_145_order__less__not__sym,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2)) ) ).

tff(fact_146_order__less__not__sym,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2)) ) ).

tff(fact_147_order__less__not__sym,axiom,
    ! [X_25: nat,Y_23: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_25),Y_23))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_23),X_25)) ) ).

tff(fact_148_less__imp__neq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_149_less__imp__neq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_150_less__imp__neq,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( X_2 != Y_2 ) ) ).

tff(fact_151_less__imp__neq,axiom,
    ! [X_24: nat,Y_22: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_24),Y_22))
     => ( X_24 != Y_22 ) ) ).

tff(fact_152_linorder__neqE,axiom,
    ! [X_23: nat,Y_21: nat] :
      ( ( X_23 != Y_21 )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_23),Y_21))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_21),X_23)) ) ) ).

tff(fact_153_linorder__antisym__conv3,axiom,
    ! [Y_2: nat,X_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_154_linorder__less__linear,axiom,
    ! [X_22: nat,Y_20: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_22),Y_20))
      | ( X_22 = Y_20 )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_20),X_22)) ) ).

tff(fact_155_not__less__iff__gr__or__eq,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_156_linorder__neq__iff,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ( X_2 != Y_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ) ).

tff(fact_157_order__less__irrefl,axiom,
    ! [X_2: fun_nat_bool] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),X_2)) ).

tff(fact_158_order__less__irrefl,axiom,
    ! [X_2: fun_Pr1643180309t_bool] : ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),X_2)) ).

tff(fact_159_order__less__irrefl,axiom,
    ! [X_2: fun_Ar552120407i_bool] : ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),X_2)) ).

tff(fact_160_order__less__irrefl,axiom,
    ! [X_21: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_21),X_21)) ).

tff(fact_161_UNIV__def,axiom,
    top_to1690334693l_bool = collec1113178622t_bool(hAPP_b1650070463l_bool(cOMBK_1216274064t_bool,fTrue)) ).

tff(fact_162_UNIV__def,axiom,
    top_to1324311617l_bool = collec1461897520t_bool(hAPP_b1849744615l_bool(cOMBK_670822686t_bool,fTrue)) ).

tff(fact_163_UNIV__def,axiom,
    top_to2013953873l_bool = collec1699798848t_bool(hAPP_b816606711l_bool(cOMBK_759924014t_bool,fTrue)) ).

tff(fact_164_UNIV__def,axiom,
    top_to126038883t_bool = collec1209019986le_alt(hAPP_b1263785481t_bool(cOMBK_1566242880le_alt,fTrue)) ).

tff(fact_165_UNIV__def,axiom,
    top_to1678393681i_bool = collec708328256e_indi(hAPP_b1439777783i_bool(cOMBK_1820189998e_indi,fTrue)) ).

tff(fact_166_UNIV__def,axiom,
    top_to1257323279t_bool = collect_Product_unit(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,fTrue)) ).

tff(fact_167_UNIV__def,axiom,
    top_top_fun_nat_bool = collect_nat(hAPP_b1013836512t_bool(cOMBK_bool_nat,fTrue)) ).

tff(fact_168_mem__def,axiom,
    ! [X_2: arrow_2115524757e_indi,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
    <=> hBOOL(hAPP_A1888055029i_bool(A,X_2)) ) ).

tff(fact_169_mem__def,axiom,
    ! [X_2: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
    <=> hBOOL(hAPP_bool_bool(A,X_2)) ) ).

tff(fact_170_mem__def,axiom,
    ! [X_2: product_unit,A: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
    <=> hBOOL(hAPP_P1676879539t_bool(A,X_2)) ) ).

tff(fact_171_mem__def,axiom,
    ! [X_2: produc1840315303le_alt,A: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
    <=> hBOOL(hAPP_P166437127t_bool(A,X_2)) ) ).

tff(fact_172_mem__def,axiom,
    ! [X_2: fun_Ar500372357t_bool,A: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
    <=> hBOOL(hAPP_f1766661605l_bool(A,X_2)) ) ).

tff(fact_173_mem__def,axiom,
    ! [X_2: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A))
    <=> hBOOL(hAPP_f611501301l_bool(A,X_2)) ) ).

tff(fact_174_mem__def,axiom,
    ! [X_2: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A))
    <=> hBOOL(hAPP_f429946033l_bool(A,X_2)) ) ).

tff(fact_175_mem__def,axiom,
    ! [X_2: nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> hBOOL(hAPP_nat_bool(A,X_2)) ) ).

tff(fact_176_Collect__def,axiom,
    ! [Pa: fun_Pr1643180309t_bool] : collect_Product_unit(Pa) = Pa ).

tff(fact_177_Collect__def,axiom,
    ! [Pa: fun_Ar552120407i_bool] : collec708328256e_indi(Pa) = Pa ).

tff(fact_178_Collect__def,axiom,
    ! [Pa: fun_nat_bool] : collect_nat(Pa) = Pa ).

tff(fact_179_in__above,axiom,
    ! [X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
       => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_1475523868_above,L_3),Aa),Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( X_2 = Ba )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Y_2)),L_3)) )
            & ( ( X_2 != Ba )
             => ( ( ( Y_2 = Ba )
                 => ( ( X_2 = Aa )
                    | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Aa)),L_3)) ) )
                & ( ( Y_2 != Ba )
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ).

tff(fact_180_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr1055212137t_bool,R_1: fun_Pr1055212137t_bool] :
      ( ! [X_1: arrow_931160158le_alt,Xa: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Xa)),R_1))
        <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Xa)),S_1)) )
    <=> ( R_1 = S_1 ) ) ).

tff(fact_181_n_I3_J,axiom,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ).

tff(fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),e)),hAPP_f792184801t_bool(f,cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_741591990_mktop),p)),e)),cOMBS_1921392482t_bool(cOMBS_811328630t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(fequal_nat),h)),n)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(cOMBB_656639247e_indi(arrow_1475523868_above),p)),c)),e)),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_f842954860t_bool(cOMBB_117136048e_indi(arrow_592884904_mkbot),p)),e))))))
  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))),lab)),lba)))) ) ).

tff(fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
    ! [I_2: arrow_2115524757e_indi] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),e)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_741591990_mktop,hAPP_A1174518481t_bool(p,I_2)),e))) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),n))
         => ( ( ( hAPP_A1450069362di_nat(h,I_2) = n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),e)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_1475523868_above,hAPP_A1174518481t_bool(p,I_2)),c),e))) )
            & ( ( hAPP_A1450069362di_nat(h,I_2) != n )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),e)),hAPP_A606737888t_bool(hAPP_f786530292t_bool(arrow_592884904_mkbot,hAPP_A1174518481t_bool(p,I_2)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),lab)) )
        & ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1450069362di_nat(h,I_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,n),one_one_nat)))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),lba)) ) ) ) ).

tff(fact_184_inv__f__eq,axiom,
    ! [X_2: arrow_2115524757e_indi,Y_2: nat,F: fun_Ar1744566822di_nat] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool))
     => ( ( hAPP_A1450069362di_nat(F,X_2) = Y_2 )
       => ( hAPP_n1048492170e_indi(hilber506087739di_nat(top_to1678393681i_bool,F),Y_2) = X_2 ) ) ) ).

tff(fact_185_inv__f__eq,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = Y_2 )
       => ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),Y_2) = X_2 ) ) ) ).

tff(fact_186_inv__f__f,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool))
     => ( hAPP_n1048492170e_indi(hilber506087739di_nat(top_to1678393681i_bool,F),hAPP_A1450069362di_nat(F,X_2)) = X_2 ) ) ).

tff(fact_187_inv__f__f,axiom,
    ! [X_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( hAPP_nat_nat(hilber195283148at_nat(top_top_fun_nat_bool,F),hAPP_nat_nat(F,X_2)) = X_2 ) ) ).

tff(fact_188_dictatorI,axiom,
    ! [I_1: arrow_2115524757e_indi,Fa: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Fa),pi_fun530160875t_bool(arrow_1190054106e_Prof,hAPP_f422714471l_bool(cOMBK_1446432t_bool,arrow_915577424le_Lin))))
     => ( ! [X_1: fun_Ar500372357t_bool] :
            ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),arrow_1190054106e_Prof))
           => ! [A_1: arrow_931160158le_alt,B_25: arrow_931160158le_alt] :
                ( ( A_1 != B_25 )
               => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_A1174518481t_bool(X_1,I_1)))
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_1),B_25)),hAPP_f792184801t_bool(Fa,X_1))) ) ) )
       => hBOOL(hAPP_A1888055029i_bool(hAPP_f740807359i_bool(arrow_1472924909ctator,Fa),I_1)) ) ) ).

tff(fact_189_PiE,axiom,
    ! [X_2: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),hAPP_P1830623733l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A)) ) ) ).

tff(fact_190_PiE,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar369661729le_alt,A: fun_Ar552120407i_bool,B: fun_Ar500372357t_bool] :
      ( hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_2)),hAPP_A1174518481t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A)) ) ) ).

tff(fact_191_PiE,axiom,
    ! [X_2: bool,F: fun_bo1479727337le_alt,A: fun_bool_bool,B: fun_bo1116297149t_bool] :
      ( hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_2)),hAPP_b1263785481t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_192_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr1887046367le_alt,A: fun_Pr1643180309t_bool,B: fun_Pr1572389447t_bool] :
      ( hBOOL(hAPP_f403597109l_bool(hAPP_f1413342797l_bool(member666484274le_alt,F),pi_Pro1041002611le_alt(A,B)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1763651581le_alt(F,X_2)),hAPP_P902017683t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_193_PiE,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar687924991t_bool,A: fun_Ar552120407i_bool,B: fun_Ar684516451l_bool] :
      ( hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_2)),hAPP_A182831535l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A)) ) ) ).

tff(fact_194_PiE,axiom,
    ! [X_2: bool,F: fun_bo266809543t_bool,A: fun_bool_bool,B: fun_bo645734555l_bool] :
      ( hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_2)),hAPP_b1849744615l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_195_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr321980605t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1223320869l_bool] :
      ( hBOOL(hAPP_f1221487891l_bool(hAPP_f1119259085l_bool(member1302538000t_bool,F),pi_Pro1008448593t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P1139363291t_bool(F,X_2)),hAPP_P1055953777l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_196_PiE,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar1939863823t_bool,A: fun_Ar552120407i_bool,B: fun_Ar1270429299l_bool] :
      ( hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_2)),hAPP_A1538515647l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A)) ) ) ).

tff(fact_197_PiE,axiom,
    ! [X_2: bool,F: fun_bo2027801303t_bool,A: fun_bool_bool,B: fun_bo979888811l_bool] :
      ( hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_2)),hAPP_b816606711l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_198_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr1337256141t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1832937781l_bool] :
      ( hBOOL(hAPP_f522449699l_bool(hAPP_f1960079821l_bool(member1948336672t_bool,F),pi_Pro1014195041t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P1339635435t_bool(F,X_2)),hAPP_P1470717569l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_199_PiE,axiom,
    ! [X_2: bool,F: fun_bo1116297149t_bool,A: fun_bool_bool,B: fun_bo96602657l_bool] :
      ( hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_2)),hAPP_b1650070463l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_200_PiE,axiom,
    ! [X_2: product_unit,F: fun_Pr1572389447t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1510236951l_bool] :
      ( hBOOL(hAPP_f922750545l_bool(hAPP_f2046606153l_bool(member488877876t_bool,F),pi_Pro278326941t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P902017683t_bool(F,X_2)),hAPP_P1132296885l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_201_PiE,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool,B: fun_Ar2045874810t_bool] :
      ( hBOOL(hAPP_f1290810160l_bool(hAPP_f516936199l_bool(member428554515di_nat,F),pi_Arr159321468di_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_A1450069362di_nat(F,X_2)),hAPP_A981395480t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A)) ) ) ).

tff(fact_202_PiE,axiom,
    ! [X_2: bool,F: fun_bool_nat,A: fun_bool_bool,B: fun_bo1570548802t_bool] :
      ( hBOOL(hAPP_f67777128l_bool(hAPP_f144393719l_bool(member_fun_bool_nat,F),pi_bool_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_bool_nat(F,X_2)),hAPP_b1013836512t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A)) ) ) ).

tff(fact_203_PiE,axiom,
    ! [X_2: product_unit,F: fun_Product_unit_nat,A: fun_Pr1643180309t_bool,B: fun_Pr1029464120t_bool] :
      ( hBOOL(hAPP_f339859954l_bool(hAPP_f1950626059l_bool(member87760213it_nat,F),pi_Product_unit_nat(A,B)))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_P426034740it_nat(F,X_2)),hAPP_P32877782t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A)) ) ) ).

tff(fact_204_PiE,axiom,
    ! [X_2: produc1840315303le_alt,F: fun_Pr1698894881e_indi,A: fun_Pr1055212137t_bool,B: fun_Pr39488737i_bool] :
      ( hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_2)),hAPP_P1326783277i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A)) ) ) ).

tff(fact_205_PiE,axiom,
    ! [X_2: produc1840315303le_alt,F: fun_Pr215145567t_unit,A: fun_Pr1055212137t_bool,B: fun_Pr1907279903t_bool] :
      ( hBOOL(hAPP_f1685685l_bool(hAPP_f106186317l_bool(member1142067122t_unit,F),pi_Pro185129843t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_P907778813t_unit(F,X_2)),hAPP_P728132331t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A)) ) ) ).

tff(fact_206_PiE,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu908353023e_indi,A: fun_fu775006535l_bool,B: fun_fu1765260675i_bool] :
      ( hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_2)),hAPP_f109229519i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A)) ) ) ).

