TPTP Problem File: SCT170

TPTP Problem File: SCT170_20.p

%------------------------------------------------------------------------------
% File     : SCT170_20 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Social Choice Theory
% Problem  : Arrow's Impossibility Theorem line 204, 500 axioms selected
% Version  : SCT170_2 with the conjecture removed
% English  :

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

% Status   : Satisfiable
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    : 2055 ( 206 unt;1248 typ;   0 def)
%            Number of atoms       : 1979 ( 555 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 1457 ( 285   ~;  69   |;  90   &)
%                                         ( 119 <=>; 894  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :   19 (   2 avg)
%            Number of types       :  468 ( 467 usr)
%            Number of type conns  :  996 ( 533   >; 463   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  780 ( 780 usr; 248 con; 0-3 aty)
%            Number of variables   : 2344 (2291   !;  53   ?;2344   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 17:28:10
%------------------------------------------------------------------------------
%----Should-be-implicit typings (467)
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tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,type,
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tff(sy_c_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_351,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__Arrow__,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__List__O,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc_352,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Arrow_,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Arrow__353,type,
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tff(sy_c_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__Arrow__354,type,
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tff(sy_c_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa_355,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa_356,type,
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tff(sy_c_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa_357,type,
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tff(sy_c_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
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tff(sy_c_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_,type,
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tff(sy_c_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
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tff(sy_c_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
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tff(sy_c_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_,type,
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tff(sy_c_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_358,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____ctui,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,type,
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tff(sy_c_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___359,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___360,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___361,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc__362,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc__363,type,
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tff(sy_c_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc__364,type,
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tff(sy_c_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_366,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_371,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_372,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_373,type,
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tff(sy_c_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_374,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___375,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___376,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___377,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_378,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_379,type,
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tff(sy_c_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_380,type,
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tff(sy_c_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
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tff(sy_c_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa_381,type,
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tff(sy_c_List_Oappend_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    append246315520t_bool: fun_li1389414228t_bool ).

tff(sy_c_List_Oappend_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    append1662967824t_bool: fun_li709301828t_bool ).

tff(sy_c_List_Oappend_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    append483908910t_bool: fun_li952503796t_bool ).

tff(sy_c_List_Oappend_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
    append1568444194le_alt: fun_li276060722le_alt ).

tff(sy_c_List_Oappend_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    append1870889072le_alt: fun_li907508836le_alt ).

tff(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    butlas730749018le_alt: list_A1748581779le_alt > list_A1748581779le_alt ).

tff(sy_c_List_Obutlast_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    butlas92561305e_indi: list_A964264886e_indi > list_A964264886e_indi ).

tff(sy_c_List_Obutlast_000tc__HOL__Obool,type,
    butlast_bool: list_bool > list_bool ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oi,type,
    butlas707526281t_bool: list_f767102118t_bool > list_f767102118t_bool ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    butlas606086553t_bool: list_f1301614006t_bool > list_f1301614006t_bool ).

tff(sy_c_List_Obutlast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctui,type,
    butlas717559397t_bool: list_f418358302t_bool > list_f418358302t_bool ).

tff(sy_c_List_Obutlast_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    butlas1000653483le_alt: list_P1216503240le_alt > list_P1216503240le_alt ).

tff(sy_c_List_Obutlast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle,type,
    butlas1911524985le_alt: list_P1493174166le_alt > list_P1493174166le_alt ).

tff(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    distin692125441le_alt: fun_li1323594581t_bool ).

tff(sy_c_List_Odistinct_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    distin455238322e_indi: fun_li60471852i_bool ).

tff(sy_c_List_Odistinct_000tc__HOL__Obool,type,
    distinct_bool: fun_list_bool_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    distin420467362t_bool: fun_li1450775836l_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctui,type,
    distin1125305010t_bool: fun_li1375950892l_bool ).

tff(sy_c_List_Odistinct_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
    distin1251351564t_bool: fun_li1766616672l_bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    distin2115974596le_alt: fun_li1818542910t_bool ).

tff(sy_c_List_Odistinct_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    distin2008613906le_alt: fun_li1991898892t_bool ).

tff(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    dropWh1772583087le_alt: ( fun_Ar1091019988t_bool * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_OdropWhile_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    dropWh1846039684e_indi: ( fun_Ar552120407i_bool * list_A964264886e_indi ) > list_A964264886e_indi ).

tff(sy_c_List_OdropWhile_000tc__HOL__Obool,type,
    dropWhile_bool: ( fun_bool_bool * list_bool ) > list_bool ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    dropWh1950353012t_bool: ( fun_fu775006535l_bool * list_f767102118t_bool ) > list_f767102118t_bool ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,type,
    dropWh1304379524t_bool: ( fun_fu1138137687l_bool * list_f1301614006t_bool ) > list_f1301614006t_bool ).

tff(sy_c_List_OdropWhile_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,type,
    dropWh693679034t_bool: ( fun_fu1015689055l_bool * list_f418358302t_bool ) > list_f418358302t_bool ).

tff(sy_c_List_OdropWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    dropWh1019479958le_alt: ( fun_Pr1055212137t_bool * list_P1216503240le_alt ) > list_P1216503240le_alt ).

tff(sy_c_List_OdropWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    dropWh2059627236le_alt: ( fun_Pr1013460023t_bool * list_P1493174166le_alt ) > list_P1493174166le_alt ).

tff(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    drop_A1802510926le_alt: fun_na1791315646le_alt ).

tff(sy_c_List_Odrop_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    drop_A134812325e_indi: fun_na1988220144e_indi ).

tff(sy_c_List_Odrop_000tc__HOL__Obool,type,
    drop_bool: fun_na1279735280t_bool ).

tff(sy_c_List_Odrop_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    drop_f1478843797t_bool: fun_na675742448t_bool ).

tff(sy_c_List_Odrop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    drop_f1457139877t_bool: fun_na1841387760t_bool ).

tff(sy_c_List_Odrop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    drop_f202273881t_bool: fun_na699842004t_bool ).

tff(sy_c_List_Odrop_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    drop_P1273017783le_alt: fun_na401775984le_alt ).

tff(sy_c_List_Odrop_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    drop_P738054021le_alt: fun_na135885296le_alt ).

tff(sy_c_List_Ofoldl_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    foldl_971653884le_alt: ( fun_li1563304834le_alt * list_A1748581779le_alt * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    hd_Arr274000865le_alt: list_A1748581779le_alt > arrow_931160158le_alt ).

tff(sy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    hd_Arr1709813202e_indi: list_A964264886e_indi > arrow_2115524757e_indi ).

tff(sy_c_List_Ohd_000tc__HOL__Obool,type,
    hd_bool: list_bool > bool ).

tff(sy_c_List_Ohd_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_M,type,
    hd_fun674840002t_bool: list_f767102118t_bool > fun_Ar500372357t_bool ).

tff(sy_c_List_Ohd_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    hd_fun1472091602t_bool: list_f1301614006t_bool > fun_fu1595299477t_bool ).

tff(sy_c_List_Ohd_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,type,
    hd_fun290318572t_bool: list_f418358302t_bool > fun_Pr1055212137t_bool ).

tff(sy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_M,type,
    hd_Pro636780772le_alt: list_P1216503240le_alt > produc1840315303le_alt ).

tff(sy_c_List_Ohd_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____c,type,
    hd_Pro156409650le_alt: list_P1493174166le_alt > produc662089077le_alt ).

tff(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    insert428884260le_alt: ( arrow_931160158le_alt * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_Oinsert_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    insert13019471e_indi: ( arrow_2115524757e_indi * list_A964264886e_indi ) > list_A964264886e_indi ).

tff(sy_c_List_Oinsert_000tc__HOL__Obool,type,
    insert_bool: ( bool * list_bool ) > list_bool ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    insert2063552063t_bool: ( fun_Ar500372357t_bool * list_f767102118t_bool ) > list_f767102118t_bool ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    insert1079671631t_bool: ( fun_fu1595299477t_bool * list_f1301614006t_bool ) > list_f1301614006t_bool ).

tff(sy_c_List_Oinsert_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    insert1909791023t_bool: ( fun_Pr1055212137t_bool * list_f418358302t_bool ) > list_f418358302t_bool ).

tff(sy_c_List_Oinsert_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
    insert1516219489le_alt: ( produc1840315303le_alt * list_P1216503240le_alt ) > list_P1216503240le_alt ).

tff(sy_c_List_Oinsert_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    insert633788207le_alt: ( produc662089077le_alt * list_P1493174166le_alt ) > list_P1493174166le_alt ).

tff(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    last_A1673116455le_alt: list_A1748581779le_alt > arrow_931160158le_alt ).

tff(sy_c_List_Olast_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    last_A989769740e_indi: list_A964264886e_indi > arrow_2115524757e_indi ).

tff(sy_c_List_Olast_000tc__HOL__Obool,type,
    last_bool: list_bool > bool ).

tff(sy_c_List_Olast_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    last_f1815194108t_bool: list_f767102118t_bool > fun_Ar500372357t_bool ).

tff(sy_c_List_Olast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    last_f766782476t_bool: list_f1301614006t_bool > fun_fu1595299477t_bool ).

tff(sy_c_List_Olast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    last_f1672818226t_bool: list_f418358302t_bool > fun_Pr1055212137t_bool ).

tff(sy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    last_P1995563806le_alt: list_P1216503240le_alt > produc1840315303le_alt ).

tff(sy_c_List_Olast_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    last_P1178810988le_alt: list_P1493174166le_alt > produc662089077le_alt ).

tff(sy_c_List_Olex_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    lex_Ar1871318386le_alt: fun_fu1275593675t_bool ).

tff(sy_c_List_Olex_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    lex_li296480639le_alt: fun_fu1167626927t_bool ).

tff(sy_c_List_Olexn_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    lexn_A626162606le_alt: ( fun_Pr1055212137t_bool * nat ) > fun_Pr1013460023t_bool ).

tff(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    lexord1413896571le_alt: fun_fu1275593675t_bool ).

tff(sy_c_List_Olexord_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    lexord200124088e_indi: fun_fu1432899755i_bool ).

tff(sy_c_List_Olexord_000tc__HOL__Obool,type,
    lexord_bool: fun_fu567784347l_bool ).

tff(sy_c_List_Olexord_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    lexord103259702le_alt: fun_fu1167626927t_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    lexord267119784t_bool: fun_fu1134695883l_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    lexord1327872696t_bool: fun_fu959050411l_bool ).

tff(sy_c_List_Olexord_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    lexord45138054t_bool: fun_fu725984545l_bool ).

tff(sy_c_List_Olexord_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oa,type,
    lexord840833482le_alt: fun_fu883932423t_bool ).

tff(sy_c_List_Olexord_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    lexord272977688le_alt: fun_fu1041472619t_bool ).

tff(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    cons_A684544190le_alt: fun_Ar283682666le_alt ).

tff(sy_c_List_Olist_OCons_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    cons_A1348960309e_indi: fun_Ar1717876185e_indi ).

tff(sy_c_List_Olist_OCons_000tc__HOL__Obool,type,
    cons_bool: fun_bo1175651857t_bool ).

tff(sy_c_List_Olist_OCons_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctu,type,
    cons_l268440883le_alt: fun_li799656667le_alt ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    cons_f54319909t_bool: fun_fu1689147625t_bool ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ct,type,
    cons_f1295695413t_bool: fun_fu785470425t_bool ).

tff(sy_c_List_Olist_OCons_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____c,type,
    cons_f976589513t_bool: fun_fu2137254965t_bool ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    cons_P105259847le_alt: fun_Pr841565895le_alt ).

tff(sy_c_List_Olist_OCons_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
    cons_P1348035861le_alt: fun_Pr283231225le_alt ).

tff(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    nil_Ar1741995278le_alt: list_A1748581779le_alt ).

tff(sy_c_List_Olist_ONil_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    nil_Ar1066084325e_indi: list_A964264886e_indi ).

tff(sy_c_List_Olist_ONil_000tc__HOL__Obool,type,
    nil_bool: list_bool ).

tff(sy_c_List_Olist_ONil_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,type,
    nil_li1540629731le_alt: list_l1735481012le_alt ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    nil_fu141734613t_bool: list_f767102118t_bool ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,type,
    nil_fu1362281957t_bool: list_f1301614006t_bool ).

tff(sy_c_List_Olist_ONil_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,type,
    nil_fu67358489t_bool: list_f418358302t_bool ).

tff(sy_c_List_Olist_ONil_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    nil_Pr1200540407le_alt: list_P1216503240le_alt ).

tff(sy_c_List_Olist_ONil_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    nil_Pr1812858053le_alt: list_P1493174166le_alt ).

tff(sy_c_List_Olist_Olist__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    list_c151649911le_alt: ( list_A1748581779le_alt * fun_Ar283682666le_alt * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_Olistrel1_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    listre372320615le_alt: fun_fu1275593675t_bool ).

tff(sy_c_List_Olistrel1_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    listre253898570le_alt: fun_fu1167626927t_bool ).

tff(sy_c_List_Olistrel_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    listre228973110le_alt: fun_fu1275593675t_bool ).

tff(sy_c_List_Olistrel_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiws,type,
    listre256509371le_alt: fun_fu1167626927t_bool ).

tff(sy_c_List_Olistrelp_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    listre1668963176le_alt: fun_Ar1414184139t_bool > fun_li954148211t_bool ).

tff(sy_c_List_Olistrelp_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    listre450023945le_alt: fun_li954148211t_bool > fun_li1505404791t_bool ).

tff(sy_c_List_Onull_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    null_A1976766230le_alt: fun_li1323594581t_bool ).

tff(sy_c_List_Opartition_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    partit1943378951le_alt: ( fun_Ar1091019988t_bool * list_A1748581779le_alt ) > produc662089077le_alt ).

tff(sy_c_List_Oreplicate_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    replic1967339976le_alt: ( nat * arrow_931160158le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    rev_Ar1562208110le_alt: list_A1748581779le_alt > list_A1748581779le_alt ).

tff(sy_c_List_Orev_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    rev_Ar1187845509e_indi: list_A964264886e_indi > list_A964264886e_indi ).

tff(sy_c_List_Orev_000tc__HOL__Obool,type,
    rev_bool: list_bool > list_bool ).

tff(sy_c_List_Orev_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_,type,
    rev_fu207962229t_bool: list_f767102118t_bool > list_f767102118t_bool ).

tff(sy_c_List_Orev_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,type,
    rev_fu762704773t_bool: list_f1301614006t_bool > list_f1301614006t_bool ).

tff(sy_c_List_Orev_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    rev_fu601479545t_bool: list_f418358302t_bool > list_f418358302t_bool ).

tff(sy_c_List_Orev_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_,type,
    rev_Pr1555478679le_alt: list_P1216503240le_alt > list_P1216503240le_alt ).

tff(sy_c_List_Orev_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    rev_Pr919241317le_alt: list_P1493174166le_alt > list_P1493174166le_alt ).

tff(sy_c_List_Orotate1_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    rotate791150427le_alt: list_A1748581779le_alt > list_A1748581779le_alt ).

tff(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    set_Ar1033255471le_alt: list_A1748581779le_alt > fun_Ar1091019988t_bool ).

tff(sy_c_List_Oset_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    set_Ar1464464132e_indi: list_A964264886e_indi > fun_Ar552120407i_bool ).

tff(sy_c_List_Oset_000tc__HOL__Obool,type,
    set_bool: list_bool > fun_bool_bool ).

tff(sy_c_List_Oset_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    set_li1265325186le_alt: list_l1735481012le_alt > fun_li1323594581t_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_,type,
    set_fu116139252t_bool: list_f767102118t_bool > fun_fu775006535l_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,type,
    set_fu1616240388t_bool: list_f1301614006t_bool > fun_fu1138137687l_bool ).

tff(sy_c_List_Oset_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    set_fu945091898t_bool: list_f418358302t_bool > fun_fu1015689055l_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_,type,
    set_Pr1864214038le_alt: list_P1216503240le_alt > fun_Pr1055212137t_bool ).

tff(sy_c_List_Oset_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    set_Pr1859340644le_alt: list_P1493174166le_alt > fun_Pr1013460023t_bool ).

tff(sy_c_List_Osplice_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    splice1976699617le_alt: ( list_A1748581779le_alt * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    takeWh4609031le_alt: ( fun_Ar1091019988t_bool * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_List_OtakeWhile_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    takeWh1517834028e_indi: ( fun_Ar552120407i_bool * list_A964264886e_indi ) > list_A964264886e_indi ).

tff(sy_c_List_OtakeWhile_000tc__HOL__Obool,type,
    takeWhile_bool: ( fun_bool_bool * list_bool ) > list_bool ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    takeWh1707174172t_bool: ( fun_fu775006535l_bool * list_f767102118t_bool ) > list_f767102118t_bool ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,type,
    takeWh1450838828t_bool: ( fun_fu1138137687l_bool * list_f1301614006t_bool ) > list_f1301614006t_bool ).

tff(sy_c_List_OtakeWhile_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,type,
    takeWh1072801554t_bool: ( fun_fu1015689055l_bool * list_f418358302t_bool ) > list_f418358302t_bool ).

tff(sy_c_List_OtakeWhile_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    takeWh641303102le_alt: ( fun_Pr1055212137t_bool * list_P1216503240le_alt ) > list_P1216503240le_alt ).

tff(sy_c_List_OtakeWhile_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    takeWh871442828le_alt: ( fun_Pr1013460023t_bool * list_P1493174166le_alt ) > list_P1493174166le_alt ).

tff(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    tl_Arr921252325le_alt: list_A1748581779le_alt > list_A1748581779le_alt ).

tff(sy_c_List_Otl_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    tl_Arr711649486e_indi: list_A964264886e_indi > list_A964264886e_indi ).

tff(sy_c_List_Otl_000tc__HOL__Obool,type,
    tl_bool: list_bool > list_bool ).

tff(sy_c_List_Otl_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_M,type,
    tl_fun436180158t_bool: list_f767102118t_bool > list_f767102118t_bool ).

tff(sy_c_List_Otl_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    tl_fun1694877902t_bool: list_f1301614006t_bool > list_f1301614006t_bool ).

tff(sy_c_List_Otl_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,type,
    tl_fun1631474416t_bool: list_f418358302t_bool > list_f418358302t_bool ).

tff(sy_c_List_Otl_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_M,type,
    tl_Pro1271790560le_alt: list_P1216503240le_alt > list_P1216503240le_alt ).

tff(sy_c_List_Otl_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____c,type,
    tl_Pro747896878le_alt: list_P1493174166le_alt > list_P1493174166le_alt ).

tff(sy_c_Nat_OSuc,type,
    suc: nat > nat ).

tff(sy_c_Nat_Onat_Onat__case_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    nat_ca1780707935le_alt: ( list_A1748581779le_alt * fun_na1941391286le_alt * nat ) > list_A1748581779le_alt ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_,type,
    size_s1492124157le_alt: list_A1748581779le_alt > nat ).

tff(sy_c_Nat_Osize__class_Osize_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Or,type,
    size_s24685002le_alt: list_l1735481012le_alt > nat ).

tff(sy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabel,type,
    order_304234630le_alt: fun_Ar1091019988t_bool > fun_fu1015689055l_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__eq_000tc__Nat__Onat,type,
    ord_less_eq_nat: fun_nat_fun_nat_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_to1888499034t_bool: fun_Ar1091019988t_bool ).

tff(sy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____c_403,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__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_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow,type,
    top_to1866544689t_bool: fun_Pr1013460023t_bool ).

tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_,type,
    produc362059031le_alt: fun_Ar2049444117le_alt ).

tff(sy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    produc609333615e_indi: fun_Ar743199503e_indi ).

tff(sy_c_Product__Type_OPair_000tc__HOL__Obool_000tc__HOL__Obool,type,
    produc1246214911l_bool: fun_bo1175459231l_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____,type,
    produc1596656747le_alt: fun_li1598912907le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__Arrow____Order____Mirabelle_____404,type,
    produc514409495e_indi: fun_li643095493e_indi ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist,type,
    produc1067887767t_bool: fun_li998062677t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order,type,
    produc1935847959le_alt: fun_li1343239489le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mira,type,
    produc1138073367t_bool: fun_li91123621t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Orde,type,
    produc1183986199t_bool: fun_li129567685t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Ord,type,
    produc1735751425t_bool: fun_li1568376929t_bool ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mir,type,
    produc2078958999le_alt: fun_li968062313le_alt ).

tff(sy_c_Product__Type_OPair_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arro,type,
    produc45587863le_alt: fun_li601079429le_alt ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvq,type,
    produc775282511t_bool: fun_fu1118404335t_bool ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle___,type,
    produc1397390703t_bool: fun_fu1922278159t_bool ).

tff(sy_c_Product__Type_OPair_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle__,type,
    produc1735284823t_bool: fun_fu1363468139t_bool ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsv,type,
    produc1783421843le_alt: fun_Pr1174154163le_alt ).

tff(sy_c_Product__Type_OPair_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mir,type,
    produc1477938991le_alt: fun_Pr975121871le_alt ).

tff(sy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    produc258050046t_bool: fun_Pr1055212137t_bool > fun_Ar1414184139t_bool ).

tff(sy_c_Product__Type_Ocurry_000tc__List__Olist_Itc__Arrow____Order____Mirabelle___,type,
    produc919986386t_bool: fun_Pr1013460023t_bool > fun_li954148211t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____ctuiw,type,
    produc2067717087t_bool: fun_Ar1414184139t_bool > fun_Pr1055212137t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M,type,
    produc1791904563t_bool: fun_li954148211t_bool > fun_Pr1013460023t_bool ).

tff(sy_c_Product__Type_Oprod_Oprod__case_000tc__List__Olist_Itc__Arrow____Order____M_405,type,
    produc1631581515le_alt: fun_li1598912907le_alt > fun_Pr799129423le_alt ).

tff(sy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    collec1197875955le_alt: fun_Ar1091019988t_bool > fun_Ar1091019988t_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__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_fFalse,type,
    fFalse: bool ).

tff(sy_c_fNot,type,
    fNot: fun_bool_bool ).

tff(sy_c_fTrue,type,
    fTrue: bool ).

tff(sy_c_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    fequal628352221le_alt: fun_Ar1414184139t_bool ).

tff(sy_c_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    fequal293925846e_indi: fun_Ar1906539123i_bool ).

tff(sy_c_fequal_000tc__HOL__Obool,type,
    fequal_bool: fun_bo1549164019l_bool ).

tff(sy_c_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    fequal414630996le_alt: fun_li954148211t_bool ).

tff(sy_c_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc,type,
    fequal1183344582t_bool: fun_fu2072229747l_bool ).

tff(sy_c_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    fequal730162134t_bool: fun_fu1756482675l_bool ).

tff(sy_c_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    fequal818396648t_bool: fun_fu1515494241l_bool ).

tff(sy_c_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc,type,
    fequal1713866472le_alt: fun_Pr973555187t_bool ).

tff(sy_c_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctu,type,
    fequal1128546102le_alt: fun_Pr2138751219t_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__List__Ol,type,
    hAPP_A1866301020le_alt: ( fun_Ar1553825290le_alt * arrow_931160158le_alt ) > list_A1748581779le_alt ).

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__406,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__407,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__408,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__409,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__410,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__411,type,
    hAPP_A662984834le_alt: ( fun_Ar283682666le_alt * arrow_931160158le_alt ) > fun_li165117579le_alt ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__412,type,
    hAPP_A449046541l_bool: ( fun_Ar370769269l_bool * arrow_931160158le_alt ) > fun_fu1818556950l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__413,type,
    hAPP_A2111843262l_bool: ( fun_Ar1236339238l_bool * arrow_931160158le_alt ) > fun_fu775006535l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__414,type,
    hAPP_A343036382t_bool: ( fun_Ar968139788t_bool * arrow_931160158le_alt ) > fun_fu1595299477t_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__415,type,
    hAPP_A1313889230l_bool: ( fun_Ar1311475510l_bool * arrow_931160158le_alt ) > fun_fu1138137687l_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000tc__fun_Itc__416,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__417,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__418,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__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_419,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_420,type,
    hAPP_A643541183i_bool: ( fun_Ar1906539123i_bool * arrow_2115524757e_indi ) > fun_Ar552120407i_bool ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_421,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_422,type,
    hAPP_A1993750875e_indi: ( fun_Ar743199503e_indi * arrow_2115524757e_indi ) > fun_Ar98554099e_indi ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_423,type,
    hAPP_A1717387813e_indi: ( fun_Ar1717876185e_indi * arrow_2115524757e_indi ) > fun_li1314718141e_indi ).

tff(sy_c_hAPP_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__fun_Itc_424,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_425,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_426,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_427,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_428,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_429,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__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000tc__prod_It_430,type,
    hAPP_A957051793e_indi: ( fun_Ar98554099e_indi * arrow_2115524757e_indi ) > produc790689273e_indi ).

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__fun_Itc__Arrow____Order____Mirabelle____ctuiw,type,
    hAPP_b1990207796t_bool: ( fun_bo687293974t_bool * bool ) > fun_Ar1091019988t_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiw_431,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_432,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__HOL__Obool_Mtc__prod_Itc__HOL__Obool,type,
    hAPP_b1115999851l_bool: ( fun_bo1175459231l_bool * bool ) > fun_bo41233099l_bool ).

tff(sy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__L,type,
    hAPP_b994696797t_bool: ( fun_bo1175651857t_bool * bool ) > fun_li107039421t_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_433,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__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__HOL__Obool_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    hAPP_b2048821609l_bool: ( fun_bo41233099l_bool * bool ) > produc373466377l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal,type,
    hAPP_l713721587t_bool: ( fun_li1323594581t_bool * list_A1748581779le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_434,type,
    hAPP_l2085326633le_alt: ( fun_li165117579le_alt * list_A1748581779le_alt ) > list_A1748581779le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_435,type,
    hAPP_l1542090656le_alt: ( fun_li1563304834le_alt * list_A1748581779le_alt ) > fun_Ar1553825290le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_436,type,
    hAPP_l1173894719t_bool: ( fun_li954148211t_bool * list_A1748581779le_alt ) > fun_li1323594581t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_437,type,
    hAPP_l38598005le_alt: ( fun_li973302697le_alt * list_A1748581779le_alt ) > fun_li165117579le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_438,type,
    hAPP_l1385346191l_bool: ( fun_li971691843l_bool * list_A1748581779le_alt ) > fun_li1990043301l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_439,type,
    hAPP_l1285746947le_alt: ( fun_li1501328101le_alt * list_A1748581779le_alt ) > fun_li1019735149le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_440,type,
    hAPP_l1949544791le_alt: ( fun_li1598912907le_alt * list_A1748581779le_alt ) > fun_li352365677le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_441,type,
    hAPP_l358314791le_alt: ( fun_li799656667le_alt * list_A1748581779le_alt ) > fun_li300043069le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_442,type,
    hAPP_l1844587084le_alt: ( fun_li816612014le_alt * list_A1748581779le_alt ) > fun_na1941391286le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_443,type,
    hAPP_l462777825l_bool: ( fun_li1644014275l_bool * list_A1748581779le_alt ) > fun_fu1794958667l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_444,type,
    hAPP_l869353033le_alt: ( fun_li897167357le_alt * list_A1748581779le_alt ) > fun_fu44355679le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_445,type,
    hAPP_l955365607le_alt: ( fun_li1459246747le_alt * list_A1748581779le_alt ) > fun_fu970110205le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_446,type,
    hAPP_l896015811l_bool: ( fun_li1990043301l_bool * list_A1748581779le_alt ) > fun_fu745710381l_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_447,type,
    hAPP_l189416837t_bool: ( fun_li1761430841t_bool * list_A1748581779le_alt ) > fun_fu794113947t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_448,type,
    hAPP_l724324921le_alt: ( fun_li1019735149le_alt * list_A1748581779le_alt ) > fun_Pr799129423le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oal_449,type,
    hAPP_l1128853771le_alt: ( fun_li352365677le_alt * list_A1748581779le_alt ) > produc662089077le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin,type,
    hAPP_l878728062i_bool: ( fun_li60471852i_bool * list_A964264886e_indi ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin_450,type,
    hAPP_l221792213e_indi: ( fun_li1314718141e_indi * list_A964264886e_indi ) > list_A964264886e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin_451,type,
    hAPP_l378231516e_indi: ( fun_li2140397636e_indi * list_A964264886e_indi ) > fun_li1314718141e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin_452,type,
    hAPP_l915221271e_indi: ( fun_li643095493e_indi * list_A964264886e_indi ) > fun_li670536054e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oin_453,type,
    hAPP_l1124485704e_indi: ( fun_li670536054e_indi * list_A964264886e_indi ) > produc645880743e_indi ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__HOL__Obool,type,
    hAPP_list_bool_bool: ( fun_list_bool_bool * list_bool ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__List__Olist_Itc__HOL__Oboo,type,
    hAPP_l1189022293t_bool: ( fun_li107039421t_bool * list_bool ) > list_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__fun_Itc__List__Olist_Itc__,type,
    hAPP_l1947611924t_bool: ( fun_li662746748t_bool * list_bool ) > fun_li107039421t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__fun_Itc__List__Olist_Itc___454,type,
    hAPP_l218095399t_bool: ( fun_li998062677t_bool * list_bool ) > fun_li1455667518t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__prod_Itc__List__Olist_Itc_,type,
    hAPP_l1349316624t_bool: ( fun_li1455667518t_bool * list_bool ) > produc1754317479t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
    hAPP_l108873084t_bool: ( fun_li31015210t_bool * list_l1735481012le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___455,type,
    hAPP_l1653688277le_alt: ( fun_li300043069le_alt * list_l1735481012le_alt ) > list_l1735481012le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___456,type,
    hAPP_l767557321t_bool: ( fun_li1505404791t_bool * list_l1735481012le_alt ) > fun_li31015210t_bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___457,type,
    hAPP_l2037867230le_alt: ( fun_li1383239238le_alt * list_l1735481012le_alt ) > fun_li300043069le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___458,type,
    hAPP_l601007891le_alt: ( fun_li1343239489le_alt * list_l1735481012le_alt ) > fun_li1994300660le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle___459,type,
    hAPP_l2013461446le_alt: ( fun_li1994300660le_alt * list_l1735481012le_alt ) > produc1655778087le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws_460,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws_461,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws_462,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiws_463,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__464,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__465,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__466,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle__467,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_468,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_469,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_470,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle_471,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw_472,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw_473,type,
    hAPP_l1749636298le_alt: ( fun_li276060722le_alt * list_P1216503240le_alt ) > fun_li1823148605le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw_474,type,
    hAPP_l196402619le_alt: ( fun_li968062313le_alt * list_P1216503240le_alt ) > fun_li143639560le_alt ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiw_475,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M,type,
    hAPP_l2093488478t_bool: ( fun_li1991898892t_bool * list_P1493174166le_alt ) > bool ).

tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_476,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_477,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_478,type,
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tff(sy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____M_479,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____Mirabelle__,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mi,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mi_480,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__Li,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__fun_Itc__Arrow____Or,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Ar,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__fun_Itc__prod_Itc__A,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__prod_Itc__Arrow____O,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olis,type,
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tff(sy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J,type,
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tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__H,type,
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order_____625,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    hAPP_f2088469003l_bool: ( fun_fu1519476973l_bool * fun_Pr1852695144le_alt ) > fun_fu2114825504l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_626,type,
    hAPP_f1165889229l_bool: ( fun_fu1286543157l_bool * fun_Pr1698894881e_indi ) > fun_fu2088415961l_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_627,type,
    hAPP_f463844874le_alt: ( fun_fu207034610le_alt * fun_Pr1055212137t_bool ) > arrow_931160158le_alt ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_628,type,
    hAPP_f2029284841e_indi: ( fun_fu2016509975e_indi * fun_Pr1055212137t_bool ) > arrow_2115524757e_indi ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_629,type,
    hAPP_f429946033l_bool: ( fun_fu1015689055l_bool * fun_Pr1055212137t_bool ) > bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_630,type,
    hAPP_f1099651112t_bool: ( fun_fu1540265814t_bool * fun_Pr1055212137t_bool ) > fun_Ar1091019988t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_631,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_632,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_633,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_634,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_635,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_636,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_637,type,
    hAPP_f414777105t_bool: ( fun_fu831091903t_bool * fun_Pr1055212137t_bool ) > fun_bo1116297149t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_638,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_639,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_640,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_641,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_642,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_643,type,
    hAPP_f557837283t_bool: ( fun_fu1275593675t_bool * fun_Pr1055212137t_bool ) > fun_Pr1013460023t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_644,type,
    hAPP_f303577849t_bool: ( fun_fu283227047t_bool * fun_Pr1055212137t_bool ) > fun_Pr1846448037t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_645,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_646,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_647,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_648,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_649,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_650,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O_651,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_Mtc__HOL__Obool,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_Mtc__HOL__Obool_652,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_653,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_654,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_655,type,
    hAPP_f1701776901t_bool: ( fun_fu212416947t_bool * fun_Pr1013460023t_bool ) > fun_fu2027003875t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_656,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_657,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_658,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_659,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_660,type,
    hAPP_f1428266567t_bool: ( fun_fu1167626927t_bool * fun_Pr1013460023t_bool ) > fun_Pr1344020457t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_661,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_662,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_663,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_664,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_665,type,
    hAPP_f498121449t_bool: ( fun_fu671378635t_bool * fun_Pr2138751219t_bool ) > fun_Pr2138751219t_bool ).

tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_666,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_667,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_668,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Oli,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____O,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order____,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow___,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order___,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____ctui,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____ctui_669,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_670,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_671,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu_672,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___,type,
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tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____673,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___674,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___675,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___676,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___677,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___678,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___679,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___680,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___681,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___682,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___683,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___684,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc___685,type,
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tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_,type,
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tff(sy_c_hAPP_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc_,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_686,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_687,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_688,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_689,type,
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tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_690,type,
    hAPP_P469411807l_bool: ( fun_Pr388821651l_bool * produc662089077le_alt ) > fun_fu1138137687l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_691,type,
    hAPP_P272697303l_bool: ( fun_Pr1671213113l_bool * produc662089077le_alt ) > fun_fu1015689055l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_692,type,
    hAPP_P518621093l_bool: ( fun_Pr1472769671l_bool * produc662089077le_alt ) > fun_fu745710381l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_693,type,
    hAPP_P385761265t_bool: ( fun_Pr1846448037t_bool * produc662089077le_alt ) > fun_Pr1055212137t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_694,type,
    hAPP_P1710235071t_bool: ( fun_Pr2138751219t_bool * produc662089077le_alt ) > fun_Pr1013460023t_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_695,type,
    hAPP_P443881687le_alt: ( fun_Pr286692619le_alt * produc662089077le_alt ) > fun_Pr799129423le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_696,type,
    hAPP_P850038171le_alt: ( fun_Pr975121871le_alt * produc662089077le_alt ) > fun_Pr1212253203le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_697,type,
    hAPP_P1831053343le_alt: ( fun_Pr1165181697le_alt * produc662089077le_alt ) > produc1840315303le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_698,type,
    hAPP_P1208706541le_alt: ( fun_Pr799129423le_alt * produc662089077le_alt ) > produc662089077le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_699,type,
    hAPP_P1169232561le_alt: ( fun_Pr1212253203le_alt * produc662089077le_alt ) > produc572918329le_alt ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiw_700,type,
    hAPP_P93441289l_bool: ( fun_Pr1565860459l_bool * produc645880743e_indi ) > fun_fu1006735199l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Olist_Itc__H,type,
    hAPP_P1870454025l_bool: ( fun_Pr852727147l_bool * produc1754317479t_bool ) > fun_fu115111519l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____M,type,
    hAPP_P456721929l_bool: ( fun_Pr1497047659l_bool * produc1655778087le_alt ) > fun_fu451305183l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
    hAPP_P767196425l_bool: ( fun_Pr468477035l_bool * produc802500007t_bool ) > fun_fu986210655l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____,type,
    hAPP_P1176599817l_bool: ( fun_Pr1317140075l_bool * produc133965735t_bool ) > fun_fu184048479l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order___,type,
    hAPP_P269910993l_bool: ( fun_Pr1780593075l_bool * produc1259318155t_bool ) > fun_fu1837767491l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabell,type,
    hAPP_P1381588489l_bool: ( fun_Pr41046891l_bool * produc1424499751le_alt ) > fun_fu2069747679l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____,type,
    hAPP_P2065070345l_bool: ( fun_Pr652626795l_bool * produc718779047le_alt ) > fun_fu1173513823l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    hAPP_P72218221l_bool: ( fun_Pr994915919l_bool * produc1905018073t_bool ) > fun_fu2014033553l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctui,type,
    hAPP_P671450285l_bool: ( fun_Pr1451345551l_bool * produc230355961t_bool ) > fun_fu749815217l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctu,type,
    hAPP_P463482505l_bool: ( fun_Pr739327979l_bool * produc23775335t_bool ) > fun_fu1054620703l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    hAPP_P142038773l_bool: ( fun_Pr324469463l_bool * produc1652795165le_alt ) > fun_fu1907438805l_bool ).

tff(sy_c_hAPP_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,type,
    hAPP_P467663149l_bool: ( fun_Pr592802831l_bool * produc572918329le_alt ) > fun_fu93166577l_bool ).

tff(sy_c_hBOOL,type,
    hBOOL: bool > $o ).

tff(sy_c_member_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt,type,
    member540164529le_alt: fun_Ar370769269l_bool ).

tff(sy_c_member_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi,type,
    member590466050e_indi: fun_Ar1380772935l_bool ).

tff(sy_c_member_000tc__HOL__Obool,type,
    member_bool: fun_bo492988759l_bool ).

tff(sy_c_member_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__O,type,
    member631477888le_alt: fun_li1644014275l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc_,type,
    member1816667497t_bool: fun_fu1606938133l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__701,type,
    member1066226041t_bool: fun_fu844367925l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__702,type,
    member1994455707t_bool: fun_fu421594869l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc__703,type,
    member542710667le_alt: fun_fu308010585l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc,type,
    member1188420050t_bool: fun_fu1591782325l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_704,type,
    member291481314t_bool: fun_fu1816256693l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_705,type,
    member1159072754t_bool: fun_fu1291054887l_bool ).

tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mtc_706,type,
    member418553588le_alt: fun_fu1338365749l_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__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,type,
    member1164470647le_alt: fun_fu1959128625l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___707,type,
    member1408848082e_indi: fun_fu1227713461l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___708,type,
    member1791451290l_bool: fun_fu81176373l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___709,type,
    member1801442306t_bool: fun_fu446267975l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___710,type,
    member1997523634le_alt: fun_fu658052661l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,type,
    member465949031le_alt: fun_fu2120515089l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_711,type,
    member2095441122e_indi: fun_fu1739677877l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_712,type,
    member213355690l_bool: fun_fu413400117l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_713,type,
    member2126235330le_alt: fun_fu2092057397l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,type,
    member925775173le_alt: fun_fu199169653l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_714,type,
    member527726724e_indi: fun_fu1041166411l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_715,type,
    member717964108l_bool: fun_fu830715227l_bool ).

tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_716,type,
    member955488100le_alt: fun_fu1925294731l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    member1558558165le_alt: fun_fu1519476973l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__717,type,
    member1747786740e_indi: fun_fu1286543157l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__718,type,
    member57118396t_bool: fun_fu1556412341l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__719,type,
    member879596244le_alt: fun_fu293053621l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,type,
    member1126314290t_bool: fun_fu194704949l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_720,type,
    member1385717314t_bool: fun_fu1051681589l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_721,type,
    member564649106t_bool: fun_fu1650235367l_bool ).

tff(sy_c_member_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_722,type,
    member326932052le_alt: fun_fu202949813l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_Mtc,type,
    member553230100le_alt: fun_Pr1228236907l_bool ).

tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_Mt,type,
    member938783462e_indi: fun_Pr2051704463l_bool ).

tff(sy_c_member_000tc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J,type,
    member624253174l_bool: fun_Pr292042671l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctu,type,
    member1475736930le_alt: fun_Pr1472769671l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____ctu_723,type,
    member1920957716e_indi: fun_Pr1565860459l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Olist_Itc_,type,
    member1058364180t_bool: fun_Pr852727147l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____Order___,type,
    member302274452le_alt: fun_Pr1497047659l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabel,type,
    member1166104852t_bool: fun_Pr468477035l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order__,type,
    member2127060244t_bool: fun_Pr1317140075l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order_,type,
    member294755704t_bool: fun_Pr1780593075l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabe,type,
    member1552328084le_alt: fun_Pr41046891l_bool ).

tff(sy_c_member_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow__,type,
    member1590082836le_alt: fun_Pr652626795l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,type,
    member1904937926t_bool: fun_Pr994915919l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ct,type,
    member710460646t_bool: fun_Pr1451345551l_bool ).

tff(sy_c_member_000tc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____c,type,
    member1092949460t_bool: fun_Pr739327979l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,type,
    member92652554le_alt: fun_Pr324469463l_bool ).

tff(sy_c_member_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabe,type,
    member1834889254le_alt: fun_Pr592802831l_bool ).

tff(sy_v_F,type,
    f: fun_fu1595299477t_bool ).

tff(sy_v_P_H____,type,
    p_1: fun_Ar500372357t_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 ).