tff(fact_207_PiE,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu775006535l_bool,A: fun_fu775006535l_bool,B: fun_fu1471766731l_bool] :
      ( hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_2)),hAPP_f84039575l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A)) ) ) ).

tff(fact_208_PiE,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu834038077t_unit,A: fun_fu775006535l_bool,B: fun_fu587068865t_bool] :
      ( hBOOL(hAPP_f345984403l_bool(hAPP_f1505765837l_bool(member1814595472t_unit,F),pi_fun1455727697t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1586642395t_unit(F,X_2)),hAPP_f290914957t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A)) ) ) ).

tff(fact_209_PiE,axiom,
    ! [X_2: fun_fu1595299477t_bool,F: fun_fu1596339983e_indi,A: fun_fu1138137687l_bool,B: fun_fu2127564915i_bool] :
      ( hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_2)),hAPP_f740807359i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A)) ) ) ).

tff(fact_210_PiE,axiom,
    ! [X_2: fun_fu1595299477t_bool,F: fun_fu1138137687l_bool,A: fun_fu1138137687l_bool,B: fun_fu1460706235l_bool] :
      ( hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_2)),hAPP_f352672903l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A)) ) ) ).

tff(fact_211_PiE,axiom,
    ! [X_2: fun_fu1595299477t_bool,F: fun_fu1193945677t_unit,A: fun_fu1138137687l_bool,B: fun_fu327311537t_bool] :
      ( hBOOL(hAPP_f1549513891l_bool(hAPP_f1065603533l_bool(member1805026208t_unit,F),pi_fun1254023521t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f1579463915t_unit(F,X_2)),hAPP_f1483290493t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A)) ) ) ).

tff(fact_212_PiE,axiom,
    ! [X_2: fun_Pr1055212137t_bool,F: fun_fu2016509975e_indi,A: fun_fu1015689055l_bool,B: fun_fu1766473067i_bool] :
      ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_2)),hAPP_f1957024259i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A)) ) ) ).

tff(fact_213_PiE,axiom,
    ! [X_2: fun_Pr1055212137t_bool,F: fun_fu1015689055l_bool,A: fun_fu1015689055l_bool,B: fun_fu44268723l_bool] :
      ( hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_2)),hAPP_f269590987l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A)) ) ) ).

tff(fact_214_PiE,axiom,
    ! [X_2: fun_Pr1055212137t_bool,F: fun_fu603957077t_unit,A: fun_fu1015689055l_bool,B: fun_fu105994665t_bool] :
      ( hBOOL(hAPP_f1919464799l_bool(hAPP_f803471205l_bool(member1667929154t_unit,F),pi_fun116255921t_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_f739946663t_unit(F,X_2)),hAPP_f862859457t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A)) ) ) ).

tff(fact_215_PiE,axiom,
    ! [X_2: nat,F: fun_na1392860600e_indi,A: fun_nat_bool,B: fun_na457272970i_bool] :
      ( hBOOL(hAPP_f728118466l_bool(hAPP_f138236715l_bool(member76848293e_indi,F),pi_nat1905227924e_indi(A,B)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_n1048492170e_indi(F,X_2)),hAPP_n924210722i_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_216_PiE,axiom,
    ! [X_2: nat,F: fun_nat_bool,A: fun_nat_bool,B: fun_na1469252690l_bool] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,F),pi_nat_bool(A,B)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_nat_bool(F,X_2)),hAPP_n1006566506l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_217_PiE,axiom,
    ! [X_2: nat,F: fun_nat_Product_unit,A: fun_nat_bool,B: fun_na1041622088t_bool] :
      ( hBOOL(hAPP_f537623936l_bool(hAPP_f1598887207l_bool(member1024687843t_unit,F),pi_nat_Product_unit(A,B)))
     => ( ~ hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,hAPP_n633340360t_unit(F,X_2)),hAPP_n454528608t_bool(B,X_2)))
       => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ).

tff(fact_218_PiE,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A: fun_fu775006535l_bool,B: fun_fu787660105l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),hAPP_f1498158055l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A)) ) ) ).

tff(fact_219_PiE,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool,B: fun_Ar1198543961l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,B)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),hAPP_A1279849719l_bool(B,X_2)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A)) ) ) ).

tff(fact_220_complete__Lin,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ? [X_1: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),arrow_915577424le_Lin))
          & hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),X_1)) ) ) ).

tff(fact_221_Pi__UNIV,axiom,
    ! [A: fun_Pr1055212137t_bool] : pi_Pro226591613t_bool(A,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,top_to1647826457l_bool)) = top_to1690334693l_bool ).

tff(fact_222_Pi__UNIV,axiom,
    ! [A: fun_fu775006535l_bool] : pi_fun530160875t_bool(A,hAPP_f422714471l_bool(cOMBK_1446432t_bool,top_to1690334693l_bool)) = top_to2013953873l_bool ).

tff(fact_223_Pi__UNIV,axiom,
    ! [A: fun_Ar552120407i_bool] : pi_Arr487970267t_bool(A,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,top_to1690334693l_bool)) = top_to1324311617l_bool ).

tff(fact_224_order__refl,axiom,
    ! [X_2: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),X_2)) ).

tff(fact_225_order__refl,axiom,
    ! [X_20: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_20),X_20)) ).

tff(fact_226_order__refl,axiom,
    ! [X_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)) ).

tff(fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I,axiom,
    ? [N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite783399747e_indi(top_to1678393681i_bool)))
      & ! [M: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
      & hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))) ) ).

tff(fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_,axiom,
    ~ ! [N: nat] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),finite783399747e_indi(top_to1678393681i_bool)))
       => ( ! [M: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),M))),lab)),lba)))) )
         => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_f792184801t_bool(f,hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,hAPP_f509814255t_bool(cOMBB_231886989e_indi(if_fun1658569689t_bool),hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,hAPP_f1381130897t_bool(cOMBB_981137617e_indi(ord_less_nat),h)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat)))),lab)),lba)))) ) ) ).

tff(fact_229_linorder__le__cases,axiom,
    ! [X_19: nat,Y_19: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_19),Y_19))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_19),X_19)) ) ).

tff(fact_230_le__funE,axiom,
    ! [X_2: nat,F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).

tff(fact_231_xt1_I6_J,axiom,
    ! [Z_1: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),X_2)) ) ) ).

tff(fact_232_xt1_I6_J,axiom,
    ! [Z_7: nat,Y_18: nat,X_18: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_18),X_18))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),Y_18))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_7),X_18)) ) ) ).

tff(fact_233_xt1_I6_J,axiom,
    ! [Z_1: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),X_2)) ) ) ).

tff(fact_234_xt1_I5_J,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_235_xt1_I5_J,axiom,
    ! [Y_17: nat,X_17: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_17),X_17))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_17),Y_17))
       => ( X_17 = Y_17 ) ) ) ).

tff(fact_236_xt1_I5_J,axiom,
    ! [Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_237_order__trans,axiom,
    ! [Z_1: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Z_1)) ) ) ).

tff(fact_238_order__trans,axiom,
    ! [Z_6: nat,X_16: nat,Y_16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Y_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_16),Z_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_16),Z_6)) ) ) ).

tff(fact_239_order__trans,axiom,
    ! [Z_1: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Z_1)) ) ) ).

tff(fact_240_order__antisym,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
       => ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_241_order__antisym,axiom,
    ! [X_15: nat,Y_15: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_15),Y_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_15),X_15))
       => ( X_15 = Y_15 ) ) ) ).

tff(fact_242_order__antisym,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_243_xt1_I4_J,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).

tff(fact_244_xt1_I4_J,axiom,
    ! [C_20: nat,B_24: nat,A_27: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_24),A_27))
     => ( ( B_24 = C_20 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_20),A_27)) ) ) ).

tff(fact_245_xt1_I4_J,axiom,
    ! [Ca: fun_nat_bool,Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).

tff(fact_246_ord__le__eq__trans,axiom,
    ! [Ca: bool,Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ( hBOOL(Ba)
        <=> hBOOL(Ca) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).

tff(fact_247_ord__le__eq__trans,axiom,
    ! [C_19: nat,A_26: nat,B_23: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),B_23))
     => ( ( B_23 = C_19 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_26),C_19)) ) ) ).

tff(fact_248_ord__le__eq__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( ( Ba = Ca )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).

tff(fact_249_xt1_I3_J,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ca),Aa)) ) ) ).

tff(fact_250_xt1_I3_J,axiom,
    ! [C_18: nat,A_25: nat,B_22: nat] :
      ( ( A_25 = B_22 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),B_22))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_18),A_25)) ) ) ).

tff(fact_251_xt1_I3_J,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ca),Aa)) ) ) ).

tff(fact_252_ord__eq__le__trans,axiom,
    ! [Ca: bool,Ba: bool,Aa: bool] :
      ( ( hBOOL(Aa)
      <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Ca))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ca)) ) ) ).

tff(fact_253_ord__eq__le__trans,axiom,
    ! [C_17: nat,A_24: nat,B_21: nat] :
      ( ( A_24 = B_21 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_21),C_17))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_24),C_17)) ) ) ).

tff(fact_254_ord__eq__le__trans,axiom,
    ! [Ca: fun_nat_bool,Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa = Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Ca))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ca)) ) ) ).

tff(fact_255_order__antisym__conv,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
      <=> ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_256_order__antisym__conv,axiom,
    ! [Y_2: nat,X_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_257_order__antisym__conv,axiom,
    ! [Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_258_le__funD,axiom,
    ! [X_2: nat,F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G,X_2))) ) ).

tff(fact_259_order__eq__refl,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).

tff(fact_260_order__eq__refl,axiom,
    ! [X_14: nat,Y_14: nat] :
      ( ( X_14 = Y_14 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_14),Y_14)) ) ).

tff(fact_261_order__eq__refl,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( ( X_2 = Y_2 )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).

tff(fact_262_order__eq__iff,axiom,
    ! [Y_2: bool,X_2: bool] :
      ( ( hBOOL(X_2)
      <=> hBOOL(Y_2) )
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).

tff(fact_263_order__eq__iff,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).

tff(fact_264_order__eq__iff,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( ( X_2 = Y_2 )
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).

tff(fact_265_linorder__linear,axiom,
    ! [X_13: nat,Y_13: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_13),Y_13))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_13),X_13)) ) ).

tff(fact_266_le__fun__def,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
    <=> ! [X_1: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1))) ) ).

tff(fact_267_linorder__not__less,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ).

tff(fact_268_linorder__not__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_2),X_2)) ) ).

tff(fact_269_linorder__le__less__linear,axiom,
    ! [X_12: nat,Y_12: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_12),Y_12))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_12)) ) ).

tff(fact_270_order__less__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_271_order__less__le,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_272_order__less__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & ~ ( hBOOL(X_2)
          <=> hBOOL(Y_2) ) ) ) ).

tff(fact_273_order__less__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_274_order__less__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & ( X_2 != Y_2 ) ) ) ).

tff(fact_275_less__le__not__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2)) ) ) ).

tff(fact_276_less__le__not__le,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Y_2),X_2)) ) ) ).

tff(fact_277_less__le__not__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2)) ) ) ).

tff(fact_278_less__le__not__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2)) ) ) ).

tff(fact_279_less__le__not__le,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_2),X_2)) ) ) ).

tff(fact_280_order__le__less,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_281_order__le__less,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_282_order__le__less,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_283_order__le__less,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_284_order__le__less,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_285_leI,axiom,
    ! [X_11: nat,Y_11: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_11))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_11),X_11)) ) ).

tff(fact_286_not__leE,axiom,
    ! [Y_10: nat,X_10: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_10),X_10))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_10)) ) ).

tff(fact_287_linorder__antisym__conv1,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_288_order__neq__le__trans,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ).

tff(fact_289_order__neq__le__trans,axiom,
    ! [Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Aa),Ba))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ba)) ) ) ).

tff(fact_290_order__neq__le__trans,axiom,
    ! [Ba: bool,Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).

tff(fact_291_order__neq__le__trans,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).

tff(fact_292_order__neq__le__trans,axiom,
    ! [A_23: nat,B_20: nat] :
      ( ( A_23 != B_20 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_23),B_20))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_23),B_20)) ) ) ).

tff(fact_293_xt1_I12_J,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ).

tff(fact_294_xt1_I12_J,axiom,
    ! [Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Ba),Aa))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Aa)) ) ) ).

tff(fact_295_xt1_I12_J,axiom,
    ! [Ba: bool,Aa: bool] :
      ( ~ ( hBOOL(Aa)
        <=> hBOOL(Ba) )
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).

tff(fact_296_xt1_I12_J,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).

tff(fact_297_xt1_I12_J,axiom,
    ! [A_22: nat,B_19: nat] :
      ( ( A_22 != B_19 )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),A_22))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_19),A_22)) ) ) ).

tff(fact_298_leD,axiom,
    ! [Y_9: nat,X_9: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_9))
     => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_9)) ) ).

tff(fact_299_order__less__imp__le,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2)) ) ).

tff(fact_300_order__less__imp__le,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2)) ) ).

tff(fact_301_order__less__imp__le,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2)) ) ).

tff(fact_302_order__less__imp__le,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2)) ) ).

tff(fact_303_order__less__imp__le,axiom,
    ! [X_8: nat,Y_8: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_8))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_8)) ) ).

tff(fact_304_linorder__antisym__conv2,axiom,
    ! [X_2: nat,Y_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),Y_2))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_2))
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_305_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_306_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_307_order__le__imp__less__or__eq,axiom,
    ! [X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
        | ( hBOOL(X_2)
        <=> hBOOL(Y_2) ) ) ) ).

tff(fact_308_order__le__imp__less__or__eq,axiom,
    ! [X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
        | ( X_2 = Y_2 ) ) ) ).

tff(fact_309_order__le__imp__less__or__eq,axiom,
    ! [X_7: nat,Y_7: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_7))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_7))
        | ( X_7 = Y_7 ) ) ) ).

tff(fact_310_order__le__neq__trans,axiom,
    ! [Aa: fun_Pr1643180309t_bool,Ba: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Aa),Ba)) ) ) ).

tff(fact_311_order__le__neq__trans,axiom,
    ! [Aa: fun_Ar552120407i_bool,Ba: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Aa),Ba)) ) ) ).

tff(fact_312_order__le__neq__trans,axiom,
    ! [Aa: bool,Ba: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),Ba))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),Ba)) ) ) ).

tff(fact_313_order__le__neq__trans,axiom,
    ! [Aa: fun_nat_bool,Ba: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),Ba))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Aa),Ba)) ) ) ).

tff(fact_314_order__le__neq__trans,axiom,
    ! [A_21: nat,B_18: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),B_18))
     => ( ( A_21 != B_18 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_21),B_18)) ) ) ).

tff(fact_315_xt1_I11_J,axiom,
    ! [Ba: fun_nat_bool,Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Ba),Aa)) ) ) ).

tff(fact_316_xt1_I11_J,axiom,
    ! [Ba: fun_Pr1643180309t_bool,Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Ba),Aa)) ) ) ).

tff(fact_317_xt1_I11_J,axiom,
    ! [Ba: fun_Ar552120407i_bool,Aa: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Ba),Aa))
     => ( ( Aa != Ba )
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Ba),Aa)) ) ) ).

tff(fact_318_xt1_I11_J,axiom,
    ! [B_17: nat,A_20: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_17),A_20))
     => ( ( A_20 != B_17 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_17),A_20)) ) ) ).

tff(fact_319_xt1_I11_J,axiom,
    ! [Ba: bool,Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Ba),Aa))
     => ( ~ ( hBOOL(Aa)
          <=> hBOOL(Ba) )
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Ba),Aa)) ) ) ).

tff(fact_320_order__less__le__trans,axiom,
    ! [Z_1: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).

tff(fact_321_order__less__le__trans,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).

tff(fact_322_order__less__le__trans,axiom,
    ! [Z_1: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Z_1)) ) ) ).

tff(fact_323_order__less__le__trans,axiom,
    ! [Z_5: nat,X_6: nat,Y_6: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_6))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Z_5)) ) ) ).

tff(fact_324_order__less__le__trans,axiom,
    ! [Z_1: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ) ).

tff(fact_325_xt1_I7_J,axiom,
    ! [Z_1: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).

tff(fact_326_xt1_I7_J,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).

tff(fact_327_xt1_I7_J,axiom,
    ! [Z_1: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Z_1),X_2)) ) ) ).

tff(fact_328_xt1_I7_J,axiom,
    ! [Z_4: nat,Y_5: nat,X_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_5),X_5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_4),Y_5))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_4),X_5)) ) ) ).

tff(fact_329_xt1_I7_J,axiom,
    ! [Z_1: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ) ).

tff(fact_330_order__le__less__trans,axiom,
    ! [Z_1: fun_nat_bool,X_2: fun_nat_bool,Y_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,X_2),Z_1)) ) ) ).

tff(fact_331_order__le__less__trans,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Y_2),Z_1))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,X_2),Z_1)) ) ) ).

tff(fact_332_order__le__less__trans,axiom,
    ! [Z_1: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,X_2),Y_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Y_2),Z_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,X_2),Z_1)) ) ) ).

tff(fact_333_order__le__less__trans,axiom,
    ! [Z_3: nat,X_4: nat,Y_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),Z_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Z_3)) ) ) ).

tff(fact_334_order__le__less__trans,axiom,
    ! [Z_1: bool,X_2: bool,Y_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,X_2),Y_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Y_2),Z_1))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,X_2),Z_1)) ) ) ).

tff(fact_335_xt1_I8_J,axiom,
    ! [Z_1: fun_nat_bool,Y_2: fun_nat_bool,X_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,Z_1),X_2)) ) ) ).

tff(fact_336_xt1_I8_J,axiom,
    ! [Z_1: fun_Pr1643180309t_bool,Y_2: fun_Pr1643180309t_bool,X_2: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),Y_2))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,Z_1),X_2)) ) ) ).

tff(fact_337_xt1_I8_J,axiom,
    ! [Z_1: fun_Ar552120407i_bool,Y_2: fun_Ar552120407i_bool,X_2: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Y_2),X_2))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Z_1),Y_2))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,Z_1),X_2)) ) ) ).

tff(fact_338_xt1_I8_J,axiom,
    ! [Z_2: nat,Y_3: nat,X_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_3)) ) ) ).

tff(fact_339_xt1_I8_J,axiom,
    ! [Z_1: bool,Y_2: bool,X_2: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Y_2),X_2))
     => ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),Y_2))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Z_1),X_2)) ) ) ).

tff(fact_340_top__greatest,axiom,
    ! [Aa: bool] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,Aa),top_top_bool)) ).

tff(fact_341_top__greatest,axiom,
    ! [Aa: fun_fu1015689055l_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,Aa),top_to1690334693l_bool)) ).

tff(fact_342_top__greatest,axiom,
    ! [Aa: fun_fu1138137687l_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,Aa),top_to2013953873l_bool)) ).

tff(fact_343_top__greatest,axiom,
    ! [Aa: fun_fu775006535l_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,Aa),top_to1324311617l_bool)) ).

tff(fact_344_top__greatest,axiom,
    ! [Aa: fun_Pr1055212137t_bool] : hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,Aa),top_to126038883t_bool)) ).

tff(fact_345_top__greatest,axiom,
    ! [Aa: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Aa),top_top_fun_nat_bool)) ).

tff(fact_346_top__greatest,axiom,
    ! [Aa: fun_Pr1643180309t_bool] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,Aa),top_to1257323279t_bool)) ).

tff(fact_347_top__greatest,axiom,
    ! [Aa: fun_Ar552120407i_bool] : hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,Aa),top_to1678393681i_bool)) ).

tff(fact_348_top__unique,axiom,
    ! [Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
    <=> ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ) ).

tff(fact_349_top__unique,axiom,
    ! [Aa: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,top_to1690334693l_bool),Aa))
    <=> ( Aa = top_to1690334693l_bool ) ) ).

tff(fact_350_top__unique,axiom,
    ! [Aa: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,top_to2013953873l_bool),Aa))
    <=> ( Aa = top_to2013953873l_bool ) ) ).

tff(fact_351_top__unique,axiom,
    ! [Aa: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,top_to1324311617l_bool),Aa))
    <=> ( Aa = top_to1324311617l_bool ) ) ).

tff(fact_352_top__unique,axiom,
    ! [Aa: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,top_to126038883t_bool),Aa))
    <=> ( Aa = top_to126038883t_bool ) ) ).

tff(fact_353_top__unique,axiom,
    ! [Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
    <=> ( Aa = top_top_fun_nat_bool ) ) ).

tff(fact_354_top__unique,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
    <=> ( Aa = top_to1257323279t_bool ) ) ).

tff(fact_355_top__unique,axiom,
    ! [Aa: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,top_to1678393681i_bool),Aa))
    <=> ( Aa = top_to1678393681i_bool ) ) ).

tff(fact_356_top__le,axiom,
    ! [Aa: bool] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,top_top_bool),Aa))
     => ( hBOOL(Aa)
      <=> hBOOL(top_top_bool) ) ) ).

tff(fact_357_top__le,axiom,
    ! [Aa: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,top_to1690334693l_bool),Aa))
     => ( Aa = top_to1690334693l_bool ) ) ).

tff(fact_358_top__le,axiom,
    ! [Aa: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,top_to2013953873l_bool),Aa))
     => ( Aa = top_to2013953873l_bool ) ) ).

tff(fact_359_top__le,axiom,
    ! [Aa: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,top_to1324311617l_bool),Aa))
     => ( Aa = top_to1324311617l_bool ) ) ).

tff(fact_360_top__le,axiom,
    ! [Aa: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,top_to126038883t_bool),Aa))
     => ( Aa = top_to126038883t_bool ) ) ).

tff(fact_361_top__le,axiom,
    ! [Aa: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,top_top_fun_nat_bool),Aa))
     => ( Aa = top_top_fun_nat_bool ) ) ).

tff(fact_362_top__le,axiom,
    ! [Aa: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,top_to1257323279t_bool),Aa))
     => ( Aa = top_to1257323279t_bool ) ) ).

tff(fact_363_top__le,axiom,
    ! [Aa: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,top_to1678393681i_bool),Aa))
     => ( Aa = top_to1678393681i_bool ) ) ).

tff(fact_364_inj__on__def,axiom,
    ! [F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
    <=> ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ! [Xa: nat] :
              ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Xa),A))
             => ( ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Xa) )
               => ( X_1 = Xa ) ) ) ) ) ).

tff(fact_365_inj__on__def,axiom,
    ! [F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
    <=> ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => ! [Xa: arrow_2115524757e_indi] :
              ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Xa),A))
             => ( ( hAPP_A1450069362di_nat(F,X_1) = hAPP_A1450069362di_nat(F,Xa) )
               => ( X_1 = Xa ) ) ) ) ) ).

tff(fact_366_inj__on__contraD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( ( X_2 != Y_2 )
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => ( hAPP_nat_nat(F,X_2) != hAPP_nat_nat(F,Y_2) ) ) ) ) ) ).

tff(fact_367_inj__on__contraD,axiom,
    ! [X_2: arrow_2115524757e_indi,Y_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
     => ( ( X_2 != Y_2 )
       => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
         => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_2),A))
           => ( hAPP_A1450069362di_nat(F,X_2) != hAPP_A1450069362di_nat(F,Y_2) ) ) ) ) ) ).

tff(fact_368_inj__on__iff,axiom,
    ! [Y_2: nat,X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
         => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
          <=> ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_369_inj__on__iff,axiom,
    ! [Y_2: arrow_2115524757e_indi,X_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_2),A))
         => ( ( hAPP_A1450069362di_nat(F,X_2) = hAPP_A1450069362di_nat(F,Y_2) )
          <=> ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_370_inj__onD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_2),A))
           => ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_371_inj__onD,axiom,
    ! [X_2: arrow_2115524757e_indi,Y_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
     => ( ( hAPP_A1450069362di_nat(F,X_2) = hAPP_A1450069362di_nat(F,Y_2) )
       => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
         => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_2),A))
           => ( X_2 = Y_2 ) ) ) ) ) ).

tff(fact_372_Pi__mem,axiom,
    ! [X_2: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,B)))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),hAPP_P1830623733l_bool(B,X_2))) ) ) ).

tff(fact_373_Pi__mem,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool,B: fun_Ar1198543961l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,B)))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),hAPP_A1279849719l_bool(B,X_2))) ) ) ).

tff(fact_374_Pi__mem,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A: fun_fu775006535l_bool,B: fun_fu787660105l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,B)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),hAPP_f1498158055l_bool(B,X_2))) ) ) ).

tff(fact_375_Prof__def,axiom,
    arrow_1190054106e_Prof = pi_Arr487970267t_bool(top_to1678393681i_bool,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,arrow_915577424le_Lin)) ).

tff(fact_376_inj__on__id2,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(cOMBI_nat),A)) ).

tff(fact_377_funcset__mem,axiom,
    ! [X_2: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),B)) ) ) ).

tff(fact_378_funcset__mem,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),B)) ) ) ).

tff(fact_379_funcset__mem,axiom,
    ! [X_2: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A: fun_fu775006535l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),B)) ) ) ).

tff(fact_380_dictator__def,axiom,
    ! [Fa: fun_fu1595299477t_bool,I_1: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_A1888055029i_bool(hAPP_f740807359i_bool(arrow_1472924909ctator,Fa),I_1))
    <=> ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),arrow_1190054106e_Prof))
         => ( hAPP_f792184801t_bool(Fa,X_1) = hAPP_A1174518481t_bool(X_1,I_1) ) ) ) ).

tff(fact_381_inj__eq,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_382_inj__eq,axiom,
    ! [X_2: arrow_2115524757e_indi,Y_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool))
     => ( ( hAPP_A1450069362di_nat(F,X_2) = hAPP_A1450069362di_nat(F,Y_2) )
      <=> ( X_2 = Y_2 ) ) ) ).

tff(fact_383_injD,axiom,
    ! [X_2: nat,Y_2: nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ( hAPP_nat_nat(F,X_2) = hAPP_nat_nat(F,Y_2) )
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_384_injD,axiom,
    ! [X_2: arrow_2115524757e_indi,Y_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool))
     => ( ( hAPP_A1450069362di_nat(F,X_2) = hAPP_A1450069362di_nat(F,Y_2) )
       => ( X_2 = Y_2 ) ) ) ).

tff(fact_385_inv__into__f__f,axiom,
    ! [X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( hAPP_nat_nat(hilber195283148at_nat(A,F),hAPP_nat_nat(F,X_2)) = X_2 ) ) ) ).

tff(fact_386_inv__into__f__f,axiom,
    ! [X_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => ( hAPP_n1048492170e_indi(hilber506087739di_nat(A,F),hAPP_A1450069362di_nat(F,X_2)) = X_2 ) ) ) ).

tff(fact_387_inv__into__f__eq,axiom,
    ! [Y_2: nat,X_2: nat,F: fun_nat_nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => ( ( hAPP_nat_nat(F,X_2) = Y_2 )
         => ( hAPP_nat_nat(hilber195283148at_nat(A,F),Y_2) = X_2 ) ) ) ) ).