%----Relevant facts (700)
tff(fact_0__096P_A_058_AProf_096,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,p),arrow_1190054106e_Prof)) ).

tff(fact_1_assms_I3_J,axiom,
    hBOOL(hAPP_f611501301l_bool(arrow_888693696le_IIA,f)) ).

tff(fact_2_u,axiom,
    hBOOL(hAPP_f611501301l_bool(arrow_22284131nimity,f)) ).

tff(fact_3__096a_A_126_061_Ab_096,axiom,
    a != b ).

tff(fact_4_dist,axiom,
    hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,a),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,b),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,c),nil_Ar1741995278le_alt))))) ).

tff(fact_5_iff,axiom,
    ! [I: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_A1174518481t_bool(p,I)))
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,b),a)),hAPP_A1174518481t_bool(p_1,I))) ) ).

tff(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_,axiom,
    ~ ! [C: arrow_931160158le_alt] : ~ hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,a),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,b),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,C),nil_Ar1741995278le_alt))))) ).

tff(fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),p)),c)),b))),b)),a)),arrow_1190054106e_Prof)) ).

tff(fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),p)),c)),b))),b)),a))),a)),c)),arrow_1190054106e_Prof)) ).

tff(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(hAPP_f293545699t_bool(cOMBC_18834461t_bool,hAPP_A102926893t_bool(hAPP_f141075873t_bool(cOMBC_1505804284t_bool,hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,arrow_636638768_below),p)),c)),b)),arrow_1190054106e_Prof)) ).

tff(fact_10_in__mkbot,axiom,
    ! [X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_1: 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_1),Y_2)),hAPP_A606737888t_bool(arrow_592884904_mkbot(L_1),Z_1)))
    <=> ( ( Y_2 != Z_1 )
        & ( ( X_1 = Z_1 )
         => ( X_1 != Y_2 ) )
        & ( ( X_1 != Z_1 )
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),L_1)) ) ) ) ).

tff(fact_11_in__mktop,axiom,
    ! [X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_1: 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_1),Y_2)),hAPP_A606737888t_bool(arrow_741591990_mktop(L_1),Z_1)))
    <=> ( ( X_1 != Z_1 )
        & ( ( Y_2 = Z_1 )
         => ( X_1 != Y_2 ) )
        & ( ( Y_2 != Z_1 )
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),L_1)) ) ) ) ).

tff(fact_12_in__below,axiom,
    ! [X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
       => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_636638768_below,L_1),Aa),Ba)))
        <=> ( ( X_1 != Y_2 )
            & ( ( Y_2 = Aa )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Ba)),L_1)) )
            & ( ( Y_2 != Aa )
             => ( ( ( X_1 = 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_1)) ) )
                & ( ( X_1 != Aa )
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),L_1)) ) ) ) ) ) ) ) ).

tff(fact_13_split__paired__All,axiom,
    ! [Pa: fun_Pr1013460023t_bool] :
      ( ! [X1: produc662089077le_alt] : hBOOL(hAPP_P274047445t_bool(Pa,X1))
    <=> ! [A: list_A1748581779le_alt,B: list_A1748581779le_alt] : hBOOL(hAPP_P274047445t_bool(Pa,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),B))) ) ).

tff(fact_14_split__paired__All,axiom,
    ! [Pa: fun_Pr1055212137t_bool] :
      ( ! [X1: produc1840315303le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,X1))
    <=> ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B))) ) ).

tff(fact_15_Pair__eq,axiom,
    ! [Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt,A_2: list_A1748581779le_alt,B_3: list_A1748581779le_alt] :
      ( ( hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba) = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A_2),B_3) )
    <=> ( ( Aa = A_2 )
        & ( Ba = B_3 ) ) ) ).

tff(fact_16_Pair__eq,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt,A_2: arrow_931160158le_alt,B_3: arrow_931160158le_alt] :
      ( ( hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba) = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_2),B_3) )
    <=> ( ( Aa = A_2 )
        & ( Ba = B_3 ) ) ) ).

tff(fact_17_Pair__inject,axiom,
    ! [A_7: list_A1748581779le_alt,B_5: list_A1748581779le_alt,A_6: list_A1748581779le_alt,B_4: list_A1748581779le_alt] :
      ( ( hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A_7),B_5) = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A_6),B_4) )
     => ~ ( ( A_7 = A_6 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_18_Pair__inject,axiom,
    ! [A_7: arrow_931160158le_alt,B_5: arrow_931160158le_alt,A_6: arrow_931160158le_alt,B_4: arrow_931160158le_alt] :
      ( ( hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_7),B_5) = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_6),B_4) )
     => ~ ( ( A_7 = A_6 )
         => ( B_5 != B_4 ) ) ) ).

tff(fact_19_in__rel__def,axiom,
    ! [R_2: fun_Pr1013460023t_bool,X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(in_rel1976830678le_alt(R_2),X_1),Y_2))
    <=> hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_2)) ) ).

tff(fact_20_in__rel__def,axiom,
    ! [R_2: fun_Pr1055212137t_bool,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(in_rel267123714le_alt(R_2),X_1),Y_2))
    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_2)) ) ).

tff(fact_21_below__Lin,axiom,
    ! [L_1: fun_Pr1055212137t_bool,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( ( X_1 != Y_2 )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_636638768_below,L_1),X_1),Y_2)),arrow_915577424le_Lin)) ) ) ).

tff(fact_22__096P_H_A_058_AProf_096,axiom,
    hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,p_1),arrow_1190054106e_Prof)) ).

tff(fact_23__C1_C,axiom,
    ! [P_a: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,A_2: arrow_931160158le_alt,B_3: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( A_2 != B_3 )
       => ( ( Aa != B_3 )
         => ( ( Ba != A_2 )
           => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
             => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_a),arrow_1190054106e_Prof))
               => ( ! [I: 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)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_2),B_3)),hAPP_A1174518481t_bool(P_a,I))) )
                 => ( 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_2),B_3)),hAPP_f792184801t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).

tff(fact_24__C2_C,axiom,
    ! [P_a: fun_Ar500372357t_bool,Pa: fun_Ar500372357t_bool,A_2: arrow_931160158le_alt,B_3: arrow_931160158le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( ( A_2 != B_3 )
       => ( ( Aa != B_3 )
         => ( ( Ba != A_2 )
           => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Pa),arrow_1190054106e_Prof))
             => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,P_a),arrow_1190054106e_Prof))
               => ( ! [I: 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)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A_2),B_3)),hAPP_A1174518481t_bool(P_a,I))) )
                 => ( 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_2),B_3)),hAPP_f792184801t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).

tff(fact_25_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_26_const__Lin__Prof,axiom,
    ! [L_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_f311418073t_bool(cOMBK_1522533360e_indi,L_1)),arrow_1190054106e_Prof)) ) ).

tff(fact_27_mkbot__Lin,axiom,
    ! [X_1: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(arrow_592884904_mkbot(L_1),X_1)),arrow_915577424le_Lin)) ) ).

tff(fact_28_mktop__Lin,axiom,
    ! [X_1: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(arrow_741591990_mktop(L_1),X_1)),arrow_915577424le_Lin)) ) ).

tff(fact_29_Lin__irrefl,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),L_1))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Ba),Aa)),L_1)) ) ) ).

tff(fact_30_notin__Lin__iff,axiom,
    ! [X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
     => ( ( X_1 != Y_2 )
       => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),L_1))
        <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Y_2),X_1)),L_1)) ) ) ) ).

tff(fact_31_third__alt,axiom,
    ! [A_5: arrow_931160158le_alt,B_2: arrow_931160158le_alt] :
      ( ( A_5 != B_2 )
     => ? [C: arrow_931160158le_alt] : hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A_5),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,B_2),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,C),nil_Ar1741995278le_alt))))) ) ).

tff(fact_32_IIA__def,axiom,
    ! [Fa: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(arrow_888693696le_IIA,Fa))
    <=> ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),arrow_1190054106e_Prof))
         => ! [Xa: fun_Ar500372357t_bool] :
              ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Xa),arrow_1190054106e_Prof))
             => ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
                  ( ! [I: arrow_2115524757e_indi] :
                      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_A1174518481t_bool(X_2,I)))
                    <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_A1174518481t_bool(Xa,I))) )
                 => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_f792184801t_bool(Fa,X_2)))
                  <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_f792184801t_bool(Fa,Xa))) ) ) ) ) ) ).

tff(fact_33_unanimity__def,axiom,
    ! [Fa: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(arrow_22284131nimity,Fa))
    <=> ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),arrow_1190054106e_Prof))
         => ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
              ( ! [I: arrow_2115524757e_indi] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_A1174518481t_bool(X_2,I)))
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_f792184801t_bool(Fa,X_2))) ) ) ) ).

tff(fact_34_complete__Lin,axiom,
    ! [Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ? [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),arrow_915577424le_Lin))
          & hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),X_2)) ) ) ).

tff(fact_35_in__above,axiom,
    ! [X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,L_1: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( ( Aa != Ba )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
       => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),hAPP_A606737888t_bool(arrow_1475523868_above(L_1,Aa),Ba)))
        <=> ( ( X_1 != Y_2 )
            & ( ( X_1 = Ba )
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Y_2)),L_1)) )
            & ( ( X_1 != Ba )
             => ( ( ( Y_2 = Ba )
                 => ( ( X_1 = Aa )
                    | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Aa)),L_1)) ) )
                & ( ( Y_2 != Ba )
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),L_1)) ) ) ) ) ) ) ) ).

tff(fact_36_distinct_Osimps_I1_J,axiom,
    hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,nil_Ar1741995278le_alt)) ).

tff(fact_37_list_Osimps_I2_J,axiom,
    ! [A_4: arrow_931160158le_alt,List_4: list_A1748581779le_alt] : ( nil_Ar1741995278le_alt != hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A_4),List_4) ) ).

tff(fact_38_list_Osimps_I3_J,axiom,
    ! [A_3: arrow_931160158le_alt,List_3: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A_3),List_3) != nil_Ar1741995278le_alt ) ).

tff(fact_39_alt3,axiom,
    ? [A: arrow_931160158le_alt,B: arrow_931160158le_alt,C: arrow_931160158le_alt] : hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,B),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,C),nil_Ar1741995278le_alt))))) ).

tff(fact_40_linear__alt,axiom,
    ? [L_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_2),arrow_915577424le_Lin)) ).

tff(fact_41_list_Oinject,axiom,
    ! [Aa: arrow_931160158le_alt,List_2: list_A1748581779le_alt,A_2: arrow_931160158le_alt,List_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Aa),List_2) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A_2),List_1) )
    <=> ( ( Aa = A_2 )
        & ( List_2 = List_1 ) ) ) ).

tff(fact_42_not__Cons__self2,axiom,
    ! [X_23: arrow_931160158le_alt,Xs_41: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_23),Xs_41) != Xs_41 ) ).

tff(fact_43_not__Cons__self,axiom,
    ! [Xs_40: list_A1748581779le_alt,X_22: arrow_931160158le_alt] : ( Xs_40 != hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_22),Xs_40) ) ).

tff(fact_44_above__Lin,axiom,
    ! [L_1: fun_Pr1055212137t_bool,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( ( X_1 != Y_2 )
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,L_1),arrow_915577424le_Lin))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(arrow_1475523868_above(L_1,X_1),Y_2)),arrow_915577424le_Lin)) ) ) ).

tff(fact_45_dictatorI,axiom,
    ! [I_4: 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_2: fun_Ar500372357t_bool] :
            ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),arrow_1190054106e_Prof))
           => ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
                ( ( A != B )
               => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_A1174518481t_bool(X_2,I_4)))
                 => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),hAPP_f792184801t_bool(Fa,X_2))) ) ) )
       => hBOOL(hAPP_A1888055029i_bool(hAPP_f740807359i_bool(arrow_1472924909ctator,Fa),I_4)) ) ) ).

tff(fact_46_PiE,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr359894313l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),hAPP_P1830623733l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1)) ) ) ).

tff(fact_47_PiE,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar836847646le_alt,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1275715144t_bool] :
      ( hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_1)),hAPP_A606737888t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1)) ) ) ).

tff(fact_48_PiE,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar369661729le_alt,A_1: fun_Ar552120407i_bool,B_1: fun_Ar500372357t_bool] :
      ( hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_1)),hAPP_A1174518481t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1)) ) ) ).

tff(fact_49_PiE,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1165181697le_alt,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr1846448037t_bool] :
      ( hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_1)),hAPP_P385761265t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1)) ) ) ).

tff(fact_50_PiE,axiom,
    ! [X_1: bool,F: fun_bo1479727337le_alt,A_1: fun_bool_bool,B_1: fun_bo1116297149t_bool] :
      ( hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_1)),hAPP_b1263785481t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).

tff(fact_51_PiE,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar421919996t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1236339238l_bool] :
      ( hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_1)),hAPP_A2111843262l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1)) ) ) ).

tff(fact_52_PiE,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar687924991t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar684516451l_bool] :
      ( hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_1)),hAPP_A182831535l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1)) ) ) ).

tff(fact_53_PiE,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1799779039t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr966099075l_bool] :
      ( hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_1)),hAPP_P725642959l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1)) ) ) ).

tff(fact_54_PiE,axiom,
    ! [X_1: bool,F: fun_bo266809543t_bool,A_1: fun_bool_bool,B_1: fun_bo645734555l_bool] :
      ( hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_1)),hAPP_b1849744615l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).

tff(fact_55_PiE,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar1275715144t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1026121174l_bool] :
      ( hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_1)),hAPP_A1787768616l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1)) ) ) ).

tff(fact_56_PiE,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1846448037t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr1671213113l_bool] :
      ( hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_1)),hAPP_P272697303l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1)) ) ) ).

tff(fact_57_PiE,axiom,
    ! [X_1: bool,F: fun_bo1116297149t_bool,A_1: fun_bool_bool,B_1: fun_bo96602657l_bool] :
      ( hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_1)),hAPP_b1650070463l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).

tff(fact_58_PiE,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar968139788t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1311475510l_bool] :
      ( hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_1)),hAPP_A1313889230l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1)) ) ) ).

tff(fact_59_PiE,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar1939863823t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar1270429299l_bool] :
      ( hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_1)),hAPP_A1538515647l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1)) ) ) ).

tff(fact_60_PiE,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1143104751t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr388821651l_bool] :
      ( hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_1)),hAPP_P469411807l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1)) ) ) ).

tff(fact_61_PiE,axiom,
    ! [X_1: bool,F: fun_bo2027801303t_bool,A_1: fun_bool_bool,B_1: fun_bo979888811l_bool] :
      ( hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_1)),hAPP_b816606711l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).

tff(fact_62_PiE,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1852695144le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr459606624t_bool] :
      ( hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_1)),hAPP_P1239753854t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1)) ) ) ).

tff(fact_63_PiE,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1698894881e_indi,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr39488737i_bool] :
      ( hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_1)),hAPP_P1326783277i_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1)) ) ) ).

tff(fact_64_PiE,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1717845889le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr1556001345t_bool] :
      ( hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_1)),hAPP_P1279976973t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1)) ) ) ).

tff(fact_65_PiE,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1917206794le_alt,A_1: fun_fu775006535l_bool,B_1: fun_fu1678217534t_bool] :
      ( hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_1)),hAPP_f87867740t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1)) ) ) ).

tff(fact_66_PiE,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu908353023e_indi,A_1: fun_fu775006535l_bool,B_1: fun_fu1765260675i_bool] :
      ( hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_1)),hAPP_f109229519i_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1)) ) ) ).

tff(fact_67_PiE,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu523504735le_alt,A_1: fun_fu775006535l_bool,B_1: fun_fu2027003875t_bool] :
      ( hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_1)),hAPP_f1203715503t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1)) ) ) ).

tff(fact_68_PiE,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu775006535l_bool,A_1: fun_fu775006535l_bool,B_1: fun_fu1471766731l_bool] :
      ( hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_1)),hAPP_f84039575l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1)) ) ) ).

tff(fact_69_PiE,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu207034610le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_fu1540265814t_bool] :
      ( hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_1)),hAPP_f1099651112t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1)) ) ) ).

tff(fact_70_PiE,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu2016509975e_indi,A_1: fun_fu1015689055l_bool,B_1: fun_fu1766473067i_bool] :
      ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_1)),hAPP_f1957024259i_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1)) ) ) ).

tff(fact_71_PiE,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu89803383le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_fu1275593675t_bool] :
      ( hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_1)),hAPP_f557837283t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1)) ) ) ).

tff(fact_72_PiE,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu1015689055l_bool,A_1: fun_fu1015689055l_bool,B_1: fun_fu44268723l_bool] :
      ( hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_1)),hAPP_f269590987l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1)) ) ) ).

tff(fact_73_PiE,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu367862778le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_fu1551598158t_bool] :
      ( hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_1)),hAPP_f735144044t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1)) ) ) ).

tff(fact_74_PiE,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1596339983e_indi,A_1: fun_fu1138137687l_bool,B_1: fun_fu2127564915i_bool] :
      ( hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_1)),hAPP_f740807359i_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1)) ) ) ).