tff(fact_388_inv__into__f__eq,axiom,
    ! [Y_2: nat,X_2: arrow_2115524757e_indi,F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => ( ( hAPP_A1450069362di_nat(F,X_2) = Y_2 )
         => ( hAPP_n1048492170e_indi(hilber506087739di_nat(A,F),Y_2) = X_2 ) ) ) ) ).

tff(fact_389_Pi__I,axiom,
    ! [F: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,A: fun_Pr1055212137t_bool] :
      ( ! [X_1: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),hAPP_P1830623733l_bool(B,X_1))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,B))) ) ).

tff(fact_390_Pi__I,axiom,
    ! [F: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),hAPP_A1279849719l_bool(B,X_1))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,B))) ) ).

tff(fact_391_Pi__I,axiom,
    ! [F: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,A: fun_fu775006535l_bool] :
      ( ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),hAPP_f1498158055l_bool(B,X_1))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,B))) ) ).

tff(fact_392_inj__imp__inv__eq,axiom,
    ! [G: fun_nat_nat,F: fun_nat_nat] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool))
     => ( ! [X_1: nat] : hAPP_nat_nat(F,hAPP_nat_nat(G,X_1)) = X_1
       => ( hilber195283148at_nat(top_top_fun_nat_bool,F) = G ) ) ) ).

tff(fact_393_inj__imp__inv__eq,axiom,
    ! [G: fun_na1392860600e_indi,F: fun_Ar1744566822di_nat] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool))
     => ( ! [X_1: nat] : hAPP_A1450069362di_nat(F,hAPP_n1048492170e_indi(G,X_1)) = X_1
       => ( hilber506087739di_nat(top_to1678393681i_bool,F) = G ) ) ) ).

tff(fact_394_less__add__one,axiom,
    ! [A_19: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_19),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_19),one_one_nat))) ).

tff(fact_395_add__less__le__mono,axiom,
    ! [C_16: nat,D_3: nat,A_18: nat,B_16: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_18),B_16))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_16),D_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_18),C_16)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_16),D_3))) ) ) ).

tff(fact_396_add__le__less__mono,axiom,
    ! [C_15: nat,D_2: nat,A_17: nat,B_15: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),B_15))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_15),D_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_17),C_15)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_15),D_2))) ) ) ).

tff(fact_397_injI,axiom,
    ! [F: fun_nat_nat] :
      ( ! [X_1: nat,Y_1: nat] :
          ( ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) )
         => ( X_1 = Y_1 ) )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),top_top_fun_nat_bool)) ) ).

tff(fact_398_injI,axiom,
    ! [F: fun_Ar1744566822di_nat] :
      ( ! [X_1: arrow_2115524757e_indi,Y_1: arrow_2115524757e_indi] :
          ( ( hAPP_A1450069362di_nat(F,X_1) = hAPP_A1450069362di_nat(F,Y_1) )
         => ( X_1 = Y_1 ) )
     => hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),top_to1678393681i_bool)) ) ).

tff(fact_399_less__fun__def,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,F),G))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,G),F)) ) ) ).

tff(fact_400_less__fun__def,axiom,
    ! [F: fun_Pr1643180309t_bool,G: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,F),G))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,F),G))
        & ~ hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,G),F)) ) ) ).

tff(fact_401_less__fun__def,axiom,
    ! [F: fun_Ar552120407i_bool,G: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,F),G))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,F),G))
        & ~ hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,G),F)) ) ) ).

tff(fact_402_Pi__anti__mono,axiom,
    ! [B: fun_Pr359894313l_bool,A_16: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A_16),A))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,pi_Pro226591613t_bool(A,B)),pi_Pro226591613t_bool(A_16,B))) ) ).

tff(fact_403_Pi__anti__mono,axiom,
    ! [B: fun_Ar1198543961l_bool,A_16: fun_Ar552120407i_bool,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A_16),A))
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,pi_Arr487970267t_bool(A,B)),pi_Arr487970267t_bool(A_16,B))) ) ).

tff(fact_404_Pi__anti__mono,axiom,
    ! [B: fun_fu787660105l_bool,A_16: fun_fu775006535l_bool,A: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A_16),A))
     => hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,pi_fun530160875t_bool(A,B)),pi_fun530160875t_bool(A_16,B))) ) ).

tff(fact_405_pred__subset__eq2,axiom,
    ! [R_1: fun_Pr1055212137t_bool,S_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1733046827l_bool(hAPP_f2062231615l_bool(ord_le1254553345t_bool,hAPP_f1810968607t_bool(hAPP_f15758621t_bool(cOMBC_1947566172t_bool,hAPP_f1435501085t_bool(cOMBB_1430402568le_alt(cOMBC_571858149l_bool),hAPP_f1176598245l_bool(cOMBB_1605735744le_alt(cOMBB_480104238le_alt(member553230100le_alt)),produc362059031le_alt))),R_1)),hAPP_f1810968607t_bool(hAPP_f15758621t_bool(cOMBC_1947566172t_bool,hAPP_f1435501085t_bool(cOMBB_1430402568le_alt(cOMBC_571858149l_bool),hAPP_f1176598245l_bool(cOMBB_1605735744le_alt(cOMBB_480104238le_alt(member553230100le_alt)),produc362059031le_alt))),S_1)))
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,R_1),S_1)) ) ).

tff(fact_406_subset__UNIV,axiom,
    ! [A: fun_fu1015689055l_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),top_to1690334693l_bool)) ).

tff(fact_407_subset__UNIV,axiom,
    ! [A: fun_fu1138137687l_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),top_to2013953873l_bool)) ).

tff(fact_408_subset__UNIV,axiom,
    ! [A: fun_fu775006535l_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),top_to1324311617l_bool)) ).

tff(fact_409_subset__UNIV,axiom,
    ! [A: fun_Pr1055212137t_bool] : hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),top_to126038883t_bool)) ).

tff(fact_410_subset__UNIV,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),top_top_fun_nat_bool)) ).

tff(fact_411_subset__UNIV,axiom,
    ! [A: fun_Pr1643180309t_bool] : hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),top_to1257323279t_bool)) ).

tff(fact_412_subset__UNIV,axiom,
    ! [A: fun_Ar552120407i_bool] : hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),top_to1678393681i_bool)) ).

tff(fact_413_subset__inj__on,axiom,
    ! [A: fun_nat_bool,F: fun_nat_nat,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ) ).

tff(fact_414_subset__inj__on,axiom,
    ! [A: fun_Ar552120407i_bool,F: fun_Ar1744566822di_nat,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
       => hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A)) ) ) ).

tff(fact_415_add__right__imp__eq,axiom,
    ! [B_14: nat,A_15: nat,C_14: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),A_15) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_14),A_15) )
     => ( B_14 = C_14 ) ) ).

tff(fact_416_add__imp__eq,axiom,
    ! [A_14: nat,B_13: nat,C_13: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_14),C_13) )
     => ( B_13 = C_13 ) ) ).

tff(fact_417_add__left__imp__eq,axiom,
    ! [A_13: nat,B_12: nat,C_12: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),C_12) )
     => ( B_12 = C_12 ) ) ).

tff(fact_418_add__right__cancel,axiom,
    ! [Ba: nat,Aa: nat,Ca: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Aa) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa) )
    <=> ( Ba = Ca ) ) ).

tff(fact_419_add__left__cancel,axiom,
    ! [Aa: nat,Ba: nat,Ca: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ba) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca) )
    <=> ( Ba = Ca ) ) ).

tff(fact_420_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_12: nat,B_11: nat,C_11: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_11)),C_11) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),C_11)) ).

tff(fact_421_one__reorient,axiom,
    ! [X_2: nat] :
      ( ( one_one_nat = X_2 )
    <=> ( X_2 = one_one_nat ) ) ).

tff(fact_422_add__le__imp__le__left,axiom,
    ! [C_10: nat,A_11: nat,B_10: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),A_11)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_10),B_10)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_11),B_10)) ) ).

tff(fact_423_add__le__imp__le__right,axiom,
    ! [A_10: nat,C_9: nat,B_9: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_10),C_9)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_9),C_9)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_10),B_9)) ) ).

tff(fact_424_add__mono,axiom,
    ! [C_8: nat,D_1: nat,A_9: nat,B_8: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_8))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_8),D_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_1))) ) ) ).

tff(fact_425_add__left__mono,axiom,
    ! [C_7: nat,A_8: nat,B_7: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_7))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),B_7))) ) ).

tff(fact_426_add__right__mono,axiom,
    ! [C_6: nat,A_7: nat,B_6: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_6))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_6),C_6))) ) ).

tff(fact_427_add__le__cancel__left,axiom,
    ! [Ca: nat,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).

tff(fact_428_add__le__cancel__right,axiom,
    ! [Aa: nat,Ca: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Aa),Ba)) ) ).

tff(fact_429_add__less__imp__less__left,axiom,
    ! [C_5: nat,A_6: nat,B_5: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),A_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_5),B_5)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_5)) ) ).

tff(fact_430_add__less__imp__less__right,axiom,
    ! [A_5: nat,C_4: nat,B_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_5),C_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_4),C_4)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_5),B_4)) ) ).

tff(fact_431_add__strict__mono,axiom,
    ! [C_3: nat,D: nat,A_4: nat,B_3: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),B_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),D))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_4),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D))) ) ) ).

tff(fact_432_add__strict__left__mono,axiom,
    ! [C_2: nat,A_3: nat,B_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),A_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_2),B_2))) ) ).

tff(fact_433_add__strict__right__mono,axiom,
    ! [C_1: nat,A_2: nat,B_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_1),C_1))) ) ).

tff(fact_434_add__less__cancel__left,axiom,
    ! [Ca: nat,Aa: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Aa)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ca),Ba)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).

tff(fact_435_add__less__cancel__right,axiom,
    ! [Aa: nat,Ca: nat,Ba: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Aa),Ca)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Ba),Ca)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Aa),Ba)) ) ).

tff(fact_436_le__funI,axiom,
    ! [F: fun_nat_bool,G: fun_nat_bool] :
      ( ! [X_1: nat] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G,X_1)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G)) ) ).

tff(fact_437_equalityI,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
       => ( A = B ) ) ) ).

tff(fact_438_subsetD,axiom,
    ! [Ca: bool,A: fun_bool_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ) ).

tff(fact_439_subsetD,axiom,
    ! [Ca: product_unit,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ) ).

tff(fact_440_subsetD,axiom,
    ! [Ca: arrow_2115524757e_indi,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Ca),A))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Ca),B)) ) ) ).

tff(fact_441_subsetD,axiom,
    ! [Ca: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ) ).

tff(fact_442_subsetD,axiom,
    ! [Ca: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),B))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Ca),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Ca),B)) ) ) ).

tff(fact_443_subsetD,axiom,
    ! [Ca: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),B))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Ca),A))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Ca),B)) ) ) ).

tff(fact_444_subsetD,axiom,
    ! [Ca: fun_Ar500372357t_bool,A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),B))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Ca),A))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Ca),B)) ) ) ).

tff(fact_445_subsetD,axiom,
    ! [Ca: produc1840315303le_alt,A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),B))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Ca),A))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Ca),B)) ) ) ).

tff(fact_446_psubset__eq,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_447_psubset__eq,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_448_psubset__eq,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
        & ( A != B ) ) ) ).

tff(fact_449_subset__iff__psubset__eq,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_450_subset__iff__psubset__eq,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
    <=> ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_451_subset__iff__psubset__eq,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
    <=> ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
        | ( A = B ) ) ) ).

tff(fact_452_psubset__imp__subset,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).

tff(fact_453_psubset__imp__subset,axiom,
    ! [A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ).

tff(fact_454_psubset__imp__subset,axiom,
    ! [A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
     => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B)) ) ).

tff(fact_455_psubset__subset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).

tff(fact_456_psubset__subset__trans,axiom,
    ! [C: fun_Pr1643180309t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).

tff(fact_457_psubset__subset__trans,axiom,
    ! [C: fun_Ar552120407i_bool,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,B),C))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),C)) ) ) ).

tff(fact_458_subset__psubset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).

tff(fact_459_subset__psubset__trans,axiom,
    ! [C: fun_Pr1643180309t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).

tff(fact_460_subset__psubset__trans,axiom,
    ! [C: fun_Ar552120407i_bool,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,B),C))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),C)) ) ) ).

tff(fact_461_equalityE,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).

tff(fact_462_subset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ) ).

tff(fact_463_set__mp,axiom,
    ! [X_2: bool,A: fun_bool_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).

tff(fact_464_set__mp,axiom,
    ! [X_2: product_unit,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).

tff(fact_465_set__mp,axiom,
    ! [X_2: arrow_2115524757e_indi,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),B)) ) ) ).

tff(fact_466_set__mp,axiom,
    ! [X_2: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_467_set__mp,axiom,
    ! [X_2: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),B))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),B)) ) ) ).

tff(fact_468_set__mp,axiom,
    ! [X_2: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),B))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),B)) ) ) ).

tff(fact_469_set__mp,axiom,
    ! [X_2: fun_Ar500372357t_bool,A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),B))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),B)) ) ) ).

tff(fact_470_set__mp,axiom,
    ! [X_2: produc1840315303le_alt,A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),B))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),B)) ) ) ).

tff(fact_471_set__rev__mp,axiom,
    ! [B: fun_bool_bool,X_2: bool,A: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).

tff(fact_472_set__rev__mp,axiom,
    ! [B: fun_Pr1643180309t_bool,X_2: product_unit,A: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).

tff(fact_473_set__rev__mp,axiom,
    ! [B: fun_Ar552120407i_bool,X_2: arrow_2115524757e_indi,A: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),B)) ) ) ).

tff(fact_474_set__rev__mp,axiom,
    ! [B: fun_nat_bool,X_2: nat,A: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_475_set__rev__mp,axiom,
    ! [B: fun_fu1015689055l_bool,X_2: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),B))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),B)) ) ) ).

tff(fact_476_set__rev__mp,axiom,
    ! [B: fun_fu1138137687l_bool,X_2: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),B))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),B)) ) ) ).

tff(fact_477_set__rev__mp,axiom,
    ! [B: fun_fu775006535l_bool,X_2: fun_Ar500372357t_bool,A: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),B))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),B)) ) ) ).

tff(fact_478_set__rev__mp,axiom,
    ! [B: fun_Pr1055212137t_bool,X_2: produc1840315303le_alt,A: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),B))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),B)) ) ) ).

tff(fact_479_predicate1D,axiom,
    ! [X_2: nat,Pa: fun_nat_bool,Q_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
     => ( hBOOL(hAPP_nat_bool(Pa,X_2))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).

tff(fact_480_in__mono,axiom,
    ! [X_2: bool,A: fun_bool_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),B)) ) ) ).

tff(fact_481_in__mono,axiom,
    ! [X_2: product_unit,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_2),B)) ) ) ).

tff(fact_482_in__mono,axiom,
    ! [X_2: arrow_2115524757e_indi,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),B)) ) ) ).

tff(fact_483_in__mono,axiom,
    ! [X_2: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).

tff(fact_484_in__mono,axiom,
    ! [X_2: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),B))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),B)) ) ) ).

tff(fact_485_in__mono,axiom,
    ! [X_2: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),B))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),B)) ) ) ).

tff(fact_486_in__mono,axiom,
    ! [X_2: fun_Ar500372357t_bool,A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),B))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),B)) ) ) ).

tff(fact_487_in__mono,axiom,
    ! [X_2: produc1840315303le_alt,A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),B))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),B)) ) ) ).

tff(fact_488_equalityD2,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ).

tff(fact_489_equalityD1,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).

tff(fact_490_rev__predicate1D,axiom,
    ! [Q_1: fun_nat_bool,Pa: fun_nat_bool,X_2: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,X_2))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Pa),Q_1))
       => hBOOL(hAPP_nat_bool(Q_1,X_2)) ) ) ).

tff(fact_491_set__eq__subset,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).

tff(fact_492_subset__refl,axiom,
    ! [A: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)) ).

tff(fact_493_pred__subset__eq,axiom,
    ! [R_1: fun_bool_bool,S_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),R_1)),hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,member_bool),S_1)))
    <=> hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,R_1),S_1)) ) ).

tff(fact_494_pred__subset__eq,axiom,
    ! [R_1: fun_Pr1643180309t_bool,S_1: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),R_1)),hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,member_Product_unit),S_1)))
    <=> hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,R_1),S_1)) ) ).

tff(fact_495_pred__subset__eq,axiom,
    ! [R_1: fun_Ar552120407i_bool,S_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,hAPP_f1282576021i_bool(hAPP_f833264203i_bool(cOMBC_31215906l_bool,member590466050e_indi),R_1)),hAPP_f1282576021i_bool(hAPP_f833264203i_bool(cOMBC_31215906l_bool,member590466050e_indi),S_1)))
    <=> hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,R_1),S_1)) ) ).

tff(fact_496_pred__subset__eq,axiom,
    ! [R_1: fun_nat_bool,S_1: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),R_1)),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),S_1)))
    <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,R_1),S_1)) ) ).

tff(fact_497_pred__subset__eq,axiom,
    ! [R_1: fun_fu1015689055l_bool,S_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,hAPP_f1050277569l_bool(hAPP_f639477379l_bool(cOMBC_437066390l_bool,member57118396t_bool),R_1)),hAPP_f1050277569l_bool(hAPP_f639477379l_bool(cOMBC_437066390l_bool,member57118396t_bool),S_1)))
    <=> hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,R_1),S_1)) ) ).

tff(fact_498_pred__subset__eq,axiom,
    ! [R_1: fun_fu1138137687l_bool,S_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,hAPP_f1077478037l_bool(hAPP_f230252107l_bool(cOMBC_1452216610l_bool,member1801442306t_bool),R_1)),hAPP_f1077478037l_bool(hAPP_f230252107l_bool(cOMBC_1452216610l_bool,member1801442306t_bool),S_1)))
    <=> hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,R_1),S_1)) ) ).

tff(fact_499_pred__subset__eq,axiom,
    ! [R_1: fun_fu775006535l_bool,S_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,hAPP_f626396309l_bool(hAPP_f228579435l_bool(cOMBC_941833506l_bool,member1159072754t_bool),R_1)),hAPP_f626396309l_bool(hAPP_f228579435l_bool(cOMBC_941833506l_bool,member1159072754t_bool),S_1)))
    <=> hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,R_1),S_1)) ) ).

tff(fact_500_pred__subset__eq,axiom,
    ! [R_1: fun_Pr1055212137t_bool,S_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,hAPP_f70231061t_bool(hAPP_f46399911t_bool(cOMBC_697226658l_bool,member553230100le_alt),R_1)),hAPP_f70231061t_bool(hAPP_f46399911t_bool(cOMBC_697226658l_bool,member553230100le_alt),S_1)))
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,R_1),S_1)) ) ).

tff(fact_501_Pi__mono,axiom,
    ! [B: fun_Pr359894313l_bool,C: fun_Pr359894313l_bool,A: fun_Pr1055212137t_bool] :
      ( ! [X_1: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,hAPP_P1830623733l_bool(B,X_1)),hAPP_P1830623733l_bool(C,X_1))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,pi_Pro226591613t_bool(A,B)),pi_Pro226591613t_bool(A,C))) ) ).

tff(fact_502_Pi__mono,axiom,
    ! [B: fun_Ar1198543961l_bool,C: fun_Ar1198543961l_bool,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,hAPP_A1279849719l_bool(B,X_1)),hAPP_A1279849719l_bool(C,X_1))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,pi_Arr487970267t_bool(A,B)),pi_Arr487970267t_bool(A,C))) ) ).

tff(fact_503_Pi__mono,axiom,
    ! [B: fun_fu787660105l_bool,C: fun_fu787660105l_bool,A: fun_fu775006535l_bool] :
      ( ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,hAPP_f1498158055l_bool(B,X_1)),hAPP_f1498158055l_bool(C,X_1))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,pi_fun530160875t_bool(A,B)),pi_fun530160875t_bool(A,C))) ) ).

tff(fact_504_subsetI,axiom,
    ! [B: fun_bool_bool,A: fun_bool_bool] :
      ( ! [X_1: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),B)) )
     => hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le742797417l_bool,A),B)) ) ).

tff(fact_505_subsetI,axiom,
    ! [B: fun_Pr1643180309t_bool,A: fun_Pr1643180309t_bool] :
      ( ! [X_1: product_unit] :
          ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),A))
         => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,X_1),B)) )
     => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1874503007t_bool,A),B)) ) ).

tff(fact_506_subsetI,axiom,
    ! [B: fun_Ar552120407i_bool,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),B)) )
     => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le351904673i_bool,A),B)) ) ).

tff(fact_507_subsetI,axiom,
    ! [B: fun_nat_bool,A: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).

tff(fact_508_subsetI,axiom,
    ! [B: fun_fu1015689055l_bool,A: fun_fu1015689055l_bool] :
      ( ! [X_1: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),B)) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le1923264405l_bool,A),B)) ) ).

tff(fact_509_subsetI,axiom,
    ! [B: fun_fu1138137687l_bool,A: fun_fu1138137687l_bool] :
      ( ! [X_1: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),B)) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le161055137l_bool,A),B)) ) ).

tff(fact_510_subsetI,axiom,
    ! [B: fun_fu775006535l_bool,A: fun_fu775006535l_bool] :
      ( ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),B)) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le1871091345l_bool,A),B)) ) ).

tff(fact_511_subsetI,axiom,
    ! [B: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool] :
      ( ! [X_1: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),B)) )
     => hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le565024179t_bool,A),B)) ) ).

tff(fact_512_psubsetD,axiom,
    ! [Ca: bool,A: fun_bool_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_f612708895l_bool(ord_le197158773l_bool,A),B))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),A))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Ca),B)) ) ) ).

tff(fact_513_psubsetD,axiom,
    ! [Ca: product_unit,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),A))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_P607165281l_bool(member_Product_unit,Ca),B)) ) ) ).

tff(fact_514_psubsetD,axiom,
    ! [Ca: arrow_2115524757e_indi,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Ca),A))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Ca),B)) ) ) ).

tff(fact_515_psubsetD,axiom,
    ! [Ca: nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Ca),B)) ) ) ).

tff(fact_516_psubsetD,axiom,
    ! [Ca: fun_Pr1055212137t_bool,A: fun_fu1015689055l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f868566847l_bool(ord_le2104736649l_bool,A),B))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Ca),A))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Ca),B)) ) ) ).

tff(fact_517_psubsetD,axiom,
    ! [Ca: fun_fu1595299477t_bool,A: fun_fu1138137687l_bool,B: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f173704847l_bool(ord_le1306091181l_bool,A),B))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Ca),A))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Ca),B)) ) ) ).

tff(fact_518_psubsetD,axiom,
    ! [Ca: fun_Ar500372357t_bool,A: fun_fu775006535l_bool,B: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f95487087l_bool(ord_le583255965l_bool,A),B))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Ca),A))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Ca),B)) ) ) ).

tff(fact_519_psubsetD,axiom,
    ! [Ca: produc1840315303le_alt,A: fun_Pr1055212137t_bool,B: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(ord_le466311871t_bool,A),B))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Ca),A))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Ca),B)) ) ) ).

tff(fact_520_psubset__trans,axiom,
    ! [C: fun_nat_bool,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),C)) ) ) ).

tff(fact_521_psubset__trans,axiom,
    ! [C: fun_Pr1643180309t_bool,A: fun_Pr1643180309t_bool,B: fun_Pr1643180309t_bool] :
      ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),B))
     => ( hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,B),C))
       => hBOOL(hAPP_f2028818269l_bool(hAPP_f272527115l_bool(ord_le1976645739t_bool,A),C)) ) ) ).

tff(fact_522_psubset__trans,axiom,
    ! [C: fun_Ar552120407i_bool,A: fun_Ar552120407i_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),B))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,B),C))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_f1938592399l_bool(ord_le1115695277i_bool,A),C)) ) ) ).

tff(fact_523_in__below,axiom,
    ! [X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_3: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
       => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),arrow_636638768_below(L_3,Aa,Ba)))
        <=> ( ( X_2 != Y_2 )
            & ( ( Y_2 = Aa )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Ba)),L_3)) )
            & ( ( Y_2 != Aa )
             => ( ( ( X_2 = Aa )
                 => ( ( Y_2 = Ba )
                    | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Y_2)),L_3)) ) )
                & ( ( X_2 != Aa )
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),L_3)) ) ) ) ) ) ) ) ).

tff(fact_524_add__leE,axiom,
    ! [M_2: nat,K_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ) ).

tff(fact_525_add__leD1,axiom,
    ! [M_2: nat,K_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).

tff(fact_526_add__leD2,axiom,
    ! [M_2: nat,K_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1)) ) ).

tff(fact_527_less__not__refl,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).

tff(fact_528_nat__neq__iff,axiom,
    ! [M_4: nat,Na: nat] :
      ( ( M_4 != Na )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4)) ) ) ).

tff(fact_529_linorder__neqE__nat,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).

tff(fact_530_less__irrefl__nat,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).

tff(fact_531_less__not__refl2,axiom,
    ! [N_1: nat,M_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
     => ( M_2 != N_1 ) ) ).

tff(fact_532_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => ( S != T ) ) ).

tff(fact_533_nat__less__cases,axiom,
    ! [Pa: fun_nat_fun_nat_bool,M_4: nat,Na: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
     => ( ( ( M_4 = Na )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M_4)) ) ) ) ).

tff(fact_534_nat__add__commute,axiom,
    ! [M_2: nat,N_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2) ).

tff(fact_535_nat__add__left__commute,axiom,
    ! [X: nat,Y: nat,Z: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)) ).

tff(fact_536_nat__add__assoc,axiom,
    ! [M_2: nat,N_1: nat,K_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),K_1)) ).

tff(fact_537_nat__add__left__cancel,axiom,
    ! [K: nat,M_4: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) )
    <=> ( M_4 = Na ) ) ).

tff(fact_538_nat__add__right__cancel,axiom,
    ! [M_4: nat,K: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) )
    <=> ( M_4 = Na ) ) ).

tff(fact_539_le__refl,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).

tff(fact_540_nat__le__linear,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) ) ).

tff(fact_541_eq__imp__le,axiom,
    ! [M_2: nat,N_1: nat] :
      ( ( M_2 = N_1 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).

tff(fact_542_le__trans,axiom,
    ! [K_1: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_2),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_1)) ) ) ).

tff(fact_543_le__antisym,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
       => ( M_2 = N_1 ) ) ) ).

tff(fact_544_below__Lin,axiom,
    ! [L_3: fun_Pr1055212137t_bool,X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( ( X_2 != Y_2 )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_3),arrow_915577424le_Lin))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,arrow_636638768_below(L_3,X_2,Y_2)),arrow_915577424le_Lin)) ) ) ).

tff(fact_545_inj__on__add__nat,axiom,
    ! [K: nat,N_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,plus_plus_nat),K)),N_2)) ).