tff(fact_75_PiE,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1883622767le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_fu2016938707t_bool] :
      ( hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_1)),hAPP_f1014198943t_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1)) ) ) ).

tff(fact_76_PiE,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1138137687l_bool,A_1: fun_fu1138137687l_bool,B_1: fun_fu1460706235l_bool] :
      ( hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_1)),hAPP_f352672903l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1)) ) ) ).

tff(fact_77_PiE,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A_1: fun_fu775006535l_bool,B_1: fun_fu787660105l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),hAPP_f1498158055l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1)) ) ) ).

tff(fact_78_PiE,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar1198543961l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,B_1)))
     => ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),hAPP_A1279849719l_bool(B_1,X_1)))
       => ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1)) ) ) ).

tff(fact_79_list_Oexhaust,axiom,
    ! [Y_5: list_A1748581779le_alt] :
      ( ( Y_5 != nil_Ar1741995278le_alt )
     => ~ ! [A: arrow_931160158le_alt,List: list_A1748581779le_alt] : ( Y_5 != hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A),List) ) ) ).

tff(fact_80_neq__Nil__conv,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( Xs != nil_Ar1741995278le_alt )
    <=> ? [Y_1: arrow_931160158le_alt,Ys: list_A1748581779le_alt] : ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Ys) ) ) ).

tff(fact_81_dictator__def,axiom,
    ! [Fa: fun_fu1595299477t_bool,I_4: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_A1888055029i_bool(hAPP_f740807359i_bool(arrow_1472924909ctator,Fa),I_4))
    <=> ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),arrow_1190054106e_Prof))
         => ( hAPP_f792184801t_bool(Fa,X_2) = hAPP_A1174518481t_bool(X_2,I_4) ) ) ) ).

tff(fact_82_funcset__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A_1: fun_Pr1055212137t_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B_1))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_83_funcset__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1852695144le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Ar1091019988t_bool] :
      ( hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,hAPP_f651702217t_bool(cOMBK_350001591le_alt,B_1))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_84_funcset__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1698894881e_indi,A_1: fun_Pr1055212137t_bool,B_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,hAPP_f324402723i_bool(cOMBK_646689008le_alt,B_1))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_1)),B_1)) ) ) ).

tff(fact_85_funcset__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1717845889le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,hAPP_f1545334371t_bool(cOMBK_1927707728le_alt,B_1))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_86_funcset__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1917206794le_alt,A_1: fun_fu775006535l_bool,B_1: fun_Ar1091019988t_bool] :
      ( hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,hAPP_f1528883111t_bool(cOMBK_841302421t_bool,B_1))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_87_funcset__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu908353023e_indi,A_1: fun_fu775006535l_bool,B_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,hAPP_f1845592261i_bool(cOMBK_1865603534t_bool,B_1))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_1)),B_1)) ) ) ).

tff(fact_88_funcset__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu523504735le_alt,A_1: fun_fu775006535l_bool,B_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,hAPP_f1701776901t_bool(cOMBK_851707182t_bool,B_1))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_89_funcset__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu775006535l_bool,A_1: fun_fu775006535l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,hAPP_f2138308309l_bool(cOMBK_768188438t_bool,B_1))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_1)),B_1)) ) ) ).

tff(fact_90_funcset__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu207034610le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_Ar1091019988t_bool] :
      ( hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,hAPP_f5211821t_bool(cOMBK_1771409497t_bool,B_1))))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_91_funcset__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu2016509975e_indi,A_1: fun_fu1015689055l_bool,B_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,hAPP_f676424105i_bool(cOMBK_854051296t_bool,B_1))))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_1)),B_1)) ) ) ).

tff(fact_92_funcset__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu89803383le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,hAPP_f2035600681t_bool(cOMBK_1082115712t_bool,B_1))))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_93_funcset__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu1015689055l_bool,A_1: fun_fu1015689055l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,hAPP_f1519524905l_bool(cOMBK_1253994904t_bool,B_1))))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_1)),B_1)) ) ) ).

tff(fact_94_funcset__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu367862778le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_Ar1091019988t_bool] :
      ( hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,hAPP_f2020309431t_bool(cOMBK_1604195493t_bool,B_1))))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_95_funcset__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1596339983e_indi,A_1: fun_fu1138137687l_bool,B_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,hAPP_f301073845i_bool(cOMBK_189636062t_bool,B_1))))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_1)),B_1)) ) ) ).

tff(fact_96_funcset__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1883622767le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,hAPP_f1729202933t_bool(cOMBK_1744775486t_bool,B_1))))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_97_funcset__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1138137687l_bool,A_1: fun_fu1138137687l_bool,B_1: fun_bool_bool] :
      ( hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,hAPP_f1090778053l_bool(cOMBK_1251240998t_bool,B_1))))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_1)),B_1)) ) ) ).

tff(fact_98_funcset__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar836847646le_alt,A_1: fun_Ar1091019988t_bool,B_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,hAPP_f786530292t_bool(cOMBK_82914883le_alt,B_1))))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_99_funcset__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar369661729le_alt,A_1: fun_Ar552120407i_bool,B_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,hAPP_f311418073t_bool(cOMBK_1522533360e_indi,B_1))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_100_funcset__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1165181697le_alt,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,hAPP_f303577849t_bool(cOMBK_1603999824le_alt,B_1))))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_101_funcset__mem,axiom,
    ! [X_1: bool,F: fun_bo1479727337le_alt,A_1: fun_bool_bool,B_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,hAPP_f414777105t_bool(cOMBK_382434616l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_1)),B_1)) ) ) ).

tff(fact_102_funcset__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar421919996t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,hAPP_f1837403508l_bool(cOMBK_1262239973le_alt,B_1))))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_103_funcset__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar687924991t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,hAPP_f2099786901l_bool(cOMBK_970693070e_indi,B_1))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_104_funcset__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1799779039t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,hAPP_f1405662645l_bool(cOMBK_1129525550le_alt,B_1))))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_105_funcset__mem,axiom,
    ! [X_1: bool,F: fun_bo266809543t_bool,A_1: fun_bool_bool,B_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,hAPP_f126479309l_bool(cOMBK_1709453334l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_106_funcset__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar1275715144t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,hAPP_f377423160l_bool(cOMBK_433524227le_alt,B_1))))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_107_funcset__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1846448037t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,hAPP_f1115980887l_bool(cOMBK_2034944144le_alt,B_1))))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_108_funcset__mem,axiom,
    ! [X_1: bool,F: fun_bo1116297149t_bool,A_1: fun_bool_bool,B_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,hAPP_f259799103l_bool(cOMBK_1489759608l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_109_funcset__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar968139788t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,hAPP_f2030964596l_bool(cOMBK_289343701le_alt,B_1))))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_110_funcset__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar1939863823t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,hAPP_f1639366069l_bool(cOMBK_1014681054e_indi,B_1))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_111_funcset__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1143104751t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,hAPP_f64308949l_bool(cOMBK_801230142le_alt,B_1))))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_112_funcset__mem,axiom,
    ! [X_1: bool,F: fun_bo2027801303t_bool,A_1: fun_bool_bool,B_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,hAPP_f1922499821l_bool(cOMBK_1417083942l_bool,B_1))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_113_funcset__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A_1: fun_fu775006535l_bool,B_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B_1))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_114_funcset__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B_1))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),B_1)) ) ) ).

tff(fact_115_splice_Osimps_I2_J,axiom,
    ! [V_1: arrow_931160158le_alt,Va: list_A1748581779le_alt] : ( splice1976699617le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,V_1),Va),nil_Ar1741995278le_alt) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,V_1),Va) ) ).

tff(fact_116_splice_Osimps_I3_J,axiom,
    ! [X_21: arrow_931160158le_alt,Xs_39: list_A1748581779le_alt,Y_4: arrow_931160158le_alt,Ys_18: list_A1748581779le_alt] : ( splice1976699617le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_21),Xs_39),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_4),Ys_18)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_21),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_4),splice1976699617le_alt(Xs_39,Ys_18))) ) ).

tff(fact_117_splice_Osimps_I1_J,axiom,
    ! [Ys_17: list_A1748581779le_alt] : ( splice1976699617le_alt(nil_Ar1741995278le_alt,Ys_17) = Ys_17 ) ).

tff(fact_118_splice__Nil2,axiom,
    ! [Xs_38: list_A1748581779le_alt] : ( splice1976699617le_alt(Xs_38,nil_Ar1741995278le_alt) = Xs_38 ) ).

tff(fact_119_Pi__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1055212137t_bool,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr359894313l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_1)),hAPP_P1830623733l_bool(B_1,X_1))) ) ) ).

tff(fact_120_Pi__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1852695144le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr459606624t_bool] :
      ( hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_1)),hAPP_P1239753854t_bool(B_1,X_1))) ) ) ).

tff(fact_121_Pi__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1698894881e_indi,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr39488737i_bool] :
      ( hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_1)),hAPP_P1326783277i_bool(B_1,X_1))) ) ) ).

tff(fact_122_Pi__mem,axiom,
    ! [X_1: produc1840315303le_alt,F: fun_Pr1717845889le_alt,A_1: fun_Pr1055212137t_bool,B_1: fun_Pr1556001345t_bool] :
      ( hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_1)),hAPP_P1279976973t_bool(B_1,X_1))) ) ) ).

tff(fact_123_Pi__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1917206794le_alt,A_1: fun_fu775006535l_bool,B_1: fun_fu1678217534t_bool] :
      ( hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_1)),hAPP_f87867740t_bool(B_1,X_1))) ) ) ).

tff(fact_124_Pi__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu908353023e_indi,A_1: fun_fu775006535l_bool,B_1: fun_fu1765260675i_bool] :
      ( hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_1)),hAPP_f109229519i_bool(B_1,X_1))) ) ) ).

tff(fact_125_Pi__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu523504735le_alt,A_1: fun_fu775006535l_bool,B_1: fun_fu2027003875t_bool] :
      ( hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_1)),hAPP_f1203715503t_bool(B_1,X_1))) ) ) ).

tff(fact_126_Pi__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu775006535l_bool,A_1: fun_fu775006535l_bool,B_1: fun_fu1471766731l_bool] :
      ( hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_1)),hAPP_f84039575l_bool(B_1,X_1))) ) ) ).

tff(fact_127_Pi__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu207034610le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_fu1540265814t_bool] :
      ( hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_1)),hAPP_f1099651112t_bool(B_1,X_1))) ) ) ).

tff(fact_128_Pi__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu2016509975e_indi,A_1: fun_fu1015689055l_bool,B_1: fun_fu1766473067i_bool] :
      ( hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_1)),hAPP_f1957024259i_bool(B_1,X_1))) ) ) ).

tff(fact_129_Pi__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu89803383le_alt,A_1: fun_fu1015689055l_bool,B_1: fun_fu1275593675t_bool] :
      ( hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_1)),hAPP_f557837283t_bool(B_1,X_1))) ) ) ).

tff(fact_130_Pi__mem,axiom,
    ! [X_1: fun_Pr1055212137t_bool,F: fun_fu1015689055l_bool,A_1: fun_fu1015689055l_bool,B_1: fun_fu44268723l_bool] :
      ( hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_1)),hAPP_f269590987l_bool(B_1,X_1))) ) ) ).

tff(fact_131_Pi__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu367862778le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_fu1551598158t_bool] :
      ( hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_1)),hAPP_f735144044t_bool(B_1,X_1))) ) ) ).

tff(fact_132_Pi__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1596339983e_indi,A_1: fun_fu1138137687l_bool,B_1: fun_fu2127564915i_bool] :
      ( hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,B_1)))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_1)),hAPP_f740807359i_bool(B_1,X_1))) ) ) ).

tff(fact_133_Pi__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1883622767le_alt,A_1: fun_fu1138137687l_bool,B_1: fun_fu2016938707t_bool] :
      ( hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_1)),hAPP_f1014198943t_bool(B_1,X_1))) ) ) ).

tff(fact_134_Pi__mem,axiom,
    ! [X_1: fun_fu1595299477t_bool,F: fun_fu1138137687l_bool,A_1: fun_fu1138137687l_bool,B_1: fun_fu1460706235l_bool] :
      ( hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
       => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_1)),hAPP_f352672903l_bool(B_1,X_1))) ) ) ).

tff(fact_135_Pi__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar836847646le_alt,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1275715144t_bool] :
      ( hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_1)),hAPP_A606737888t_bool(B_1,X_1))) ) ) ).

tff(fact_136_Pi__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar369661729le_alt,A_1: fun_Ar552120407i_bool,B_1: fun_Ar500372357t_bool] :
      ( hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_1)),hAPP_A1174518481t_bool(B_1,X_1))) ) ) ).

tff(fact_137_Pi__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1165181697le_alt,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr1846448037t_bool] :
      ( hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_1)),hAPP_P385761265t_bool(B_1,X_1))) ) ) ).

tff(fact_138_Pi__mem,axiom,
    ! [X_1: bool,F: fun_bo1479727337le_alt,A_1: fun_bool_bool,B_1: fun_bo1116297149t_bool] :
      ( hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_1)),hAPP_b1263785481t_bool(B_1,X_1))) ) ) ).

tff(fact_139_Pi__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar421919996t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1236339238l_bool] :
      ( hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_1)),hAPP_A2111843262l_bool(B_1,X_1))) ) ) ).

tff(fact_140_Pi__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar687924991t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar684516451l_bool] :
      ( hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_1)),hAPP_A182831535l_bool(B_1,X_1))) ) ) ).

tff(fact_141_Pi__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1799779039t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr966099075l_bool] :
      ( hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_1)),hAPP_P725642959l_bool(B_1,X_1))) ) ) ).

tff(fact_142_Pi__mem,axiom,
    ! [X_1: bool,F: fun_bo266809543t_bool,A_1: fun_bool_bool,B_1: fun_bo645734555l_bool] :
      ( hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_1)),hAPP_b1849744615l_bool(B_1,X_1))) ) ) ).

tff(fact_143_Pi__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar1275715144t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1026121174l_bool] :
      ( hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_1)),hAPP_A1787768616l_bool(B_1,X_1))) ) ) ).

tff(fact_144_Pi__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1846448037t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr1671213113l_bool] :
      ( hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_1)),hAPP_P272697303l_bool(B_1,X_1))) ) ) ).

tff(fact_145_Pi__mem,axiom,
    ! [X_1: bool,F: fun_bo1116297149t_bool,A_1: fun_bool_bool,B_1: fun_bo96602657l_bool] :
      ( hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_1)),hAPP_b1650070463l_bool(B_1,X_1))) ) ) ).

tff(fact_146_Pi__mem,axiom,
    ! [X_1: arrow_931160158le_alt,F: fun_Ar968139788t_bool,A_1: fun_Ar1091019988t_bool,B_1: fun_Ar1311475510l_bool] :
      ( hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_1)),hAPP_A1313889230l_bool(B_1,X_1))) ) ) ).

tff(fact_147_Pi__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar1939863823t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar1270429299l_bool] :
      ( hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_1)),hAPP_A1538515647l_bool(B_1,X_1))) ) ) ).

tff(fact_148_Pi__mem,axiom,
    ! [X_1: produc662089077le_alt,F: fun_Pr1143104751t_bool,A_1: fun_Pr1013460023t_bool,B_1: fun_Pr388821651l_bool] :
      ( hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_1)),hAPP_P469411807l_bool(B_1,X_1))) ) ) ).

tff(fact_149_Pi__mem,axiom,
    ! [X_1: bool,F: fun_bo2027801303t_bool,A_1: fun_bool_bool,B_1: fun_bo979888811l_bool] :
      ( hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
       => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_1)),hAPP_b816606711l_bool(B_1,X_1))) ) ) ).

tff(fact_150_Pi__mem,axiom,
    ! [X_1: fun_Ar500372357t_bool,F: fun_fu1595299477t_bool,A_1: fun_fu775006535l_bool,B_1: fun_fu787660105l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_1)),hAPP_f1498158055l_bool(B_1,X_1))) ) ) ).

tff(fact_151_Pi__mem,axiom,
    ! [X_1: arrow_2115524757e_indi,F: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool,B_1: fun_Ar1198543961l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,B_1)))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
       => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_1)),hAPP_A1279849719l_bool(B_1,X_1))) ) ) ).

tff(fact_152_Pi__I,axiom,
    ! [F: fun_Pr1852695144le_alt,B_1: fun_Pr459606624t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_2)),hAPP_P1239753854t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,B_1))) ) ).

tff(fact_153_Pi__I,axiom,
    ! [F: fun_Pr1698894881e_indi,B_1: fun_Pr39488737i_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_2)),hAPP_P1326783277i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,B_1))) ) ).

tff(fact_154_Pi__I,axiom,
    ! [F: fun_Pr1717845889le_alt,B_1: fun_Pr1556001345t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_2)),hAPP_P1279976973t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,B_1))) ) ).

tff(fact_155_Pi__I,axiom,
    ! [F: fun_fu1917206794le_alt,B_1: fun_fu1678217534t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_2)),hAPP_f87867740t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,B_1))) ) ).

tff(fact_156_Pi__I,axiom,
    ! [F: fun_fu908353023e_indi,B_1: fun_fu1765260675i_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_2)),hAPP_f109229519i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,B_1))) ) ).

tff(fact_157_Pi__I,axiom,
    ! [F: fun_fu523504735le_alt,B_1: fun_fu2027003875t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_2)),hAPP_f1203715503t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,B_1))) ) ).

tff(fact_158_Pi__I,axiom,
    ! [F: fun_fu775006535l_bool,B_1: fun_fu1471766731l_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_2)),hAPP_f84039575l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,B_1))) ) ).

tff(fact_159_Pi__I,axiom,
    ! [F: fun_fu207034610le_alt,B_1: fun_fu1540265814t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_2)),hAPP_f1099651112t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,B_1))) ) ).

tff(fact_160_Pi__I,axiom,
    ! [F: fun_fu2016509975e_indi,B_1: fun_fu1766473067i_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_2)),hAPP_f1957024259i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,B_1))) ) ).

tff(fact_161_Pi__I,axiom,
    ! [F: fun_fu89803383le_alt,B_1: fun_fu1275593675t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_2)),hAPP_f557837283t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,B_1))) ) ).

tff(fact_162_Pi__I,axiom,
    ! [F: fun_fu1015689055l_bool,B_1: fun_fu44268723l_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_2)),hAPP_f269590987l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,B_1))) ) ).

tff(fact_163_Pi__I,axiom,
    ! [F: fun_fu367862778le_alt,B_1: fun_fu1551598158t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_2)),hAPP_f735144044t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,B_1))) ) ).

tff(fact_164_Pi__I,axiom,
    ! [F: fun_fu1596339983e_indi,B_1: fun_fu2127564915i_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_2)),hAPP_f740807359i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,B_1))) ) ).

tff(fact_165_Pi__I,axiom,
    ! [F: fun_fu1883622767le_alt,B_1: fun_fu2016938707t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_2)),hAPP_f1014198943t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,B_1))) ) ).

tff(fact_166_Pi__I,axiom,
    ! [F: fun_fu1138137687l_bool,B_1: fun_fu1460706235l_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_2)),hAPP_f352672903l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,B_1))) ) ).

tff(fact_167_Pi__I,axiom,
    ! [F: fun_Ar836847646le_alt,B_1: fun_Ar1275715144t_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_2)),hAPP_A606737888t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,B_1))) ) ).