tff(fact_546_not__add__less1,axiom,
    ! [I: nat,J_2: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),I)) ).

tff(fact_547_not__add__less2,axiom,
    ! [J_2: nat,I: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),I)),I)) ).

tff(fact_548_nat__add__left__cancel__less,axiom,
    ! [K: nat,M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).

tff(fact_549_trans__less__add1,axiom,
    ! [M_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ) ).

tff(fact_550_trans__less__add2,axiom,
    ! [M_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ) ).

tff(fact_551_add__less__mono1,axiom,
    ! [K_1: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ) ).

tff(fact_552_add__less__mono,axiom,
    ! [K_1: nat,L_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ) ).

tff(fact_553_less__add__eq__less,axiom,
    ! [M_2: nat,N_1: nat,K_1: nat,L_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_2))
     => ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),L_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N_1) )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ) ).

tff(fact_554_add__lessD1,axiom,
    ! [I: nat,J_2: nat,K_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),J_2)),K_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1)) ) ).

tff(fact_555_nat__less__le,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        & ( M_4 != Na ) ) ) ).

tff(fact_556_le__eq__less__or__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ( M_4 = Na ) ) ) ).

tff(fact_557_less__imp__le__nat,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).

tff(fact_558_le__neq__implies__less,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => ( ( M_2 != N_1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ) ).

tff(fact_559_less__or__eq__imp__le,axiom,
    ! [M_2: nat,N_1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
        | ( M_2 = N_1 ) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).

tff(fact_560_le__add2,axiom,
    ! [N_1: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1))) ).

tff(fact_561_le__add1,axiom,
    ! [N_1: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),M_2))) ).

tff(fact_562_le__iff__add,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> ? [K_2: nat] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2) ) ).

tff(fact_563_nat__add__left__cancel__le,axiom,
    ! [K: nat,M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M_4)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ).

tff(fact_564_trans__le__add1,axiom,
    ! [M_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),M_2))) ) ).

tff(fact_565_trans__le__add2,axiom,
    ! [M_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),J_2))) ) ).

tff(fact_566_add__le__mono1,axiom,
    ! [K_1: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),K_1))) ) ).

tff(fact_567_add__le__mono,axiom,
    ! [K_1: nat,L_2: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_2))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J_2),L_2))) ) ) ).

tff(fact_568_mono__nat__linear__lb,axiom,
    ! [M_4: nat,K: nat,F: fun_nat_nat] :
      ( ! [M: nat,N: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M)),hAPP_nat_nat(F,N))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M_4)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K)))) ) ).

tff(fact_569_less__mono__imp__le__mono,axiom,
    ! [I_1: nat,J_1: nat,F: fun_nat_nat] :
      ( ! [I_2: nat,J: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_1)),hAPP_nat_nat(F,J_1))) ) ) ).

tff(fact_570_termination__basic__simps_I3_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_571_termination__basic__simps_I4_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_572_termination__basic__simps_I2_J,axiom,
    ! [Y: nat,X: nat,Z: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_573_termination__basic__simps_I1_J,axiom,
    ! [Z: nat,X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ) ).

tff(fact_574_termination__basic__simps_I5_J,axiom,
    ! [X: nat,Y: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).

tff(fact_575_in__rel__def,axiom,
    ! [R_1: fun_Pr1055212137t_bool,X_2: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( hBOOL(in_rel267123714le_alt(R_1,X_2,Y_2))
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),R_1)) ) ).

tff(fact_576_funcsetI,axiom,
    ! [F: fun_Pr1055212137t_bool,B: fun_bool_bool,A: fun_Pr1055212137t_bool] :
      ( ! [X_1: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),B)) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B)))) ) ).

tff(fact_577_funcsetI,axiom,
    ! [F: fun_Ar500372357t_bool,B: fun_fu1015689055l_bool,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),B)) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B)))) ) ).

tff(fact_578_funcsetI,axiom,
    ! [F: fun_fu1595299477t_bool,B: fun_fu1015689055l_bool,A: fun_fu775006535l_bool] :
      ( ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),B)) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B)))) ) ).

tff(fact_579_linear__alt,axiom,
    ? [L_1: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin)) ).

tff(fact_580_Pi__cong,axiom,
    ! [B: fun_Pr359894313l_bool,G: fun_Pr1055212137t_bool,F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool] :
      ( ! [W: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,W),A))
         => ( hBOOL(hAPP_P166437127t_bool(F,W))
          <=> hBOOL(hAPP_P166437127t_bool(G,W)) ) )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,B)))
      <=> hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,G),pi_Pro226591613t_bool(A,B))) ) ) ).

tff(fact_581_Pi__cong,axiom,
    ! [B: fun_Ar1198543961l_bool,F: fun_Ar500372357t_bool,G: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool] :
      ( ! [W: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,W),A))
         => ( hAPP_A1174518481t_bool(F,W) = hAPP_A1174518481t_bool(G,W) ) )
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,B)))
      <=> hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,G),pi_Arr487970267t_bool(A,B))) ) ) ).

tff(fact_582_Pi__cong,axiom,
    ! [B: fun_fu787660105l_bool,F: fun_fu1595299477t_bool,G: fun_fu1595299477t_bool,A: fun_fu775006535l_bool] :
      ( ! [W: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,W),A))
         => ( hAPP_f792184801t_bool(F,W) = hAPP_f792184801t_bool(G,W) ) )
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,B)))
      <=> hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,G),pi_fun530160875t_bool(A,B))) ) ) ).

tff(fact_583_Pi__I_H,axiom,
    ! [F: fun_Pr1055212137t_bool,B: fun_Pr359894313l_bool,A: fun_Pr1055212137t_bool] :
      ( ! [X_1: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),hAPP_P1830623733l_bool(B,X_1))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,B))) ) ).

tff(fact_584_Pi__I_H,axiom,
    ! [F: fun_Ar500372357t_bool,B: fun_Ar1198543961l_bool,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),hAPP_A1279849719l_bool(B,X_1))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,B))) ) ).

tff(fact_585_Pi__I_H,axiom,
    ! [F: fun_fu1595299477t_bool,B: fun_fu787660105l_bool,A: fun_fu775006535l_bool] :
      ( ! [X_1: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),hAPP_f1498158055l_bool(B,X_1))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,B))) ) ).

tff(fact_586_card__inj,axiom,
    ! [F: fun_nat_nat,A: fun_nat_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f1426445843l_bool(hAPP_f2040535501l_bool(member_fun_nat_nat,F),pi_nat_nat(A,hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,B))))
     => ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
       => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite_card_nat(A)),finite_card_nat(B))) ) ) ) ).

tff(fact_587_card__inj,axiom,
    ! [F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool,B: fun_nat_bool] :
      ( hBOOL(hAPP_f1290810160l_bool(hAPP_f516936199l_bool(member428554515di_nat,F),pi_Arr159321468di_nat(A,hAPP_f426535095t_bool(cOMBK_2091851729e_indi,B))))
     => ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
       => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite783399747e_indi(A)),finite_card_nat(B))) ) ) ) ).

tff(fact_588_card__inj,axiom,
    ! [F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B))))
     => ( hBOOL(hAPP_f429946033l_bool(inj_on899118883t_bool(F),A))
       => ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite876838485le_alt(A)),finite_card_bool(B))) ) ) ) ).

tff(fact_589_card__inj,axiom,
    ! [F: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B))))
     => ( hBOOL(hAPP_f1397511071l_bool(inj_on194063285t_bool(F),A))
       => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite783399747e_indi(A)),finite1445836347t_bool(B))) ) ) ) ).

tff(fact_590_card__inj,axiom,
    ! [F: fun_fu1595299477t_bool,A: fun_fu775006535l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B))))
     => ( hBOOL(hAPP_f1465510031l_bool(inj_on937360581t_bool(F),A))
       => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,B))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,finite1418900531t_bool(A)),finite1445836347t_bool(B))) ) ) ) ).

tff(fact_591_inj__onI,axiom,
    ! [F: fun_nat_nat,A: fun_nat_bool] :
      ( ! [X_1: nat,Y_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,Y_1),A))
           => ( ( hAPP_nat_nat(F,X_1) = hAPP_nat_nat(F,Y_1) )
             => ( X_1 = Y_1 ) ) ) )
     => hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A)) ) ).

tff(fact_592_inj__onI,axiom,
    ! [F: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( ! [X_1: arrow_2115524757e_indi,Y_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A))
         => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_1),A))
           => ( ( hAPP_A1450069362di_nat(F,X_1) = hAPP_A1450069362di_nat(F,Y_1) )
             => ( X_1 = Y_1 ) ) ) )
     => hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A)) ) ).

tff(fact_593_inj__on__cong,axiom,
    ! [F: fun_nat_nat,G: fun_nat_nat,A: fun_nat_bool] :
      ( ! [A_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
         => ( hAPP_nat_nat(F,A_1) = hAPP_nat_nat(G,A_1) ) )
     => ( hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(F),A))
      <=> hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(G),A)) ) ) ).

tff(fact_594_inj__on__cong,axiom,
    ! [F: fun_Ar1744566822di_nat,G: fun_Ar1744566822di_nat,A: fun_Ar552120407i_bool] :
      ( ! [A_1: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,A_1),A))
         => ( hAPP_A1450069362di_nat(F,A_1) = hAPP_A1450069362di_nat(G,A_1) ) )
     => ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(F),A))
      <=> hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(G),A)) ) ) ).

tff(fact_595_finite__indi,axiom,
    hBOOL(hAPP_f1397511071l_bool(finite1350902018e_indi,top_to1678393681i_bool)) ).

tff(fact_596_card__bij,axiom,
    ! [G: fun_Ar500372357t_bool,F: fun_fu2016509975e_indi,A: fun_fu1015689055l_bool,B: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A,hAPP_f676424105i_bool(cOMBK_854051296t_bool,B))))
     => ( hBOOL(hAPP_f1021703871l_bool(inj_on1048829645e_indi(F),A))
       => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,G),pi_Arr487970267t_bool(B,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,A))))
         => ( hBOOL(hAPP_f1397511071l_bool(inj_on194063285t_bool(G),B))
           => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,A))
             => ( hBOOL(hAPP_f1397511071l_bool(finite1350902018e_indi,B))
               => ( finite1445836347t_bool(A) = finite783399747e_indi(B) ) ) ) ) ) ) ) ).

tff(fact_597_card__bij,axiom,
    ! [G: fun_fu1595299477t_bool,F: fun_fu243393031t_bool,A: fun_fu1015689055l_bool,B: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f2106732305l_bool(hAPP_f2071392713l_bool(member449535860t_bool,F),pi_fun49394147t_bool(A,hAPP_f1197023401l_bool(cOMBK_2140692976t_bool,B))))
     => ( hBOOL(hAPP_f1021703871l_bool(inj_on456593853t_bool(F),A))
       => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,G),pi_fun530160875t_bool(B,hAPP_f422714471l_bool(cOMBK_1446432t_bool,A))))
         => ( hBOOL(hAPP_f1465510031l_bool(inj_on937360581t_bool(G),B))
           => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,A))
             => ( hBOOL(hAPP_f1465510031l_bool(finite1217814770t_bool,B))
               => ( finite1445836347t_bool(A) = finite1418900531t_bool(B) ) ) ) ) ) ) ) ).

tff(fact_598_card__bij,axiom,
    ! [G: fun_bo1479727337le_alt,F: fun_Pr1055212137t_bool,A: fun_Pr1055212137t_bool,B: fun_bool_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B))))
     => ( hBOOL(hAPP_f429946033l_bool(inj_on899118883t_bool(F),A))
       => ( hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,G),pi_boo1374671485le_alt(B,hAPP_f414777105t_bool(cOMBK_382434616l_bool,A))))
         => ( hBOOL(hAPP_f387058535l_bool(inj_on2047198755le_alt(G),B))
           => ( hBOOL(hAPP_f429946033l_bool(finite788329492le_alt,A))
             => ( hBOOL(hAPP_f387058535l_bool(finite_finite_bool,B))
               => ( finite876838485le_alt(A) = finite_card_bool(B) ) ) ) ) ) ) ) ).

tff(fact_599_card__bij,axiom,
    ! [G: fun_fu2016509975e_indi,F: fun_Ar500372357t_bool,A: fun_Ar552120407i_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B))))
     => ( hBOOL(hAPP_f1397511071l_bool(inj_on194063285t_bool(F),A))
       => ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,G),pi_fun1342736627e_indi(B,hAPP_f676424105i_bool(cOMBK_854051296t_bool,A))))
         => ( hBOOL(hAPP_f1021703871l_bool(inj_on1048829645e_indi(G),B))
           => ( hBOOL(hAPP_f1397511071l_bool(finite1350902018e_indi,A))
             => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,B))
               => ( finite783399747e_indi(A) = finite1445836347t_bool(B) ) ) ) ) ) ) ) ).

tff(fact_600_card__bij,axiom,
    ! [G: fun_fu243393031t_bool,F: fun_fu1595299477t_bool,A: fun_fu775006535l_bool,B: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B))))
     => ( hBOOL(hAPP_f1465510031l_bool(inj_on937360581t_bool(F),A))
       => ( hBOOL(hAPP_f2106732305l_bool(hAPP_f2071392713l_bool(member449535860t_bool,G),pi_fun49394147t_bool(B,hAPP_f1197023401l_bool(cOMBK_2140692976t_bool,A))))
         => ( hBOOL(hAPP_f1021703871l_bool(inj_on456593853t_bool(G),B))
           => ( hBOOL(hAPP_f1465510031l_bool(finite1217814770t_bool,A))
             => ( hBOOL(hAPP_f1021703871l_bool(finite775027132t_bool,B))
               => ( finite1418900531t_bool(A) = finite1445836347t_bool(B) ) ) ) ) ) ) ) ).

tff(fact_601_finite__Collect__less__nat,axiom,
    ! [K: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),K)))) ).

tff(fact_602_finite__Collect__le__nat,axiom,
    ! [K: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),K)))) ).

tff(fact_603_card__UNIV__unit,axiom,
    finite1949902593t_unit(top_to1257323279t_bool) = one_one_nat ).

tff(fact_604_card__Collect__less__nat,axiom,
    ! [Na: nat] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),Na))) = Na ).

tff(fact_605_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,top_top_fun_nat_bool)) ).

tff(fact_606_finite__M__bounded__by__nat,axiom,
    ! [Pa: fun_nat_bool,I_1: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),Pa),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) ).

tff(fact_607_finite__nat__set__iff__bounded__le,axiom,
    ! [N_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M: nat] :
        ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ) ).

tff(fact_608_finite__nat__set__iff__bounded,axiom,
    ! [N_2: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M: nat] :
        ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),M)) ) ) ).

tff(fact_609_finite__less__ub,axiom,
    ! [U: nat,F: fun_nat_nat] :
      ( ! [N: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(F,N)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,hAPP_f618557131t_bool(cOMBB_800536526ol_nat(ord_less_eq_nat),F)),U)))) ) ).

tff(fact_610_bounded__nat__set__is__finite,axiom,
    ! [Na: nat,N_2: fun_nat_bool] :
      ( ! [X_1: nat] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Na)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ).

tff(fact_611_less__zeroE,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).

tff(fact_612_le0,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).

tff(fact_613_gr0I,axiom,
    ! [N_1: nat] :
      ( ( N_1 != zero_zero_nat )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ).

tff(fact_614_gr__implies__not0,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => ( N_1 != zero_zero_nat ) ) ).

tff(fact_615_less__nat__zero__code,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).

tff(fact_616_neq0__conv,axiom,
    ! [Na: nat] :
      ( ( Na != zero_zero_nat )
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ).

tff(fact_617_not__less0,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),zero_zero_nat)) ).

tff(fact_618_plus__nat_Oadd__0,axiom,
    ! [N_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N_1) = N_1 ).

tff(fact_619_Nat_Oadd__0__right,axiom,
    ! [M_2: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),zero_zero_nat) = M_2 ).

tff(fact_620_add__is__0,axiom,
    ! [M_4: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = zero_zero_nat )
    <=> ( ( M_4 = zero_zero_nat )
        & ( Na = zero_zero_nat ) ) ) ).

tff(fact_621_add__eq__self__zero,axiom,
    ! [M_2: nat,N_1: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1) = M_2 )
     => ( N_1 = zero_zero_nat ) ) ).

tff(fact_622_le__0__eq,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
    <=> ( Na = zero_zero_nat ) ) ).

tff(fact_623_less__eq__nat_Osimps_I1_J,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N_1)) ).

tff(fact_624_add__gr__0,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_4))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ) ).

tff(fact_625_ex__least__nat__less,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na))
            & ! [I_2: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
            & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat))) ) ) ) ).

tff(fact_626_ex__least__nat__le,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na))
            & ! [I_2: nat] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I_2)) )
            & hBOOL(hAPP_nat_bool(Pa,K_2)) ) ) ) ).

tff(fact_627_less__imp__add__positive,axiom,
    ! [I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ? [K_2: nat] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2))
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),K_2) = J_2 ) ) ) ).

tff(fact_628_lessI,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,N_1))) ).

tff(fact_629_Suc__mono,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1))) ) ).

tff(fact_630_zero__less__Suc,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N_1))) ).

tff(fact_631_Suc__n__not__le__n,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)) ).

tff(fact_632_not__less__eq__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ) ).

tff(fact_633_le__Suc__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
        | ( M_4 = hAPP_nat_nat(suc,Na) ) ) ) ).

tff(fact_634_Suc__le__mono,axiom,
    ! [Na: nat,M_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_4)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_4)) ) ).

tff(fact_635_le__SucI,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).

tff(fact_636_le__SucE,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
       => ( M_2 = hAPP_nat_nat(suc,N_1) ) ) ) ).

tff(fact_637_Suc__leD,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).

tff(fact_638_Suc__inject,axiom,
    ! [X: nat,Y: nat] :
      ( ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y) )
     => ( X = Y ) ) ).

tff(fact_639_nat_Oinject,axiom,
    ! [Nat_4: nat,Nat_3: nat] :
      ( ( hAPP_nat_nat(suc,Nat_4) = hAPP_nat_nat(suc,Nat_3) )
    <=> ( Nat_4 = Nat_3 ) ) ).

tff(fact_640_Suc__n__not__n,axiom,
    ! [N_1: nat] : hAPP_nat_nat(suc,N_1) != N_1 ).

tff(fact_641_n__not__Suc__n,axiom,
    ! [N_1: nat] : N_1 != hAPP_nat_nat(suc,N_1) ).

tff(fact_642_add__Suc__shift,axiom,
    ! [M_2: nat,N_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) ).

tff(fact_643_add__Suc,axiom,
    ! [M_2: nat,N_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)) ).

tff(fact_644_add__Suc__right,axiom,
    ! [M_2: nat,N_1: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),N_1)) ).

tff(fact_645_not__less__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4))) ) ).

tff(fact_646_less__Suc__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
        | ( M_4 = Na ) ) ) ).

tff(fact_647_Suc__less__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_4)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).

tff(fact_648_not__less__less__Suc__eq,axiom,
    ! [Na: nat,M_4: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
      <=> ( Na = M_4 ) ) ) ).

tff(fact_649_less__antisym,axiom,
    ! [N_1: nat,M_2: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),hAPP_nat_nat(suc,M_2)))
       => ( M_2 = N_1 ) ) ) ).

tff(fact_650_less__SucI,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).

tff(fact_651_Suc__lessI,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => ( ( hAPP_nat_nat(suc,M_2) != N_1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1)) ) ) ).

tff(fact_652_less__trans__Suc,axiom,
    ! [K_1: nat,I: nat,J_2: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1)) ) ) ).

tff(fact_653_less__SucE,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
       => ( M_2 = N_1 ) ) ) ).

tff(fact_654_Suc__lessD,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).

tff(fact_655_Suc__less__SucD,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).

tff(fact_656_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat) ).

tff(fact_657_Suc__le__lessD,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ).

tff(fact_658_le__less__Suc__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M_4)))
      <=> ( Na = M_4 ) ) ) ).

tff(fact_659_Suc__leI,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ) ).

tff(fact_660_le__imp__less__Suc,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).

tff(fact_661_Suc__le__eq,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_4)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na)) ) ).

tff(fact_662_less__Suc__eq__le,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_4),Na)) ) ).

tff(fact_663_less__eq__Suc__le,axiom,
    ! [Na: nat,M_4: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M_4))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_4)) ) ).

tff(fact_664_less__iff__Suc__add,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),Na))
    <=> ? [K_2: nat] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),K_2)) ) ).

tff(fact_665_less__add__Suc2,axiom,
    ! [I: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),I)))) ).

tff(fact_666_less__add__Suc1,axiom,
    ! [I: nat,M_2: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),M_2)))) ).

tff(fact_667_one__is__add,axiom,
    ! [M_4: nat,Na: nat] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) )
    <=> ( ( ( M_4 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( Na = zero_zero_nat ) )
        | ( ( M_4 = zero_zero_nat )
          & ( Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_668_add__is__1,axiom,
    ! [M_4: nat,Na: nat] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_4),Na) = hAPP_nat_nat(suc,zero_zero_nat) )
    <=> ( ( ( M_4 = hAPP_nat_nat(suc,zero_zero_nat) )
          & ( Na = zero_zero_nat ) )
        | ( ( M_4 = zero_zero_nat )
          & ( Na = hAPP_nat_nat(suc,zero_zero_nat) ) ) ) ) ).

tff(fact_669_gr0__conv__Suc,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
    <=> ? [M: nat] : Na = hAPP_nat_nat(suc,M) ) ).

tff(fact_670_less__Suc0,axiom,
    ! [Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> ( Na = zero_zero_nat ) ) ).

tff(fact_671_less__Suc__eq__0__disj,axiom,
    ! [M_4: nat,Na: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_4),hAPP_nat_nat(suc,Na)))
    <=> ( ( M_4 = zero_zero_nat )
        | ? [J: nat] :
            ( ( M_4 = hAPP_nat_nat(suc,J) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),Na)) ) ) ) ).

tff(fact_672_inj__Suc,axiom,
    ! [N_2: fun_nat_bool] : hBOOL(hAPP_f54304608l_bool(inj_on_nat_nat(suc),N_2)) ).

tff(fact_673_Suc__neq__Zero,axiom,
    ! [M_2: nat] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).

tff(fact_674_Zero__neq__Suc,axiom,
    ! [M_2: nat] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).

tff(fact_675_nat_Osimps_I3_J,axiom,
    ! [Nat_2: nat] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat ).

tff(fact_676_Suc__not__Zero,axiom,
    ! [M_2: nat] : hAPP_nat_nat(suc,M_2) != zero_zero_nat ).

tff(fact_677_nat_Osimps_I2_J,axiom,
    ! [Nat_1: nat] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1) ).

tff(fact_678_Zero__not__Suc,axiom,
    ! [M_2: nat] : zero_zero_nat != hAPP_nat_nat(suc,M_2) ).

tff(fact_679_less__eq__Suc__le__raw,axiom,
    ! [X_1: nat] : hAPP_n1699378549t_bool(ord_less_nat,X_1) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_1)) ).

tff(fact_680_card__Collect__le__nat,axiom,
    ! [Na: nat] : finite_card_nat(collect_nat(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na) ).

tff(fact_681_card__less__Suc,axiom,
    ! [I_1: nat,M_3: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => ( hAPP_nat_nat(suc,finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1))))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ) ) ).

tff(fact_682_card__less,axiom,
    ! [I_1: nat,M_3: fun_nat_bool] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) != zero_zero_nat ) ) ).

tff(fact_683_card__less__Suc2,axiom,
    ! [I_1: nat,M_3: fun_nat_bool] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => ( finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(member_nat),suc)),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),I_1)))) = finite_card_nat(collect_nat(cOMBS_nat_bool_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(fconj),hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,member_nat),M_3)),hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,ord_less_nat),hAPP_nat_nat(suc,I_1))))) ) ) ).

tff(fact_684_inc__induct,axiom,
    ! [Pa: fun_nat_bool,I_1: nat,J_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J_1))
     => ( hBOOL(hAPP_nat_bool(Pa,J_1))
       => ( ! [I_2: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),J_1))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I_2)))
               => hBOOL(hAPP_nat_bool(Pa,I_2)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I_1)) ) ) ) ).

tff(fact_685_less__imp__Suc__add,axiom,
    ! [M_2: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
     => ? [K_2: nat] : N_1 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_2),K_2)) ) ).

tff(fact_686_gr0__implies__Suc,axiom,
    ! [N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1))
     => ? [M: nat] : N_1 = hAPP_nat_nat(suc,M) ) ).

tff(fact_687_Suc__eq__plus1__left,axiom,
    ! [N_1: nat] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N_1) ).

tff(fact_688_Suc__eq__plus1,axiom,
    ! [N_1: nat] : hAPP_nat_nat(suc,N_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N_1),one_one_nat) ).

tff(fact_689_Suc__le__D,axiom,
    ! [N_1: nat,M_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1))
     => ? [M: nat] : M_1 = hAPP_nat_nat(suc,M) ) ).

tff(fact_690_lessE,axiom,
    ! [I: nat,K_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_1))
     => ( ( K_1 != hAPP_nat_nat(suc,I) )
       => ~ ! [J: nat] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
             => ( K_1 != hAPP_nat_nat(suc,J) ) ) ) ) ).

tff(fact_691_Suc__lessE,axiom,
    ! [I: nat,K_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I)),K_1))
     => ~ ! [J: nat] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J))
           => ( K_1 != hAPP_nat_nat(suc,J) ) ) ) ).

tff(fact_692_not0__implies__Suc,axiom,
    ! [N_1: nat] :
      ( ( N_1 != zero_zero_nat )
     => ? [M: nat] : N_1 = hAPP_nat_nat(suc,M) ) ).

tff(fact_693_nat_Oexhaust,axiom,
    ! [Y: nat] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat: nat] : Y != hAPP_nat_nat(suc,Nat) ) ).

tff(fact_694_zero__induct,axiom,
    ! [Pa: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N)))
           => hBOOL(hAPP_nat_bool(Pa,N)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ).

tff(fact_695_nat__induct,axiom,
    ! [Na: nat,Pa: fun_nat_bool] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N: nat] :
            ( hBOOL(hAPP_nat_bool(Pa,N))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N))) )
       => hBOOL(hAPP_nat_bool(Pa,Na)) ) ) ).

tff(fact_696_surjh,axiom,
    image_391852738di_nat(h,top_to1678393681i_bool) = hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite783399747e_indi(top_to1678393681i_bool)) ).

tff(fact_697_finite__atLeastLessThan,axiom,
    ! [L: nat,U: nat] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_n1699378549t_bool(ord_at4362885an_nat(L),U))) ).

tff(fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123,axiom,
    ~ ! [H: fun_Ar1744566822di_nat] :
        ( hBOOL(hAPP_f1397511071l_bool(inj_on886403158di_nat(H),top_to1678393681i_bool))
       => ( image_391852738di_nat(H,top_to1678393681i_bool) != hAPP_n1699378549t_bool(ord_at4362885an_nat(zero_zero_nat),finite783399747e_indi(top_to1678393681i_bool)) ) ) ).

tff(fact_699_subset__card__intvl__is__intvl,axiom,
    ! [A: fun_nat_bool,K: nat] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A)))))
     => ( A = hAPP_n1699378549t_bool(ord_at4362885an_nat(K),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),finite_card_nat(A))) ) ) ).