tff(fact_168_Pi__I,axiom,
    ! [F: fun_Ar369661729le_alt,B_1: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_2)),hAPP_A1174518481t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,B_1))) ) ).

tff(fact_169_Pi__I,axiom,
    ! [F: fun_Pr1165181697le_alt,B_1: fun_Pr1846448037t_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_2)),hAPP_P385761265t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,B_1))) ) ).

tff(fact_170_Pi__I,axiom,
    ! [F: fun_bo1479727337le_alt,B_1: fun_bo1116297149t_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_2)),hAPP_b1263785481t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,B_1))) ) ).

tff(fact_171_Pi__I,axiom,
    ! [F: fun_Ar421919996t_bool,B_1: fun_Ar1236339238l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_2)),hAPP_A2111843262l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,B_1))) ) ).

tff(fact_172_Pi__I,axiom,
    ! [F: fun_Ar687924991t_bool,B_1: fun_Ar684516451l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_2)),hAPP_A182831535l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,B_1))) ) ).

tff(fact_173_Pi__I,axiom,
    ! [F: fun_Pr1799779039t_bool,B_1: fun_Pr966099075l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_2)),hAPP_P725642959l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,B_1))) ) ).

tff(fact_174_Pi__I,axiom,
    ! [F: fun_bo266809543t_bool,B_1: fun_bo645734555l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_2)),hAPP_b1849744615l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,B_1))) ) ).

tff(fact_175_Pi__I,axiom,
    ! [F: fun_Ar1275715144t_bool,B_1: fun_Ar1026121174l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_2)),hAPP_A1787768616l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,B_1))) ) ).

tff(fact_176_Pi__I,axiom,
    ! [F: fun_Pr1846448037t_bool,B_1: fun_Pr1671213113l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_2)),hAPP_P272697303l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,B_1))) ) ).

tff(fact_177_Pi__I,axiom,
    ! [F: fun_bo1116297149t_bool,B_1: fun_bo96602657l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_2)),hAPP_b1650070463l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,B_1))) ) ).

tff(fact_178_Pi__I,axiom,
    ! [F: fun_Ar968139788t_bool,B_1: fun_Ar1311475510l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_2)),hAPP_A1313889230l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,B_1))) ) ).

tff(fact_179_Pi__I,axiom,
    ! [F: fun_Ar1939863823t_bool,B_1: fun_Ar1270429299l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_2)),hAPP_A1538515647l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,B_1))) ) ).

tff(fact_180_Pi__I,axiom,
    ! [F: fun_Pr1143104751t_bool,B_1: fun_Pr388821651l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_2)),hAPP_P469411807l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,B_1))) ) ).

tff(fact_181_Pi__I,axiom,
    ! [F: fun_bo2027801303t_bool,B_1: fun_bo979888811l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_2)),hAPP_b816606711l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,B_1))) ) ).

tff(fact_182_Pi__I,axiom,
    ! [F: fun_Pr1055212137t_bool,B_1: fun_Pr359894313l_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),hAPP_P1830623733l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,B_1))) ) ).

tff(fact_183_Pi__I,axiom,
    ! [F: fun_fu1595299477t_bool,B_1: fun_fu787660105l_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),hAPP_f1498158055l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,B_1))) ) ).

tff(fact_184_Pi__I,axiom,
    ! [F: fun_Ar500372357t_bool,B_1: fun_Ar1198543961l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),hAPP_A1279849719l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,B_1))) ) ).

tff(fact_185_funcsetI,axiom,
    ! [F: fun_Pr1852695144le_alt,B_1: fun_Ar1091019988t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,hAPP_f651702217t_bool(cOMBK_350001591le_alt,B_1)))) ) ).

tff(fact_186_funcsetI,axiom,
    ! [F: fun_Pr1698894881e_indi,B_1: fun_Ar552120407i_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_2)),B_1)) )
     => hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,hAPP_f324402723i_bool(cOMBK_646689008le_alt,B_1)))) ) ).

tff(fact_187_funcsetI,axiom,
    ! [F: fun_Pr1717845889le_alt,B_1: fun_Pr1013460023t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,hAPP_f1545334371t_bool(cOMBK_1927707728le_alt,B_1)))) ) ).

tff(fact_188_funcsetI,axiom,
    ! [F: fun_fu1917206794le_alt,B_1: fun_Ar1091019988t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,hAPP_f1528883111t_bool(cOMBK_841302421t_bool,B_1)))) ) ).

tff(fact_189_funcsetI,axiom,
    ! [F: fun_fu908353023e_indi,B_1: fun_Ar552120407i_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,hAPP_f1845592261i_bool(cOMBK_1865603534t_bool,B_1)))) ) ).

tff(fact_190_funcsetI,axiom,
    ! [F: fun_fu523504735le_alt,B_1: fun_Pr1013460023t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,hAPP_f1701776901t_bool(cOMBK_851707182t_bool,B_1)))) ) ).

tff(fact_191_funcsetI,axiom,
    ! [F: fun_fu775006535l_bool,B_1: fun_bool_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,hAPP_f2138308309l_bool(cOMBK_768188438t_bool,B_1)))) ) ).

tff(fact_192_funcsetI,axiom,
    ! [F: fun_fu207034610le_alt,B_1: fun_Ar1091019988t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,hAPP_f5211821t_bool(cOMBK_1771409497t_bool,B_1)))) ) ).

tff(fact_193_funcsetI,axiom,
    ! [F: fun_fu2016509975e_indi,B_1: fun_Ar552120407i_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_2)),B_1)) )
     => hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,hAPP_f676424105i_bool(cOMBK_854051296t_bool,B_1)))) ) ).

tff(fact_194_funcsetI,axiom,
    ! [F: fun_fu89803383le_alt,B_1: fun_Pr1013460023t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,hAPP_f2035600681t_bool(cOMBK_1082115712t_bool,B_1)))) ) ).

tff(fact_195_funcsetI,axiom,
    ! [F: fun_fu1015689055l_bool,B_1: fun_bool_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,hAPP_f1519524905l_bool(cOMBK_1253994904t_bool,B_1)))) ) ).

tff(fact_196_funcsetI,axiom,
    ! [F: fun_fu367862778le_alt,B_1: fun_Ar1091019988t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,hAPP_f2020309431t_bool(cOMBK_1604195493t_bool,B_1)))) ) ).

tff(fact_197_funcsetI,axiom,
    ! [F: fun_fu1596339983e_indi,B_1: fun_Ar552120407i_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,hAPP_f301073845i_bool(cOMBK_189636062t_bool,B_1)))) ) ).

tff(fact_198_funcsetI,axiom,
    ! [F: fun_fu1883622767le_alt,B_1: fun_Pr1013460023t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,hAPP_f1729202933t_bool(cOMBK_1744775486t_bool,B_1)))) ) ).

tff(fact_199_funcsetI,axiom,
    ! [F: fun_fu1138137687l_bool,B_1: fun_bool_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,hAPP_f1090778053l_bool(cOMBK_1251240998t_bool,B_1)))) ) ).

tff(fact_200_funcsetI,axiom,
    ! [F: fun_Ar836847646le_alt,B_1: fun_Pr1055212137t_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,hAPP_f786530292t_bool(cOMBK_82914883le_alt,B_1)))) ) ).

tff(fact_201_funcsetI,axiom,
    ! [F: fun_Ar369661729le_alt,B_1: fun_Pr1055212137t_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,hAPP_f311418073t_bool(cOMBK_1522533360e_indi,B_1)))) ) ).

tff(fact_202_funcsetI,axiom,
    ! [F: fun_Pr1165181697le_alt,B_1: fun_Pr1055212137t_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,hAPP_f303577849t_bool(cOMBK_1603999824le_alt,B_1)))) ) ).

tff(fact_203_funcsetI,axiom,
    ! [F: fun_bo1479727337le_alt,B_1: fun_Pr1055212137t_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,hAPP_f414777105t_bool(cOMBK_382434616l_bool,B_1)))) ) ).

tff(fact_204_funcsetI,axiom,
    ! [F: fun_Ar421919996t_bool,B_1: fun_fu775006535l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,hAPP_f1837403508l_bool(cOMBK_1262239973le_alt,B_1)))) ) ).

tff(fact_205_funcsetI,axiom,
    ! [F: fun_Ar687924991t_bool,B_1: fun_fu775006535l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,hAPP_f2099786901l_bool(cOMBK_970693070e_indi,B_1)))) ) ).

tff(fact_206_funcsetI,axiom,
    ! [F: fun_Pr1799779039t_bool,B_1: fun_fu775006535l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,hAPP_f1405662645l_bool(cOMBK_1129525550le_alt,B_1)))) ) ).

tff(fact_207_funcsetI,axiom,
    ! [F: fun_bo266809543t_bool,B_1: fun_fu775006535l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,hAPP_f126479309l_bool(cOMBK_1709453334l_bool,B_1)))) ) ).

tff(fact_208_funcsetI,axiom,
    ! [F: fun_Ar1275715144t_bool,B_1: fun_fu1015689055l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,hAPP_f377423160l_bool(cOMBK_433524227le_alt,B_1)))) ) ).

tff(fact_209_funcsetI,axiom,
    ! [F: fun_Pr1846448037t_bool,B_1: fun_fu1015689055l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,hAPP_f1115980887l_bool(cOMBK_2034944144le_alt,B_1)))) ) ).

tff(fact_210_funcsetI,axiom,
    ! [F: fun_bo1116297149t_bool,B_1: fun_fu1015689055l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,hAPP_f259799103l_bool(cOMBK_1489759608l_bool,B_1)))) ) ).

tff(fact_211_funcsetI,axiom,
    ! [F: fun_Ar968139788t_bool,B_1: fun_fu1138137687l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,hAPP_f2030964596l_bool(cOMBK_289343701le_alt,B_1)))) ) ).

tff(fact_212_funcsetI,axiom,
    ! [F: fun_Ar1939863823t_bool,B_1: fun_fu1138137687l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,hAPP_f1639366069l_bool(cOMBK_1014681054e_indi,B_1)))) ) ).

tff(fact_213_funcsetI,axiom,
    ! [F: fun_Pr1143104751t_bool,B_1: fun_fu1138137687l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,hAPP_f64308949l_bool(cOMBK_801230142le_alt,B_1)))) ) ).

tff(fact_214_funcsetI,axiom,
    ! [F: fun_bo2027801303t_bool,B_1: fun_fu1138137687l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,hAPP_f1922499821l_bool(cOMBK_1417083942l_bool,B_1)))) ) ).

tff(fact_215_funcsetI,axiom,
    ! [F: fun_Pr1055212137t_bool,B_1: fun_bool_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,B_1)))) ) ).

tff(fact_216_funcsetI,axiom,
    ! [F: fun_fu1595299477t_bool,B_1: fun_fu1015689055l_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,hAPP_f422714471l_bool(cOMBK_1446432t_bool,B_1)))) ) ).

tff(fact_217_funcsetI,axiom,
    ! [F: fun_Ar500372357t_bool,B_1: fun_fu1015689055l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),B_1)) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,B_1)))) ) ).

tff(fact_218_Pi__I_H,axiom,
    ! [F: fun_Pr1852695144le_alt,B_1: fun_Pr459606624t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_P1117185332le_alt(F,X_2)),hAPP_P1239753854t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1639338610l_bool(hAPP_f2088469003l_bool(member1558558165le_alt,F),pi_Pro469632574le_alt(A_1,B_1))) ) ).

tff(fact_219_Pi__I_H,axiom,
    ! [F: fun_Pr1698894881e_indi,B_1: fun_Pr39488737i_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_P1031342399e_indi(F,X_2)),hAPP_P1326783277i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f932587383l_bool(hAPP_f1165889229l_bool(member1747786740e_indi,F),pi_Pro1592011445e_indi(A_1,B_1))) ) ).

tff(fact_220_Pi__I_H,axiom,
    ! [F: fun_Pr1717845889le_alt,B_1: fun_Pr1556001345t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_P791400223le_alt(F,X_2)),hAPP_P1279976973t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f511502807l_bool(hAPP_f1919248077l_bool(member879596244le_alt,F),pi_Pro1731350421le_alt(A_1,B_1))) ) ).

tff(fact_221_Pi__I_H,axiom,
    ! [F: fun_fu1917206794le_alt,B_1: fun_fu1678217534t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f61189590le_alt(F,X_2)),hAPP_f87867740t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1553901844l_bool(hAPP_f863364943l_bool(member1164470647le_alt,F),pi_fun2004166880le_alt(A_1,B_1))) ) ).

tff(fact_222_Pi__I_H,axiom,
    ! [F: fun_fu908353023e_indi,B_1: fun_fu1765260675i_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f146696477e_indi(F,X_2)),hAPP_f109229519i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1298495829l_bool(hAPP_f1690559309l_bool(member1408848082e_indi,F),pi_fun64467091e_indi(A_1,B_1))) ) ).

tff(fact_223_Pi__I_H,axiom,
    ! [F: fun_fu523504735le_alt,B_1: fun_fu2027003875t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f818852349le_alt(F,X_2)),hAPP_f1203715503t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1710145205l_bool(hAPP_f378296397l_bool(member1997523634le_alt,F),pi_fun1331320947le_alt(A_1,B_1))) ) ).

tff(fact_224_Pi__I_H,axiom,
    ! [F: fun_fu775006535l_bool,B_1: fun_fu1471766731l_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1766661605l_bool(F,X_2)),hAPP_f84039575l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1223452061l_bool(hAPP_f120150093l_bool(member1791451290l_bool,F),pi_fun1624909403l_bool(A_1,B_1))) ) ).

tff(fact_225_Pi__I_H,axiom,
    ! [F: fun_fu207034610le_alt,B_1: fun_fu1540265814t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f463844874le_alt(F,X_2)),hAPP_f1099651112t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f630783048l_bool(hAPP_f209710093l_bool(member925775173le_alt,F),pi_fun1202206848le_alt(A_1,B_1))) ) ).

tff(fact_226_Pi__I_H,axiom,
    ! [F: fun_fu2016509975e_indi,B_1: fun_fu1766473067i_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f2029284841e_indi(F,X_2)),hAPP_f1957024259i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f372503329l_bool(hAPP_f43388905l_bool(member527726724e_indi,F),pi_fun1342736627e_indi(A_1,B_1))) ) ).

tff(fact_227_Pi__I_H,axiom,
    ! [F: fun_fu89803383le_alt,B_1: fun_fu1275593675t_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1322099913le_alt(F,X_2)),hAPP_f557837283t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f562996865l_bool(hAPP_f672930729l_bool(member955488100le_alt,F),pi_fun83337427le_alt(A_1,B_1))) ) ).

tff(fact_228_Pi__I_H,axiom,
    ! [F: fun_fu1015689055l_bool,B_1: fun_fu44268723l_bool,A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f429946033l_bool(F,X_2)),hAPP_f269590987l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1656729961l_bool(hAPP_f717334393l_bool(member717964108l_bool,F),pi_fun1412468411l_bool(A_1,B_1))) ) ).

tff(fact_229_Pi__I_H,axiom,
    ! [F: fun_fu367862778le_alt,B_1: fun_fu1551598158t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hAPP_f245324486le_alt(F,X_2)),hAPP_f735144044t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1099589124l_bool(hAPP_f340174383l_bool(member465949031le_alt,F),pi_fun1276940240le_alt(A_1,B_1))) ) ).

tff(fact_230_Pi__I_H,axiom,
    ! [F: fun_fu1596339983e_indi,B_1: fun_fu2127564915i_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hAPP_f1763702829e_indi(F,X_2)),hAPP_f740807359i_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1616443493l_bool(hAPP_f1536115021l_bool(member2095441122e_indi,F),pi_fun1073350051e_indi(A_1,B_1))) ) ).

tff(fact_231_Pi__I_H,axiom,
    ! [F: fun_fu1883622767le_alt,B_1: fun_fu2016938707t_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_f1027549453le_alt(F,X_2)),hAPP_f1014198943t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1015621061l_bool(hAPP_f1757769293l_bool(member2126235330le_alt,F),pi_fun1064473987le_alt(A_1,B_1))) ) ).

tff(fact_232_Pi__I_H,axiom,
    ! [F: fun_fu1138137687l_bool,B_1: fun_fu1460706235l_bool,A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f611501301l_bool(F,X_2)),hAPP_f352672903l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2081160365l_bool(hAPP_f481662541l_bool(member213355690l_bool,F),pi_fun351900523l_bool(A_1,B_1))) ) ).

tff(fact_233_Pi__I_H,axiom,
    ! [F: fun_Ar836847646le_alt,B_1: fun_Ar1275715144t_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(F,X_2)),hAPP_A606737888t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f628920872l_bool(hAPP_f1473673847l_bool(member542710667le_alt,F),pi_Arr665814522le_alt(A_1,B_1))) ) ).

tff(fact_234_Pi__I_H,axiom,
    ! [F: fun_Ar369661729le_alt,B_1: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A353813823le_alt(F,X_2)),hAPP_A1174518481t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1625336439l_bool(hAPP_f1269190349l_bool(member418553588le_alt,F),pi_Arr914482869le_alt(A_1,B_1))) ) ).

tff(fact_235_Pi__I_H,axiom,
    ! [F: fun_Pr1165181697le_alt,B_1: fun_Pr1846448037t_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_P1831053343le_alt(F,X_2)),hAPP_P385761265t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f708603223l_bool(hAPP_f462440141l_bool(member326932052le_alt,F),pi_Pro623519893le_alt(A_1,B_1))) ) ).

tff(fact_236_Pi__I_H,axiom,
    ! [F: fun_bo1479727337le_alt,B_1: fun_bo1116297149t_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_b1314516999le_alt(F,X_2)),hAPP_b1263785481t_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1339624767l_bool(hAPP_f1862158541l_bool(member481633596le_alt,F),pi_boo1374671485le_alt(A_1,B_1))) ) ).

tff(fact_237_Pi__I_H,axiom,
    ! [F: fun_Ar421919996t_bool,B_1: fun_Ar1236339238l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A658738638t_bool(F,X_2)),hAPP_A2111843262l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f34841350l_bool(hAPP_f70893619l_bool(member1816667497t_bool,F),pi_Arr454232280t_bool(A_1,B_1))) ) ).

tff(fact_238_Pi__I_H,axiom,
    ! [F: fun_Ar687924991t_bool,B_1: fun_Ar684516451l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_A1458779421t_bool(F,X_2)),hAPP_A182831535l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1037107797l_bool(hAPP_f162243405l_bool(member1188420050t_bool,F),pi_Arr1376550035t_bool(A_1,B_1))) ) ).

tff(fact_239_Pi__I_H,axiom,
    ! [F: fun_Pr1799779039t_bool,B_1: fun_Pr966099075l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_P273283069t_bool(F,X_2)),hAPP_P725642959l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2119607605l_bool(hAPP_f1031370829l_bool(member1126314290t_bool,F),pi_Pro785751667t_bool(A_1,B_1))) ) ).

tff(fact_240_Pi__I_H,axiom,
    ! [F: fun_bo266809543t_bool,B_1: fun_bo645734555l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hAPP_b715352037t_bool(F,X_2)),hAPP_b1849744615l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f976121117l_bool(hAPP_f621492301l_bool(member1283254298t_bool,F),pi_boo573599835t_bool(A_1,B_1))) ) ).

tff(fact_241_Pi__I_H,axiom,
    ! [F: fun_Ar1275715144t_bool,B_1: fun_Ar1026121174l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A606737888t_bool(F,X_2)),hAPP_A1787768616l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1677589406l_bool(hAPP_f1341663117l_bool(member1994455707t_bool,F),pi_Arr1345099862t_bool(A_1,B_1))) ) ).