%----Helper facts (57)
tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fconj_1_1_U,axiom,
    ! [Q: bool,P: bool] :
      ( ~ hBOOL(P)
      | ~ hBOOL(Q)
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).

tff(help_fconj_2_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(P) ) ).

tff(help_fconj_3_1_U,axiom,
    ! [P: bool,Q: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | hBOOL(Q) ) ).

tff(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [P: nat] : hAPP_nat_nat(cOMBI_nat,P) = P ).

tff(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P: bool,Q: nat] : hAPP_nat_bool(hAPP_b1013836512t_bool(cOMBK_bool_nat,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U,axiom,
    ! [P: bool,Q: product_unit] : hAPP_P1676879539t_bool(hAPP_b1096750261t_bool(cOMBK_790042732t_unit,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U,axiom,
    ! [P: fun_nat_fun_nat_nat,Q: nat,R: nat] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(hAPP_f416620757at_nat(cOMBC_nat_nat_nat,P),Q),R) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: nat,R: nat] : hAPP_nat_bool(hAPP_n1699378549t_bool(hAPP_f229349961t_bool(cOMBC_nat_nat_bool,P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_na1469252690l_bool,Q: fun_nat_bool,R: nat] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona,axiom,
    ! [P: fun_nat_bool,Q: nat] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBK_583454926ol_nat,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctu,axiom,
    ! [P: bool,Q: arrow_2115524757e_indi] : hAPP_A1888055029i_bool(hAPP_b1439777783i_bool(cOMBK_1820189998e_indi,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: fun_nat_nat,R: nat] : hAPP_n1699378549t_bool(hAPP_f618557131t_bool(cOMBB_800536526ol_nat(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_bool,R: nat] : hAPP_nat_bool(hAPP_f800510211t_bool(hAPP_f1722879237t_bool(cOMBC_226598744l_bool,P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo1549164019l_bool,Q: fun_nat_bool,R: nat] : hAPP_n1006566506l_bool(hAPP_f1146629647l_bool(cOMBB_1015721476ol_nat(P),Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P: fun_bo492988759l_bool,Q: fun_bool_bool,R: bool] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1996228283l_bool(cOMBC_1455277858l_bool,P),Q),R) = hAPP_f387058535l_bool(hAPP_b1787118453l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000,axiom,
    ! [P: fun_Ar2045874810t_bool,Q: nat,R: arrow_2115524757e_indi] : hAPP_A1888055029i_bool(hAPP_n924210722i_bool(hAPP_f62620517i_bool(cOMBC_922322901t_bool,P),Q),R) = hAPP_nat_bool(hAPP_A981395480t_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___,axiom,
    ! [P: fun_nat_bool,Q: arrow_2115524757e_indi] : hAPP_A981395480t_bool(hAPP_f426535095t_bool(cOMBK_2091851729e_indi,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
    ! [P: fun_na1436237685l_bool,Q: fun_nat_nat,R: nat] : hAPP_n215258509l_bool(hAPP_f66927821l_bool(cOMBB_1146692694ol_nat(P),Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty,axiom,
    ! [P: fun_Pr1863373635l_bool,Q: fun_Pr1643180309t_bool,R: product_unit] : hAPP_P1676879539t_bool(hAPP_f427533077t_bool(hAPP_f1458726223t_bool(cOMBC_2133163426l_bool,P),Q),R) = hAPP_f2028818269l_bool(hAPP_P607165281l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__318,axiom,
    ! [P: fun_nat_fun_nat_bool,Q: fun_Ar1744566822di_nat,R: arrow_2115524757e_indi] : hAPP_A981395480t_bool(hAPP_f1381130897t_bool(cOMBB_981137617e_indi(P),Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1450069362di_nat(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: bool,Q: produc1840315303le_alt] : hAPP_P166437127t_bool(hAPP_b1263785481t_bool(cOMBK_1566242880le_alt,P),Q) = P ).

tff(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq,axiom,
    ! [X: fun_Pr1055212137t_bool,Y: fun_Pr1055212137t_bool] : hAPP_f70231061t_bool(hAPP_f1409483817t_bool(hAPP_b1061655857t_bool(if_fun1658569689t_bool,fTrue),X),Y) = X ).

tff(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq,axiom,
    ! [X: fun_Pr1055212137t_bool,Y: fun_Pr1055212137t_bool] : hAPP_f70231061t_bool(hAPP_f1409483817t_bool(hAPP_b1061655857t_bool(if_fun1658569689t_bool,fFalse),X),Y) = Y ).

tff(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_319,axiom,
    ! [P: fun_Ar1380772935l_bool,Q: fun_Ar552120407i_bool,R: arrow_2115524757e_indi] : hAPP_A1888055029i_bool(hAPP_f1282576021i_bool(hAPP_f833264203i_bool(cOMBC_31215906l_bool,P),Q),R) = hAPP_f1397511071l_bool(hAPP_A605074405l_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
    ! [P: bool,Q: fun_Pr1055212137t_bool] : hAPP_f429946033l_bool(hAPP_b1650070463l_bool(cOMBK_1216274064t_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
    ! [P: fun_bool_bool,Q: produc1840315303le_alt] : hAPP_P1830623733l_bool(hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [P: fun_Pr1055212137t_bool,Q: bool] : hAPP_b1263785481t_bool(hAPP_f414777105t_bool(cOMBK_382434616l_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_320,axiom,
    ! [P: fun_Pr1055212137t_bool,Q: arrow_2115524757e_indi] : hAPP_A1174518481t_bool(hAPP_f311418073t_bool(cOMBK_1522533360e_indi,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t,axiom,
    ! [P: fun_Ar1026121174l_bool,Q: fun_Pr1055212137t_bool,R: arrow_931160158le_alt] : hAPP_A674791462t_bool(hAPP_f1099651112t_bool(hAPP_f2087965871t_bool(cOMBC_571858149l_bool,P),Q),R) = hAPP_f429946033l_bool(hAPP_A1787768616l_bool(P,R),Q) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: bool,Q: fun_Ar500372357t_bool] : hAPP_f1766661605l_bool(hAPP_b1849744615l_bool(cOMBK_670822686t_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,axiom,
    ! [P: fun_Ar552120407i_bool,Q: fun_Pr1055212137t_bool] : hAPP_f1957024259i_bool(hAPP_f676424105i_bool(cOMBK_854051296t_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
    ! [P: fun_fu1015689055l_bool,Q: arrow_2115524757e_indi] : hAPP_A1279849719l_bool(hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,P),Q) = P ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_321,axiom,
    ! [P: fun_Ar698916836t_bool,Q: arrow_931160158le_alt,R: arrow_2115524757e_indi] : hAPP_A1174518481t_bool(hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,P),Q),R) = hAPP_A606737888t_bool(hAPP_A1020253872t_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t_322,axiom,
    ! [P: fun_Ar1364097613t_bool,Q: fun_Pr1055212137t_bool,R: arrow_931160158le_alt] : hAPP_A1858212765t_bool(hAPP_f1810968607t_bool(hAPP_f15758621t_bool(cOMBC_1947566172t_bool,P),Q),R) = hAPP_f1099651112t_bool(hAPP_A1770325791t_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,axiom,
    ! [P: fun_Pr1228236907l_bool,Q: fun_Pr1055212137t_bool,R: produc1840315303le_alt] : hAPP_P166437127t_bool(hAPP_f70231061t_bool(hAPP_f46399911t_bool(cOMBC_697226658l_bool,P),Q),R) = hAPP_f429946033l_bool(hAPP_P840149257l_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_323,axiom,
    ! [P: fun_Ar1583656131t_bool,Q: arrow_931160158le_alt,R: arrow_2115524757e_indi] : hAPP_A1020253872t_bool(hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,P),Q),R) = hAPP_A501825983t_bool(hAPP_A131904271t_bool(P,R),Q) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [P: fun_fu1556412341l_bool,Q: fun_fu1015689055l_bool,R: fun_Pr1055212137t_bool] : hAPP_f429946033l_bool(hAPP_f1050277569l_bool(hAPP_f639477379l_bool(cOMBC_437066390l_bool,P),Q),R) = hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,axiom,
    ! [P: fun_Pr1228236907l_bool,Q: fun_Ar836847646le_alt,R: arrow_931160158le_alt] : hAPP_A1787768616l_bool(hAPP_f1395387255l_bool(cOMBB_480104238le_alt(P),Q),R) = hAPP_P840149257l_bool(P,hAPP_A1313367280le_alt(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_324,axiom,
    ! [P: fun_Ar1492469401t_bool,Q: fun_Pr1055212137t_bool,R: arrow_2115524757e_indi] : hAPP_A1174518481t_bool(hAPP_f311418073t_bool(hAPP_f1302245795t_bool(cOMBC_1490589522t_bool,P),Q),R) = hAPP_f70231061t_bool(hAPP_A892860133t_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000,axiom,
    ! [P: fun_Ar1492469401t_bool,Q: fun_Ar500372357t_bool,R: arrow_2115524757e_indi] : hAPP_A1174518481t_bool(cOMBS_1921392482t_bool(P,Q),R) = hAPP_f70231061t_bool(hAPP_A892860133t_bool(P,R),hAPP_A1174518481t_bool(Q,R)) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
    ! [P: bool,Q: fun_fu1595299477t_bool] : hAPP_f611501301l_bool(hAPP_b816606711l_bool(cOMBK_759924014t_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,axiom,
    ! [P: fun_fu775006535l_bool,Q: fun_Pr1055212137t_bool] : hAPP_f1410143987l_bool(hAPP_f1197023401l_bool(cOMBK_2140692976t_bool,P),Q) = P ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_325,axiom,
    ! [P: fun_fu1015689055l_bool,Q: fun_Ar500372357t_bool] : hAPP_f1498158055l_bool(hAPP_f422714471l_bool(cOMBK_1446432t_bool,P),Q) = P ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [P: fun_fu1628463836t_bool,Q: fun_Ar500372357t_bool,R: arrow_2115524757e_indi] : hAPP_A1020253872t_bool(hAPP_f842954860t_bool(cOMBB_117136048e_indi(P),Q),R) = hAPP_f786530292t_bool(P,hAPP_A1174518481t_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,axiom,
    ! [P: fun_fu1291054887l_bool,Q: fun_fu775006535l_bool,R: fun_Ar500372357t_bool] : hAPP_f1766661605l_bool(hAPP_f626396309l_bool(hAPP_f228579435l_bool(cOMBC_941833506l_bool,P),Q),R) = hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(P,R),Q) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,axiom,
    ! [P: fun_fu1476972377l_bool,Q: fun_Ar2049444117le_alt,R: arrow_931160158le_alt] : hAPP_A1256181151l_bool(hAPP_f1176598245l_bool(cOMBB_1605735744le_alt(P),Q),R) = hAPP_f1395387255l_bool(P,hAPP_A1485971815le_alt(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_326,axiom,
    ! [P: fun_fu699199419t_bool,Q: fun_Ar500372357t_bool,R: arrow_2115524757e_indi] : hAPP_A131904271t_bool(hAPP_f576849227t_bool(cOMBB_656639247e_indi(P),Q),R) = hAPP_f1909595219t_bool(P,hAPP_A1174518481t_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_327,axiom,
    ! [P: fun_Ar1519997101t_bool,Q: fun_Pr1055212137t_bool,R: arrow_2115524757e_indi] : hAPP_A892860133t_bool(hAPP_f1755759597t_bool(hAPP_f1328803787t_bool(cOMBC_1190055014t_bool,P),Q),R) = hAPP_f1409483817t_bool(hAPP_A594708985t_bool(P,R),Q) ).

tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_328,axiom,
    ! [P: fun_Ar1519997101t_bool,Q: fun_Ar500372357t_bool,R: arrow_2115524757e_indi] : hAPP_A892860133t_bool(cOMBS_811328630t_bool(P,Q),R) = hAPP_f1409483817t_bool(hAPP_A594708985t_bool(P,R),hAPP_A1174518481t_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___329,axiom,
    ! [P: fun_fu709917073t_bool,Q: fun_Ar1689125069l_bool,R: arrow_931160158le_alt] : hAPP_A1770325791t_bool(hAPP_f1435501085t_bool(cOMBB_1430402568le_alt(P),Q),R) = hAPP_f2087965871t_bool(P,hAPP_A1256181151l_bool(Q,R)) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
    ! [P: fun_bo462718181t_bool,Q: fun_Ar552120407i_bool,R: arrow_2115524757e_indi] : hAPP_A594708985t_bool(hAPP_f509814255t_bool(cOMBB_231886989e_indi(P),Q),R) = hAPP_b1061655857t_bool(P,hAPP_A1888055029i_bool(Q,R)) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,axiom,
    ! [P: fun_fu446267975l_bool,Q: fun_fu1138137687l_bool,R: fun_fu1595299477t_bool] : hAPP_f611501301l_bool(hAPP_f1077478037l_bool(hAPP_f230252107l_bool(cOMBC_1452216610l_bool,P),Q),R) = hAPP_f361555359l_bool(hAPP_f1709225957l_bool(P,R),Q) ).

%----Conjectures (1)
tff(conj_0,conjecture,
    hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,c),d)),hAPP_f792184801t_bool(f,p))) ).

%------------------------------------------------------------------------------