tff(fact_242_Pi__I_H,axiom,
    ! [F: fun_Pr1846448037t_bool,B_1: fun_Pr1671213113l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_P385761265t_bool(F,X_2)),hAPP_P272697303l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1500482991l_bool(hAPP_f823377925l_bool(member564649106t_bool,F),pi_Pro1294482427t_bool(A_1,B_1))) ) ).

tff(fact_243_Pi__I_H,axiom,
    ! [F: fun_bo1116297149t_bool,B_1: fun_bo96602657l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_b1263785481t_bool(F,X_2)),hAPP_b1650070463l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2041629639l_bool(hAPP_f134102069l_bool(member818572202t_bool,F),pi_boo98824211t_bool(A_1,B_1))) ) ).

tff(fact_244_Pi__I_H,axiom,
    ! [F: fun_Ar968139788t_bool,B_1: fun_Ar1311475510l_bool,A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A343036382t_bool(F,X_2)),hAPP_A1313889230l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1106117654l_bool(hAPP_f1934104915l_bool(member1066226041t_bool,F),pi_Arr1374652136t_bool(A_1,B_1))) ) ).

tff(fact_245_Pi__I_H,axiom,
    ! [F: fun_Ar1939863823t_bool,B_1: fun_Ar1270429299l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_A1044336685t_bool(F,X_2)),hAPP_A1538515647l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f2076228197l_bool(hAPP_f467714381l_bool(member291481314t_bool,F),pi_Arr353983907t_bool(A_1,B_1))) ) ).

tff(fact_246_Pi__I_H,axiom,
    ! [F: fun_Pr1143104751t_bool,B_1: fun_Pr388821651l_bool,A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_P164754189t_bool(F,X_2)),hAPP_P469411807l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f375536965l_bool(hAPP_f1960201805l_bool(member1385717314t_bool,F),pi_Pro201678723t_bool(A_1,B_1))) ) ).

tff(fact_247_Pi__I_H,axiom,
    ! [F: fun_bo2027801303t_bool,B_1: fun_bo979888811l_bool,A_1: fun_bool_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
         => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hAPP_b510135029t_bool(F,X_2)),hAPP_b816606711l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1812901165l_bool(hAPP_f674575949l_bool(member1103019306t_bool,F),pi_boo250534251t_bool(A_1,B_1))) ) ).

tff(fact_248_Pi__I_H,axiom,
    ! [F: fun_Pr1055212137t_bool,B_1: fun_Pr359894313l_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
         => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P166437127t_bool(F,X_2)),hAPP_P1830623733l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,F),pi_Pro226591613t_bool(A_1,B_1))) ) ).

tff(fact_249_Pi__I_H,axiom,
    ! [F: fun_fu1595299477t_bool,B_1: fun_fu787660105l_bool,A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_f792184801t_bool(F,X_2)),hAPP_f1498158055l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,B_1))) ) ).

tff(fact_250_Pi__I_H,axiom,
    ! [F: fun_Ar500372357t_bool,B_1: fun_Ar1198543961l_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
         => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hAPP_A1174518481t_bool(F,X_2)),hAPP_A1279849719l_bool(B_1,X_2))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,B_1))) ) ).

tff(fact_251_Pi__cong,axiom,
    ! [B_1: fun_Pr359894313l_bool,G: fun_Pr1055212137t_bool,F: fun_Pr1055212137t_bool,A_1: fun_Pr1055212137t_bool] :
      ( ! [W: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,W),A_1))
         => ( 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_1,B_1)))
      <=> hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,G),pi_Pro226591613t_bool(A_1,B_1))) ) ) ).

tff(fact_252_Pi__cong,axiom,
    ! [B_1: fun_fu787660105l_bool,F: fun_fu1595299477t_bool,G: fun_fu1595299477t_bool,A_1: fun_fu775006535l_bool] :
      ( ! [W: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,W),A_1))
         => ( hAPP_f792184801t_bool(F,W) = hAPP_f792184801t_bool(G,W) ) )
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,F),pi_fun530160875t_bool(A_1,B_1)))
      <=> hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,G),pi_fun530160875t_bool(A_1,B_1))) ) ) ).

tff(fact_253_Pi__cong,axiom,
    ! [B_1: fun_Ar1198543961l_bool,F: fun_Ar500372357t_bool,G: fun_Ar500372357t_bool,A_1: fun_Ar552120407i_bool] :
      ( ! [W: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,W),A_1))
         => ( hAPP_A1174518481t_bool(F,W) = hAPP_A1174518481t_bool(G,W) ) )
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,F),pi_Arr487970267t_bool(A_1,B_1)))
      <=> hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,G),pi_Arr487970267t_bool(A_1,B_1))) ) ) ).

tff(fact_254_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr1013460023t_bool,R_2: fun_Pr1013460023t_bool] :
      ( ! [X_2: list_A1748581779le_alt,Xa: list_A1748581779le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Xa)),R_2))
        <=> hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Xa)),S_1)) )
    <=> ( R_2 = S_1 ) ) ).

tff(fact_255_pred__equals__eq2,axiom,
    ! [S_1: fun_Pr1055212137t_bool,R_2: fun_Pr1055212137t_bool] :
      ( ! [X_2: 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_2),Xa)),R_2))
        <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Xa)),S_1)) )
    <=> ( R_2 = S_1 ) ) ).

tff(fact_256_prod_Oexhaust,axiom,
    ! [Y_3: produc662089077le_alt] :
      ~ ! [A: list_A1748581779le_alt,B: list_A1748581779le_alt] : ( Y_3 != hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),B) ) ).

tff(fact_257_prod_Oexhaust,axiom,
    ! [Y_3: produc1840315303le_alt] :
      ~ ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] : ( Y_3 != hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B) ) ).

tff(fact_258_PairE,axiom,
    ! [P_2: produc662089077le_alt] :
      ~ ! [X_2: list_A1748581779le_alt,Y_1: list_A1748581779le_alt] : ( P_2 != hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_1) ) ).

tff(fact_259_PairE,axiom,
    ! [P_2: produc1840315303le_alt] :
      ~ ! [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt] : ( P_2 != hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_1) ) ).

tff(fact_260_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1013460023t_bool] :
      ( ? [X1: produc662089077le_alt] : hBOOL(hAPP_P274047445t_bool(Pa,X1))
    <=> ? [A: list_A1748581779le_alt,B: list_A1748581779le_alt] : hBOOL(hAPP_P274047445t_bool(Pa,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),B))) ) ).

tff(fact_261_split__paired__Ex,axiom,
    ! [Pa: fun_Pr1055212137t_bool] :
      ( ? [X1: produc1840315303le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,X1))
    <=> ? [A: arrow_931160158le_alt,B: arrow_931160158le_alt] : hBOOL(hAPP_P166437127t_bool(Pa,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B))) ) ).

tff(fact_262_insert__Nil,axiom,
    ! [X_20: arrow_931160158le_alt] : ( insert428884260le_alt(X_20,nil_Ar1741995278le_alt) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_20),nil_Ar1741995278le_alt) ) ).

tff(fact_263_distinct__insert,axiom,
    ! [X_19: arrow_931160158le_alt,Xs_37: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs_37))
     => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,insert428884260le_alt(X_19,Xs_37))) ) ).

tff(fact_264_mem__def,axiom,
    ! [X_1: arrow_931160158le_alt,A_1: fun_Ar1091019988t_bool] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),A_1))
    <=> hBOOL(hAPP_A674791462t_bool(A_1,X_1)) ) ).

tff(fact_265_mem__def,axiom,
    ! [X_1: arrow_2115524757e_indi,A_1: fun_Ar552120407i_bool] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),A_1))
    <=> hBOOL(hAPP_A1888055029i_bool(A_1,X_1)) ) ).

tff(fact_266_mem__def,axiom,
    ! [X_1: produc662089077le_alt,A_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),A_1))
    <=> hBOOL(hAPP_P274047445t_bool(A_1,X_1)) ) ).

tff(fact_267_mem__def,axiom,
    ! [X_1: bool,A_1: fun_bool_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
    <=> hBOOL(hAPP_bool_bool(A_1,X_1)) ) ).

tff(fact_268_mem__def,axiom,
    ! [X_1: produc1840315303le_alt,A_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),A_1))
    <=> hBOOL(hAPP_P166437127t_bool(A_1,X_1)) ) ).

tff(fact_269_mem__def,axiom,
    ! [X_1: fun_Ar500372357t_bool,A_1: fun_fu775006535l_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),A_1))
    <=> hBOOL(hAPP_f1766661605l_bool(A_1,X_1)) ) ).

tff(fact_270_mem__def,axiom,
    ! [X_1: fun_Pr1055212137t_bool,A_1: fun_fu1015689055l_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),A_1))
    <=> hBOOL(hAPP_f429946033l_bool(A_1,X_1)) ) ).

tff(fact_271_mem__def,axiom,
    ! [X_1: fun_fu1595299477t_bool,A_1: fun_fu1138137687l_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),A_1))
    <=> hBOOL(hAPP_f611501301l_bool(A_1,X_1)) ) ).

tff(fact_272_Collect__def,axiom,
    ! [Pa: fun_Ar1091019988t_bool] : ( collec1197875955le_alt(Pa) = Pa ) ).

tff(fact_273_Collect__def,axiom,
    ! [Pa: fun_Ar552120407i_bool] : ( collec708328256e_indi(Pa) = Pa ) ).

tff(fact_274_Collect__def,axiom,
    ! [Pa: fun_fu1015689055l_bool] : ( collec1113178622t_bool(Pa) = Pa ) ).

tff(fact_275_list__nonempty__induct,axiom,
    ! [Pa: fun_li1323594581t_bool,Xs: list_A1748581779le_alt] :
      ( ( Xs != nil_Ar1741995278le_alt )
     => ( ! [X_2: arrow_931160158le_alt] : hBOOL(hAPP_l713721587t_bool(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),nil_Ar1741995278le_alt)))
       => ( ! [X_2: arrow_931160158le_alt,Xs_9: list_A1748581779le_alt] :
              ( ( Xs_9 != nil_Ar1741995278le_alt )
             => ( hBOOL(hAPP_l713721587t_bool(Pa,Xs_9))
               => hBOOL(hAPP_l713721587t_bool(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Xs_9))) ) )
         => hBOOL(hAPP_l713721587t_bool(Pa,Xs)) ) ) ) ).

tff(fact_276_curry__def,axiom,
    ! [X_2: fun_Pr1055212137t_bool,Xa: arrow_931160158le_alt,Xb: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(produc258050046t_bool(X_2),Xa),Xb))
    <=> hBOOL(hAPP_P166437127t_bool(X_2,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Xa),Xb))) ) ).

tff(fact_277_curryI,axiom,
    ! [F: fun_Pr1013460023t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_P274047445t_bool(F,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba)))
     => hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(produc919986386t_bool(F),Aa),Ba)) ) ).

tff(fact_278_curryI,axiom,
    ! [F: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_P166437127t_bool(F,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)))
     => hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(produc258050046t_bool(F),Aa),Ba)) ) ).

tff(fact_279_null__rec_I2_J,axiom,
    hBOOL(hAPP_l713721587t_bool(null_A1976766230le_alt,nil_Ar1741995278le_alt)) ).

tff(fact_280_List_Onull__def,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(null_A1976766230le_alt,Xs))
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_281_eq__Nil__null,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( Xs = nil_Ar1741995278le_alt )
    <=> hBOOL(hAPP_l713721587t_bool(null_A1976766230le_alt,Xs)) ) ).

tff(fact_282_null__rec_I1_J,axiom,
    ! [X_18: arrow_931160158le_alt,Xs_36: list_A1748581779le_alt] : ~ hBOOL(hAPP_l713721587t_bool(null_A1976766230le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_18),Xs_36))) ).

tff(fact_283_curryD,axiom,
    ! [F: fun_Pr1013460023t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(produc919986386t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P274047445t_bool(F,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba))) ) ).

tff(fact_284_curryD,axiom,
    ! [F: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(produc258050046t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P166437127t_bool(F,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba))) ) ).

tff(fact_285_curryE,axiom,
    ! [F: fun_Pr1013460023t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(produc919986386t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P274047445t_bool(F,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba))) ) ).

tff(fact_286_curryE,axiom,
    ! [F: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(produc258050046t_bool(F),Aa),Ba))
     => hBOOL(hAPP_P166437127t_bool(F,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba))) ) ).

tff(fact_287_curry__conv,axiom,
    ! [F: fun_Pr1055212137t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(produc258050046t_bool(F),Aa),Ba))
    <=> hBOOL(hAPP_P166437127t_bool(F,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba))) ) ).

tff(fact_288_equal__Nil__null,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(equal_117954737le_alt,Xs),nil_Ar1741995278le_alt))
    <=> hBOOL(hAPP_l713721587t_bool(null_A1976766230le_alt,Xs)) ) ).

tff(fact_289_Prof__def,axiom,
    arrow_1190054106e_Prof = pi_Arr487970267t_bool(top_to1678393681i_bool,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,arrow_915577424le_Lin)) ).

tff(fact_290_lexord__cons__cons,axiom,
    ! [Aa: list_A1748581779le_alt,X_1: list_l1735481012le_alt,Ba: list_A1748581779le_alt,Y_2: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Aa),X_1)),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Ba),Y_2))),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1)))
    <=> ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba)),R_1))
        | ( ( Aa = Ba )
          & hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,X_1),Y_2)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ) ) ).

tff(fact_291_lexord__cons__cons,axiom,
    ! [Aa: arrow_931160158le_alt,X_1: list_A1748581779le_alt,Ba: arrow_931160158le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Aa),X_1)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Ba),Y_2))),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
    <=> ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),R_1))
        | ( ( Aa = Ba )
          & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ) ) ).

tff(fact_292_distinct__butlast,axiom,
    ! [Xs_35: list_A1748581779le_alt] :
      ( ( Xs_35 != nil_Ar1741995278le_alt )
     => ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs_35))
       => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,butlas730749018le_alt(Xs_35))) ) ) ).

tff(fact_293_last__ConsL,axiom,
    ! [X_17: arrow_931160158le_alt,Xs_34: list_A1748581779le_alt] :
      ( ( Xs_34 = nil_Ar1741995278le_alt )
     => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_17),Xs_34)) = X_17 ) ) ).

tff(fact_294_last__ConsR,axiom,
    ! [X_16: arrow_931160158le_alt,Xs_33: list_A1748581779le_alt] :
      ( ( Xs_33 != nil_Ar1741995278le_alt )
     => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_16),Xs_33)) = last_A1673116455le_alt(Xs_33) ) ) ).

tff(fact_295_top1I,axiom,
    ! [X_1: fun_fu1595299477t_bool] : hBOOL(hAPP_f611501301l_bool(top_to2013953873l_bool,X_1)) ).

tff(fact_296_top1I,axiom,
    ! [X_1: fun_Pr1055212137t_bool] : hBOOL(hAPP_f429946033l_bool(top_to1690334693l_bool,X_1)) ).

tff(fact_297_top1I,axiom,
    ! [X_1: fun_Ar500372357t_bool] : hBOOL(hAPP_f1766661605l_bool(top_to1324311617l_bool,X_1)) ).

tff(fact_298_top1I,axiom,
    ! [X_1: produc1840315303le_alt] : hBOOL(hAPP_P166437127t_bool(top_to126038883t_bool,X_1)) ).

tff(fact_299_top1I,axiom,
    ! [X_1: arrow_2115524757e_indi] : hBOOL(hAPP_A1888055029i_bool(top_to1678393681i_bool,X_1)) ).

tff(fact_300_top1I,axiom,
    ! [X_1: arrow_931160158le_alt] : hBOOL(hAPP_A674791462t_bool(top_to1888499034t_bool,X_1)) ).

tff(fact_301_equal__list__def,axiom,
    ! [X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(equal_117954737le_alt,X_1),Y_2))
    <=> ( X_1 = Y_2 ) ) ).

tff(fact_302_Pi__UNIV,axiom,
    ! [A_1: fun_Pr1055212137t_bool] : ( pi_Pro226591613t_bool(A_1,hAPP_f1426772275l_bool(cOMBK_1506144056le_alt,top_to1647826457l_bool)) = top_to1690334693l_bool ) ).

tff(fact_303_Pi__UNIV,axiom,
    ! [A_1: fun_fu775006535l_bool] : ( pi_fun530160875t_bool(A_1,hAPP_f422714471l_bool(cOMBK_1446432t_bool,top_to1690334693l_bool)) = top_to2013953873l_bool ) ).

tff(fact_304_Pi__UNIV,axiom,
    ! [A_1: fun_Ar552120407i_bool] : ( pi_Arr487970267t_bool(A_1,hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,top_to1690334693l_bool)) = top_to1324311617l_bool ) ).

tff(fact_305_butlast_Osimps_I1_J,axiom,
    butlas730749018le_alt(nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ).

tff(fact_306_lexord__Nil__right,axiom,
    ! [X_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),nil_Ar1741995278le_alt)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ).

tff(fact_307_butlast_Osimps_I2_J,axiom,
    ! [X_15: arrow_931160158le_alt,Xs_32: list_A1748581779le_alt] :
      ( ( ( Xs_32 = nil_Ar1741995278le_alt )
       => ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_15),Xs_32)) = nil_Ar1741995278le_alt ) )
      & ( ( Xs_32 != nil_Ar1741995278le_alt )
       => ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_15),Xs_32)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_15),butlas730749018le_alt(Xs_32)) ) ) ) ).

tff(fact_308_last_Osimps,axiom,
    ! [X_14: arrow_931160158le_alt,Xs_31: list_A1748581779le_alt] :
      ( ( ( Xs_31 = nil_Ar1741995278le_alt )
       => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_14),Xs_31)) = X_14 ) )
      & ( ( Xs_31 != nil_Ar1741995278le_alt )
       => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_14),Xs_31)) = last_A1673116455le_alt(Xs_31) ) ) ) ).

tff(fact_309_lexord__Nil__left,axiom,
    ! [Y_2: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),Y_2)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
    <=> ? [A: arrow_931160158le_alt,X_2: list_A1748581779le_alt] : ( Y_2 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,A),X_2) ) ) ).

tff(fact_310_lexord__irreflexive,axiom,
    ! [Xs: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: list_A1748581779le_alt] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),X_2)),R_1))
     => ~ hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Xs)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ).

tff(fact_311_lexord__irreflexive,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: arrow_931160158le_alt] : ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),X_2)),R_1))
     => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Xs)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ).

tff(fact_312_lexord__linear,axiom,
    ! [X_1: list_l1735481012le_alt,Y_2: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( ! [A: list_A1748581779le_alt,B: list_A1748581779le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),B)),R_1))
          | ( A = B )
          | hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,B),A)),R_1)) )
     => ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,X_1),Y_2)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1)))
        | ( X_1 = Y_2 )
        | hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Y_2),X_1)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ) ).

tff(fact_313_lexord__linear,axiom,
    ! [X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B)),R_1))
          | ( A = B )
          | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,B),A)),R_1)) )
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
        | ( X_1 = Y_2 )
        | hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Y_2),X_1)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ) ).

tff(fact_314_UNIV__I,axiom,
    ! [X_1: produc662089077le_alt] : hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),top_to1866544689t_bool)) ).

tff(fact_315_UNIV__I,axiom,
    ! [X_1: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) ).

tff(fact_316_UNIV__I,axiom,
    ! [X_1: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),top_to1678393681i_bool)) ).

tff(fact_317_UNIV__I,axiom,
    ! [X_1: arrow_931160158le_alt] : hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),top_to1888499034t_bool)) ).

tff(fact_318_UNIV__I,axiom,
    ! [X_1: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),top_to126038883t_bool)) ).

tff(fact_319_UNIV__I,axiom,
    ! [X_1: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),top_to1324311617l_bool)) ).

tff(fact_320_UNIV__I,axiom,
    ! [X_1: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),top_to1690334693l_bool)) ).

tff(fact_321_UNIV__I,axiom,
    ! [X_1: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),top_to2013953873l_bool)) ).

tff(fact_322_iso__tuple__UNIV__I,axiom,
    ! [X_1: produc662089077le_alt] : hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),top_to1866544689t_bool)) ).

tff(fact_323_iso__tuple__UNIV__I,axiom,
    ! [X_1: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) ).

tff(fact_324_iso__tuple__UNIV__I,axiom,
    ! [X_1: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),top_to1678393681i_bool)) ).

tff(fact_325_iso__tuple__UNIV__I,axiom,
    ! [X_1: arrow_931160158le_alt] : hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),top_to1888499034t_bool)) ).

tff(fact_326_iso__tuple__UNIV__I,axiom,
    ! [X_1: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),top_to126038883t_bool)) ).

tff(fact_327_iso__tuple__UNIV__I,axiom,
    ! [X_1: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),top_to1324311617l_bool)) ).

tff(fact_328_iso__tuple__UNIV__I,axiom,
    ! [X_1: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),top_to1690334693l_bool)) ).

tff(fact_329_iso__tuple__UNIV__I,axiom,
    ! [X_1: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),top_to2013953873l_bool)) ).

tff(fact_330_top__apply,axiom,
    ! [X_1: fun_fu1595299477t_bool] :
      ( hBOOL(hAPP_f611501301l_bool(top_to2013953873l_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_331_top__apply,axiom,
    ! [X_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(top_to1690334693l_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_332_top__apply,axiom,
    ! [X_1: fun_Ar500372357t_bool] :
      ( hBOOL(hAPP_f1766661605l_bool(top_to1324311617l_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_333_top__apply,axiom,
    ! [X_1: produc1840315303le_alt] :
      ( hBOOL(hAPP_P166437127t_bool(top_to126038883t_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_334_top__apply,axiom,
    ! [X_1: arrow_2115524757e_indi] :
      ( hBOOL(hAPP_A1888055029i_bool(top_to1678393681i_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_335_top__apply,axiom,
    ! [X_1: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(top_to1888499034t_bool,X_1))
    <=> hBOOL(top_top_bool) ) ).

tff(fact_336_takeWhile__not__last,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( Xs != nil_Ar1741995278le_alt )
     => ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs))
       => ( takeWh4609031le_alt(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,fNot),hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,fequal628352221le_alt),last_A1673116455le_alt(Xs))),Xs) = butlas730749018le_alt(Xs) ) ) ) ).

tff(fact_337_partition_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar1091019988t_bool] : ( partit1943378951le_alt(Pa,nil_Ar1741995278le_alt) = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),nil_Ar1741995278le_alt) ) ).

tff(fact_338_takeWhile_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar1091019988t_bool] : ( takeWh4609031le_alt(Pa,nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ) ).

tff(fact_339_distinct__takeWhile,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs))
     => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,takeWh4609031le_alt(Pa,Xs))) ) ).

tff(fact_340_takeWhile_Osimps_I2_J,axiom,
    ! [Xs: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt] :
      ( ( hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( takeWh4609031le_alt(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),takeWh4609031le_alt(Pa,Xs)) ) )
      & ( ~ hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( takeWh4609031le_alt(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = nil_Ar1741995278le_alt ) ) ) ).

tff(fact_341_UNIV__def,axiom,
    top_to2013953873l_bool = collec1699798848t_bool(hAPP_b816606711l_bool(cOMBK_759924014t_bool,fTrue)) ).

tff(fact_342_UNIV__def,axiom,
    top_to1324311617l_bool = collec1461897520t_bool(hAPP_b1849744615l_bool(cOMBK_670822686t_bool,fTrue)) ).

tff(fact_343_UNIV__def,axiom,
    top_to126038883t_bool = collec1209019986le_alt(hAPP_b1263785481t_bool(cOMBK_1566242880le_alt,fTrue)) ).

tff(fact_344_UNIV__def,axiom,
    top_to1678393681i_bool = collec708328256e_indi(hAPP_b1439777783i_bool(cOMBK_1820189998e_indi,fTrue)) ).

tff(fact_345_UNIV__def,axiom,
    top_to1888499034t_bool = collec1197875955le_alt(hAPP_b1990207796t_bool(cOMBK_1114709381le_alt,fTrue)) ).

tff(fact_346_UNIV__def,axiom,
    top_to1690334693l_bool = collec1113178622t_bool(hAPP_b1650070463l_bool(cOMBK_1216274064t_bool,fTrue)) ).

tff(fact_347_UNIV__eq__I,axiom,
    ! [A_1: fun_Pr1013460023t_bool] :
      ( ! [X_2: produc662089077le_alt] : hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),A_1))
     => ( top_to1866544689t_bool = A_1 ) ) ).

tff(fact_348_UNIV__eq__I,axiom,
    ! [A_1: fun_bool_bool] :
      ( ! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
     => ( top_to1647826457l_bool = A_1 ) ) ).

tff(fact_349_UNIV__eq__I,axiom,
    ! [A_1: fun_Ar552120407i_bool] :
      ( ! [X_2: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),A_1))
     => ( top_to1678393681i_bool = A_1 ) ) ).

tff(fact_350_UNIV__eq__I,axiom,
    ! [A_1: fun_Ar1091019988t_bool] :
      ( ! [X_2: arrow_931160158le_alt] : hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),A_1))
     => ( top_to1888499034t_bool = A_1 ) ) ).

tff(fact_351_UNIV__eq__I,axiom,
    ! [A_1: fun_Pr1055212137t_bool] :
      ( ! [X_2: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),A_1))
     => ( top_to126038883t_bool = A_1 ) ) ).

tff(fact_352_UNIV__eq__I,axiom,
    ! [A_1: fun_fu775006535l_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),A_1))
     => ( top_to1324311617l_bool = A_1 ) ) ).

tff(fact_353_UNIV__eq__I,axiom,
    ! [A_1: fun_fu1015689055l_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),A_1))
     => ( top_to1690334693l_bool = A_1 ) ) ).

tff(fact_354_UNIV__eq__I,axiom,
    ! [A_1: fun_fu1138137687l_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),A_1))
     => ( top_to2013953873l_bool = A_1 ) ) ).

tff(fact_355_UNIV__witness,axiom,
    ? [X_2: produc662089077le_alt] : hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),top_to1866544689t_bool)) ).

tff(fact_356_UNIV__witness,axiom,
    ? [X_2: bool] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ).

tff(fact_357_UNIV__witness,axiom,
    ? [X_2: arrow_2115524757e_indi] : hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),top_to1678393681i_bool)) ).

tff(fact_358_UNIV__witness,axiom,
    ? [X_2: arrow_931160158le_alt] : hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),top_to1888499034t_bool)) ).

tff(fact_359_UNIV__witness,axiom,
    ? [X_2: produc1840315303le_alt] : hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),top_to126038883t_bool)) ).

tff(fact_360_UNIV__witness,axiom,
    ? [X_2: fun_Ar500372357t_bool] : hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),top_to1324311617l_bool)) ).

tff(fact_361_UNIV__witness,axiom,
    ? [X_2: fun_Pr1055212137t_bool] : hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),top_to1690334693l_bool)) ).

tff(fact_362_UNIV__witness,axiom,
    ? [X_2: fun_fu1595299477t_bool] : hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),top_to2013953873l_bool)) ).

tff(fact_363_Lin__def,axiom,
    arrow_915577424le_Lin = collec1113178622t_bool(order_304234630le_alt(top_to1888499034t_bool)) ).

tff(fact_364_append__butlast__last__id,axiom,
    ! [Xs_30: list_A1748581779le_alt] :
      ( ( Xs_30 != nil_Ar1741995278le_alt )
     => ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,butlas730749018le_alt(Xs_30)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,last_A1673116455le_alt(Xs_30)),nil_Ar1741995278le_alt)) = Xs_30 ) ) ).

tff(fact_365_snoc__eq__iff__butlast,axiom,
    ! [Xs: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt)) = Ys_1 )
    <=> ( ( Ys_1 != nil_Ar1741995278le_alt )
        & ( butlas730749018le_alt(Ys_1) = Xs )
        & ( last_A1673116455le_alt(Ys_1) = X_1 ) ) ) ).

tff(fact_366_Nil2__notin__lex,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),nil_Ar1741995278le_alt)),hAPP_f557837283t_bool(lex_Ar1871318386le_alt,R_1))) ).

tff(fact_367_Nil__notin__lex,axiom,
    ! [Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),Ys_1)),hAPP_f557837283t_bool(lex_Ar1871318386le_alt,R_1))) ).

tff(fact_368_append__eq__appendI,axiom,
    ! [Ys_16: list_A1748581779le_alt,Us_2: list_A1748581779le_alt,Xs_29: list_A1748581779le_alt,Xs1_1: list_A1748581779le_alt,Zs_4: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_29),Xs1_1) = Zs_4 )
     => ( ( Ys_16 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs1_1),Us_2) )
       => ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_29),Ys_16) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Zs_4),Us_2) ) ) ) ).

tff(fact_369_append__same__eq,axiom,
    ! [Ys_1: list_A1748581779le_alt,Xs: list_A1748581779le_alt,Zs_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),Xs) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Zs_1),Xs) )
    <=> ( Ys_1 = Zs_1 ) ) ).

tff(fact_370_same__append__eq,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,Zs_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Zs_1) )
    <=> ( Ys_1 = Zs_1 ) ) ).

tff(fact_371_append__eq__append__conv2,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,Zs_1: list_A1748581779le_alt,Ts: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Zs_1),Ts) )
    <=> ? [Us: list_A1748581779le_alt] :
          ( ( ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Zs_1),Us) )
            & ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us),Ys_1) = Ts ) )
          | ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Us) = Zs_1 )
            & ( Ys_1 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us),Ts) ) ) ) ) ).

tff(fact_372_append__assoc,axiom,
    ! [Xs_28: list_A1748581779le_alt,Ys_15: list_A1748581779le_alt,Zs_3: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_28),Ys_15)),Zs_3) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_28),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_15),Zs_3)) ) ).

tff(fact_373_append__Cons,axiom,
    ! [X_13: arrow_931160158le_alt,Xs_27: list_A1748581779le_alt,Ys_14: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_13),Xs_27)),Ys_14) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_13),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_27),Ys_14)) ) ).

tff(fact_374_Cons__eq__appendI,axiom,
    ! [Xs_26: list_A1748581779le_alt,Zs_2: list_A1748581779le_alt,X_12: arrow_931160158le_alt,Xs1: list_A1748581779le_alt,Ys_13: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_12),Xs1) = Ys_13 )
     => ( ( Xs_26 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs1),Zs_2) )
       => ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_12),Xs_26) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_13),Zs_2) ) ) ) ).

tff(fact_375_append__Nil,axiom,
    ! [Ys_12: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,nil_Ar1741995278le_alt),Ys_12) = Ys_12 ) ).

tff(fact_376_Nil__is__append__conv,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( nil_Ar1741995278le_alt = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) )
    <=> ( ( Xs = nil_Ar1741995278le_alt )
        & ( Ys_1 = nil_Ar1741995278le_alt ) ) ) ).

tff(fact_377_append__Nil2,axiom,
    ! [Xs_25: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_25),nil_Ar1741995278le_alt) = Xs_25 ) ).

tff(fact_378_self__append__conv,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) )
    <=> ( Ys_1 = nil_Ar1741995278le_alt ) ) ).

tff(fact_379_self__append__conv2,axiom,
    ! [Ys_1: list_A1748581779le_alt,Xs: list_A1748581779le_alt] :
      ( ( Ys_1 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) )
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_380_append__is__Nil__conv,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) = nil_Ar1741995278le_alt )
    <=> ( ( Xs = nil_Ar1741995278le_alt )
        & ( Ys_1 = nil_Ar1741995278le_alt ) ) ) ).

tff(fact_381_append__self__conv,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) = Xs )
    <=> ( Ys_1 = nil_Ar1741995278le_alt ) ) ).

tff(fact_382_append__self__conv2,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1) = Ys_1 )
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_383_eq__Nil__appendI,axiom,
    ! [Xs_24: list_A1748581779le_alt,Ys_11: list_A1748581779le_alt] :
      ( ( Xs_24 = Ys_11 )
     => ( Xs_24 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,nil_Ar1741995278le_alt),Ys_11) ) ) ).

tff(fact_384_append__eq__Cons__conv,axiom,
    ! [Ys_1: list_A1748581779le_alt,Zs_1: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),Zs_1) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) )
    <=> ( ( ( Ys_1 = nil_Ar1741995278le_alt )
          & ( Zs_1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) ) )
        | ? [Ys_10: list_A1748581779le_alt] :
            ( ( Ys_1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Ys_10) )
            & ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_10),Zs_1) = Xs ) ) ) ) ).

tff(fact_385_Cons__eq__append__conv,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,Zs_1: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),Zs_1) )
    <=> ( ( ( Ys_1 = nil_Ar1741995278le_alt )
          & ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) = Zs_1 ) )
        | ? [Ys_10: list_A1748581779le_alt] :
            ( ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Ys_10) = Ys_1 )
            & ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_10),Zs_1) ) ) ) ) ).

tff(fact_386_append1__eq__conv,axiom,
    ! [Xs: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,Y_2: arrow_931160158le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),nil_Ar1741995278le_alt)) )
    <=> ( ( Xs = Ys_1 )
        & ( X_1 = Y_2 ) ) ) ).

tff(fact_387_takeWhile__tail,axiom,
    ! [Xs: list_A1748581779le_alt,L: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt] :
      ( ~ hBOOL(hAPP_A674791462t_bool(Pa,X_1))
     => ( takeWh4609031le_alt(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),L))) = takeWh4609031le_alt(Pa,Xs) ) ) ).

tff(fact_388_butlast__append,axiom,
    ! [Xs_23: list_A1748581779le_alt,Ys_9: list_A1748581779le_alt] :
      ( ( ( Ys_9 = nil_Ar1741995278le_alt )
       => ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_23),Ys_9)) = butlas730749018le_alt(Xs_23) ) )
      & ( ( Ys_9 != nil_Ar1741995278le_alt )
       => ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_23),Ys_9)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_23),butlas730749018le_alt(Ys_9)) ) ) ) ).

tff(fact_389_last__append,axiom,
    ! [Xs_22: list_A1748581779le_alt,Ys_8: list_A1748581779le_alt] :
      ( ( ( Ys_8 = nil_Ar1741995278le_alt )
       => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_22),Ys_8)) = last_A1673116455le_alt(Xs_22) ) )
      & ( ( Ys_8 != nil_Ar1741995278le_alt )
       => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_22),Ys_8)) = last_A1673116455le_alt(Ys_8) ) ) ) ).

tff(fact_390_last__appendR,axiom,
    ! [Xs_21: list_A1748581779le_alt,Ys_7: list_A1748581779le_alt] :
      ( ( Ys_7 != nil_Ar1741995278le_alt )
     => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_21),Ys_7)) = last_A1673116455le_alt(Ys_7) ) ) ).

tff(fact_391_last__appendL,axiom,
    ! [Xs_20: list_A1748581779le_alt,Ys_6: list_A1748581779le_alt] :
      ( ( Ys_6 = nil_Ar1741995278le_alt )
     => ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_20),Ys_6)) = last_A1673116455le_alt(Xs_20) ) ) ).

tff(fact_392_lexord__append__leftI,axiom,
    ! [X_1: list_A1748581779le_alt,U: list_A1748581779le_alt,V: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,U),V)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,X_1),U)),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,X_1),V))),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ).

tff(fact_393_butlast__snoc,axiom,
    ! [Xs_19: list_A1748581779le_alt,X_11: arrow_931160158le_alt] : ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_19),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_11),nil_Ar1741995278le_alt))) = Xs_19 ) ).

tff(fact_394_last__snoc,axiom,
    ! [Xs_18: list_A1748581779le_alt,X_10: arrow_931160158le_alt] : ( last_A1673116455le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_18),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_10),nil_Ar1741995278le_alt))) = X_10 ) ).

tff(fact_395_lexord__append__left__rightI,axiom,
    ! [U: list_A1748581779le_alt,X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)),R_1))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,U),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Aa),X_1))),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,U),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Ba),Y_2)))),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ).

tff(fact_396_lexord__append__left__rightI,axiom,
    ! [U: list_l1735481012le_alt,X_1: list_l1735481012le_alt,Y_2: list_l1735481012le_alt,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba)),R_1))
     => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,U),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Aa),X_1))),hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,U),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Ba),Y_2)))),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ).

tff(fact_397_lexord__append__rightI,axiom,
    ! [X_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool,Y_2: list_A1748581779le_alt] :
      ( ? [B: arrow_931160158le_alt,Z: list_A1748581779le_alt] : ( Y_2 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,B),Z) )
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,X_1),Y_2))),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ).

tff(fact_398_lexord__append__leftD,axiom,
    ! [X_1: list_l1735481012le_alt,U: list_l1735481012le_alt,V: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,X_1),U)),hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,X_1),V))),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1)))
     => ( ! [A: list_A1748581779le_alt] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),A)),R_1))
       => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,U),V)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ) ).

tff(fact_399_lexord__append__leftD,axiom,
    ! [X_1: list_A1748581779le_alt,U: list_A1748581779le_alt,V: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,X_1),U)),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,X_1),V))),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
     => ( ! [A: arrow_931160158le_alt] : ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),A)),R_1))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,U),V)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ) ).

tff(fact_400_rev__induct,axiom,
    ! [Xs: list_A1748581779le_alt,Pa: fun_li1323594581t_bool] :
      ( hBOOL(hAPP_l713721587t_bool(Pa,nil_Ar1741995278le_alt))
     => ( ! [X_2: arrow_931160158le_alt,Xs_9: list_A1748581779le_alt] :
            ( hBOOL(hAPP_l713721587t_bool(Pa,Xs_9))
           => hBOOL(hAPP_l713721587t_bool(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_9),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),nil_Ar1741995278le_alt)))) )
       => hBOOL(hAPP_l713721587t_bool(Pa,Xs)) ) ) ).

tff(fact_401_rev__cases,axiom,
    ! [Xs_17: list_A1748581779le_alt] :
      ( ( Xs_17 != nil_Ar1741995278le_alt )
     => ~ ! [Ys: list_A1748581779le_alt,Y_1: arrow_931160158le_alt] : ( Xs_17 != hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),nil_Ar1741995278le_alt)) ) ) ).

tff(fact_402_snoc__listrel1__snoc__iff,axiom,
    ! [Xs: list_l1735481012le_alt,X_1: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Xs),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),nil_li1540629731le_alt))),hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Ys_1),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),nil_li1540629731le_alt)))),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
          & ( X_1 = Y_2 ) )
        | ( ( Xs = Ys_1 )
          & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1)) ) ) ) ).

tff(fact_403_snoc__listrel1__snoc__iff,axiom,
    ! [Xs: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt))),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),nil_Ar1741995278le_alt)))),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
          & ( X_1 = Y_2 ) )
        | ( ( Xs = Ys_1 )
          & hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1)) ) ) ) ).

tff(fact_404_rotate1__def,axiom,
    ! [Xs: list_A1748581779le_alt] : ( rotate791150427le_alt(Xs) = list_c151649911le_alt(nil_Ar1741995278le_alt,hAPP_f566168733le_alt(hAPP_f293521405le_alt(cOMBB_764295458le_alt,hAPP_f1762369621le_alt(cOMBC_67621220le_alt,append634883619le_alt)),hAPP_l1542090656le_alt(hAPP_f1593322349le_alt(cOMBC_1067846133le_alt,cons_A684544190le_alt),nil_Ar1741995278le_alt)),Xs) ) ).

tff(fact_405_rotate1__is__Nil__conv,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( rotate791150427le_alt(Xs) = nil_Ar1741995278le_alt )
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_406_distinct1__rotate,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,rotate791150427le_alt(Xs)))
    <=> hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs)) ) ).

tff(fact_407_listrel1I2,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Ys_1))),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ).

tff(fact_408_not__listrel1__Nil,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),nil_Ar1741995278le_alt)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ).

tff(fact_409_not__Nil__listrel1,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] : ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),Xs)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ).

tff(fact_410_append__listrel1I,axiom,
    ! [Us_1: list_A1748581779le_alt,Vs_1: list_A1748581779le_alt,Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
          & ( Us_1 = Vs_1 ) )
        | ( ( Xs = Ys_1 )
          & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Us_1),Vs_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) )
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Us_1)),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys_1),Vs_1))),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ).

tff(fact_411_Cons__listrel1__Cons,axiom,
    ! [X_1: list_A1748581779le_alt,Xs: list_l1735481012le_alt,Y_2: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Xs)),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1))),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1))
          & ( Xs = Ys_1 ) )
        | ( ( X_1 = Y_2 )
          & hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1))) ) ) ) ).

tff(fact_412_Cons__listrel1__Cons,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1))
          & ( Xs = Ys_1 ) )
        | ( ( X_1 = Y_2 )
          & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ) ) ).

tff(fact_413_listrel1I1,axiom,
    ! [Xs: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Xs))),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ).

tff(fact_414_listrel1I1,axiom,
    ! [Xs: list_l1735481012le_alt,X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1))
     => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Xs)),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Xs))),hAPP_f1428266567t_bool(listre253898570le_alt,R_1))) ) ).

tff(fact_415_listrel1I,axiom,
    ! [Ys_1: list_A1748581779le_alt,Xs: list_A1748581779le_alt,Us_1: list_A1748581779le_alt,Vs_1: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1))
     => ( ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us_1),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Vs_1)) )
       => ( ( Ys_1 = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us_1),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Vs_1)) )
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ) ) ).

tff(fact_416_listrel1I,axiom,
    ! [Ys_1: list_l1735481012le_alt,Xs: list_l1735481012le_alt,Us_1: list_l1735481012le_alt,Vs_1: list_l1735481012le_alt,X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1))
     => ( ( Xs = hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Us_1),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Vs_1)) )
       => ( ( Ys_1 = hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Us_1),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Vs_1)) )
         => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1))) ) ) ) ).

tff(fact_417_listrel1E,axiom,
    ! [Xs: list_l1735481012le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
     => ~ ! [X_2: list_A1748581779le_alt,Y_1: list_A1748581779le_alt] :
            ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_1)),R_1))
           => ! [Us: list_l1735481012le_alt,Vs: list_l1735481012le_alt] :
                ( ( Xs = hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Us),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_2),Vs)) )
               => ( Ys_1 != hAPP_l1653688277le_alt(hAPP_l2037867230le_alt(append799344526le_alt,Us),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_1),Vs)) ) ) ) ) ).

tff(fact_418_listrel1E,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
     => ~ ! [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt] :
            ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_1)),R_1))
           => ! [Us: list_A1748581779le_alt,Vs: list_A1748581779le_alt] :
                ( ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Vs)) )
               => ( Ys_1 != hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Us),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Vs)) ) ) ) ) ).

tff(fact_419_Cons__listrel1E1,axiom,
    ! [X_1: list_A1748581779le_alt,Xs: list_l1735481012le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Xs)),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
     => ( ! [Y_1: list_A1748581779le_alt] :
            ( ( Ys_1 = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_1),Xs) )
           => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_1)),R_1)) )
       => ~ ! [Zs: list_l1735481012le_alt] :
              ( ( Ys_1 = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Zs) )
             => ~ hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Zs)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1))) ) ) ) ).

tff(fact_420_Cons__listrel1E1,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
     => ( ! [Y_1: arrow_931160158le_alt] :
            ( ( Ys_1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Xs) )
           => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_1)),R_1)) )
       => ~ ! [Zs: list_A1748581779le_alt] :
              ( ( Ys_1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Zs) )
             => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Zs)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ) ) ).

tff(fact_421_Cons__listrel1E2,axiom,
    ! [Xs: list_l1735481012le_alt,Y_2: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1))),hAPP_f1428266567t_bool(listre253898570le_alt,R_1)))
     => ( ! [X_2: list_A1748581779le_alt] :
            ( ( Xs = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_2),Ys_1) )
           => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_2)),R_1)) )
       => ~ ! [Zs: list_l1735481012le_alt] :
              ( ( Xs = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Zs) )
             => ~ hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Zs),Ys_1)),hAPP_f1428266567t_bool(listre253898570le_alt,R_1))) ) ) ) ).

tff(fact_422_Cons__listrel1E2,axiom,
    ! [Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
     => ( ! [X_2: arrow_931160158le_alt] :
            ( ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Ys_1) )
           => ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),R_1)) )
       => ~ ! [Zs: list_A1748581779le_alt] :
              ( ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Zs) )
             => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Zs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1))) ) ) ) ).

tff(fact_423_Cons__in__lex,axiom,
    ! [X_1: list_A1748581779le_alt,Xs: list_l1735481012le_alt,Y_2: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Xs)),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1))),hAPP_f1428266567t_bool(lex_li296480639le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1))
          & ( size_s24685002le_alt(Xs) = size_s24685002le_alt(Ys_1) ) )
        | ( ( X_1 = Y_2 )
          & hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(lex_li296480639le_alt,R_1))) ) ) ) ).

tff(fact_424_Cons__in__lex,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))),hAPP_f557837283t_bool(lex_Ar1871318386le_alt,R_1)))
    <=> ( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1))
          & ( size_s1492124157le_alt(Xs) = size_s1492124157le_alt(Ys_1) ) )
        | ( ( X_1 = Y_2 )
          & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(lex_Ar1871318386le_alt,R_1))) ) ) ) ).

tff(fact_425_dropWhile__eq__Cons__conv,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( dropWh1772583087le_alt(Pa,Xs) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1) )
    <=> ( ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,takeWh4609031le_alt(Pa,Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1)) )
        & ~ hBOOL(hAPP_A674791462t_bool(Pa,Y_2)) ) ) ).

tff(fact_426_partition_Osimps_I2_J,axiom,
    ! [Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] : ( partit1943378951le_alt(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = hAPP_P1208706541le_alt(produc1631581515le_alt(hAPP_f186933785le_alt(hAPP_f1043429597le_alt(cOMBS_384423136le_alt,hAPP_f1817977963le_alt(hAPP_f1428546141le_alt(cOMBB_202310119le_alt,cOMBS_1384849976le_alt),hAPP_f1272206039le_alt(hAPP_f1730519937le_alt(cOMBB_1090121759le_alt,hAPP_f675875329le_alt(cOMBB_1744225841le_alt,if_Pro1761812485le_alt(hAPP_A674791462t_bool(Pa,X_1)))),hAPP_f2007624449le_alt(hAPP_f760536509le_alt(cOMBB_991641265le_alt,produc1596656747le_alt),hAPP_A662984834le_alt(cons_A684544190le_alt,X_1))))),hAPP_f2007624449le_alt(hAPP_f724120879le_alt(cOMBC_1169880370le_alt,hAPP_f74494859le_alt(hAPP_f489798931le_alt(cOMBB_1371834305le_alt,cOMBB_1257018821le_alt),produc1596656747le_alt)),hAPP_A662984834le_alt(cons_A684544190le_alt,X_1)))),partit1943378951le_alt(Pa,Xs)) ) ).

tff(fact_427_dropWhile_Osimps_I2_J,axiom,
    ! [Xs: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt] :
      ( ( hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( dropWh1772583087le_alt(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = dropWh1772583087le_alt(Pa,Xs) ) )
      & ( ~ hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( dropWh1772583087le_alt(Pa,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) ) ) ) ).

tff(fact_428_dropWhile_Osimps_I1_J,axiom,
    ! [Pa: fun_Ar1091019988t_bool] : ( dropWh1772583087le_alt(Pa,nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ) ).

tff(fact_429_distinct__dropWhile,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs))
     => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,dropWh1772583087le_alt(Pa,Xs))) ) ).

tff(fact_430_split__curry,axiom,
    ! [F: fun_Pr1055212137t_bool] : ( produc2067717087t_bool(produc258050046t_bool(F)) = F ) ).

tff(fact_431_curry__split,axiom,
    ! [F: fun_Ar1414184139t_bool] : ( produc258050046t_bool(produc2067717087t_bool(F)) = F ) ).

tff(fact_432_listrel1__eq__len,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre372320615le_alt,R_1)))
     => ( size_s1492124157le_alt(Xs) = size_s1492124157le_alt(Ys_1) ) ) ).

tff(fact_433_takeWhile__dropWhile__id,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,takeWh4609031le_alt(Pa,Xs)),dropWh1772583087le_alt(Pa,Xs)) = Xs ) ).

tff(fact_434_lexord__lex,axiom,
    ! [X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),hAPP_f557837283t_bool(lex_Ar1871318386le_alt,R_1)))
    <=> ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
        & ( size_s1492124157le_alt(X_1) = size_s1492124157le_alt(Y_2) ) ) ) ).

tff(fact_435_lexn__length,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool,N: nat] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),lexn_A626162606le_alt(R_1,N)))
     => ( ( size_s1492124157le_alt(Xs) = N )
        & ( size_s1492124157le_alt(Ys_1) = N ) ) ) ).

tff(fact_436_splitI,axiom,
    ! [F: fun_li954148211t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(F,Aa),Ba))
     => hBOOL(hAPP_P274047445t_bool(produc1791904563t_bool(F),hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba))) ) ).

tff(fact_437_splitI,axiom,
    ! [F: fun_Ar1414184139t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(F,Aa),Ba))
     => hBOOL(hAPP_P166437127t_bool(produc2067717087t_bool(F),hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba))) ) ).

tff(fact_438_prod__caseI,axiom,
    ! [F1: fun_li954148211t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(F1,Aa),Ba))
     => hBOOL(hAPP_P274047445t_bool(produc1791904563t_bool(F1),hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba))) ) ).

tff(fact_439_prod__caseI,axiom,
    ! [F1: fun_Ar1414184139t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(F1,Aa),Ba))
     => hBOOL(hAPP_P166437127t_bool(produc2067717087t_bool(F1),hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba))) ) ).

tff(fact_440_splitD,axiom,
    ! [F: fun_li954148211t_bool,Aa: list_A1748581779le_alt,Ba: list_A1748581779le_alt] :
      ( hBOOL(hAPP_P274047445t_bool(produc1791904563t_bool(F),hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Aa),Ba)))
     => hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(F,Aa),Ba)) ) ).

tff(fact_441_splitD,axiom,
    ! [F: fun_Ar1414184139t_bool,Aa: arrow_931160158le_alt,Ba: arrow_931160158le_alt] :
      ( hBOOL(hAPP_P166437127t_bool(produc2067717087t_bool(F),hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Aa),Ba)))
     => hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(F,Aa),Ba)) ) ).

tff(fact_442_splitI2,axiom,
    ! [Ca: fun_li954148211t_bool,P_1: produc662089077le_alt] :
      ( ! [A: list_A1748581779le_alt,B: list_A1748581779le_alt] :
          ( ( P_1 = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A),B) )
         => hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(Ca,A),B)) )
     => hBOOL(hAPP_P274047445t_bool(produc1791904563t_bool(Ca),P_1)) ) ).

tff(fact_443_splitI2,axiom,
    ! [Ca: fun_Ar1414184139t_bool,P_1: produc1840315303le_alt] :
      ( ! [A: arrow_931160158le_alt,B: arrow_931160158le_alt] :
          ( ( P_1 = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,A),B) )
         => hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(Ca,A),B)) )
     => hBOOL(hAPP_P166437127t_bool(produc2067717087t_bool(Ca),P_1)) ) ).

tff(fact_444_splitE,axiom,
    ! [Ca: fun_li954148211t_bool,P_1: produc662089077le_alt] :
      ( hBOOL(hAPP_P274047445t_bool(produc1791904563t_bool(Ca),P_1))
     => ~ ! [X_2: list_A1748581779le_alt,Y_1: list_A1748581779le_alt] :
            ( ( P_1 = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_1) )
           => ~ hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(Ca,X_2),Y_1)) ) ) ).

tff(fact_445_splitE,axiom,
    ! [Ca: fun_Ar1414184139t_bool,P_1: produc1840315303le_alt] :
      ( hBOOL(hAPP_P166437127t_bool(produc2067717087t_bool(Ca),P_1))
     => ~ ! [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt] :
            ( ( P_1 = hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_1) )
           => ~ hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(Ca,X_2),Y_1)) ) ) ).

tff(fact_446_not__distinct__decomp,axiom,
    ! [Ws: list_A1748581779le_alt] :
      ( ~ hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Ws))
     => ? [Xs_9: list_A1748581779le_alt,Ys: list_A1748581779le_alt,Zs: list_A1748581779le_alt,Y_1: arrow_931160158le_alt] : ( Ws = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_9),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),nil_Ar1741995278le_alt)),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),nil_Ar1741995278le_alt)),Zs)))) ) ) ).

tff(fact_447_listrel_OCons,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_1),Y_2)),R_1))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
       => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ) ) ).

tff(fact_448_listrel_OCons,axiom,
    ! [Xs: list_l1735481012le_alt,Ys_1: list_l1735481012le_alt,X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_1),Y_2)),R_1))
     => ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1)))
       => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_1),Xs)),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1))),hAPP_f1428266567t_bool(listre256509371le_alt,R_1))) ) ) ).

tff(fact_449_tl__append,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt] : ( tl_Arr921252325le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1)) = list_c151649911le_alt(tl_Arr921252325le_alt(Ys_1),hAPP_f2067535732le_alt(cOMBK_313903393le_alt,hAPP_l38598005le_alt(hAPP_f1762369621le_alt(cOMBC_67621220le_alt,append634883619le_alt),Ys_1)),Xs) ) ).

tff(fact_450_listrel__Nil2,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),nil_Ar1741995278le_alt)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
     => ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_451_listrel__Nil1,axiom,
    ! [Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),Xs)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
     => ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_452_tl_Osimps_I2_J,axiom,
    ! [X_9: arrow_931160158le_alt,Xs_16: list_A1748581779le_alt] : ( tl_Arr921252325le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_9),Xs_16)) = Xs_16 ) ).

tff(fact_453_tl_Osimps_I1_J,axiom,
    tl_Arr921252325le_alt(nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ).

tff(fact_454_distinct__tl,axiom,
    ! [Xs_15: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs_15))
     => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,tl_Arr921252325le_alt(Xs_15))) ) ).

tff(fact_455_listrel_ONil,axiom,
    ! [R_1: fun_Pr1055212137t_bool] : hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,nil_Ar1741995278le_alt),nil_Ar1741995278le_alt)),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ).

tff(fact_456_listrel__eq__len,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
     => ( size_s1492124157le_alt(Xs) = size_s1492124157le_alt(Ys_1) ) ) ).

tff(fact_457_tl__append2,axiom,
    ! [Ys_5: list_A1748581779le_alt,Xs_14: list_A1748581779le_alt] :
      ( ( Xs_14 != nil_Ar1741995278le_alt )
     => ( tl_Arr921252325le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_14),Ys_5)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,tl_Arr921252325le_alt(Xs_14)),Ys_5) ) ) ).

tff(fact_458_listrel__Cons2,axiom,
    ! [Xs: list_l1735481012le_alt,Y_2: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1))),hAPP_f1428266567t_bool(listre256509371le_alt,R_1)))
     => ~ ! [X_2: list_A1748581779le_alt,Xs_9: list_l1735481012le_alt] :
            ( ( Xs = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_2),Xs_9) )
           => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_2)),R_1))
             => ~ hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs_9),Ys_1)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1))) ) ) ) ).

tff(fact_459_listrel__Cons2,axiom,
    ! [Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
     => ~ ! [X_2: arrow_931160158le_alt,Xs_9: list_A1748581779le_alt] :
            ( ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Xs_9) )
           => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_2)),R_1))
             => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs_9),Ys_1)),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ) ) ) ).

tff(fact_460_listrel__Cons1,axiom,
    ! [Y_2: list_A1748581779le_alt,Ys_1: list_l1735481012le_alt,Xs: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_2),Ys_1)),Xs)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1)))
     => ~ ! [Y_1: list_A1748581779le_alt,Ys: list_l1735481012le_alt] :
            ( ( Xs = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_1),Ys) )
           => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Y_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Ys_1),Ys)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1))) ) ) ) ).

tff(fact_461_listrel__Cons1,axiom,
    ! [Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt,Xs: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1)),Xs)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
     => ~ ! [Y_1: arrow_931160158le_alt,Ys: list_A1748581779le_alt] :
            ( ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Ys) )
           => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Y_2),Y_1)),R_1))
             => ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Ys_1),Ys)),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ) ) ) ).

tff(fact_462_listrelp__listrel__eq,axiom,
    ! [R_1: fun_Pr1055212137t_bool,X_2: list_A1748581779le_alt,Xa: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(hAPP_f1810968607t_bool(hAPP_f15758621t_bool(cOMBC_1947566172t_bool,hAPP_f1435501085t_bool(hAPP_f318336003t_bool(cOMBB_1430402568le_alt,cOMBC_571858149l_bool),hAPP_f1176598245l_bool(hAPP_f695996419l_bool(cOMBB_1605735744le_alt,hAPP_f1650801283l_bool(cOMBB_480104238le_alt,member553230100le_alt)),produc362059031le_alt))),R_1)),X_2),Xa))
    <=> hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Xa)),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ) ).

tff(fact_463_listrelp__listrel__eq,axiom,
    ! [R_1: fun_Pr1013460023t_bool,X_2: list_l1735481012le_alt,Xa: list_l1735481012le_alt] :
      ( hBOOL(hAPP_l108873084t_bool(hAPP_l767557321t_bool(listre450023945le_alt(hAPP_f615584405t_bool(hAPP_f1269493503t_bool(cOMBC_1004503918t_bool,hAPP_f133408895t_bool(hAPP_f1802448643t_bool(cOMBB_1898463941le_alt,cOMBC_307006084l_bool),hAPP_f1120297681l_bool(hAPP_f788365459l_bool(cOMBB_1398787847le_alt,hAPP_f270961347l_bool(cOMBB_2055762783le_alt,member1475736930le_alt)),produc1596656747le_alt))),R_1)),X_2),Xa))
    <=> hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,X_2),Xa)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1))) ) ).

tff(fact_464_rotate1__hd__tl,axiom,
    ! [Xs_13: list_A1748581779le_alt] :
      ( ( Xs_13 != nil_Ar1741995278le_alt )
     => ( rotate791150427le_alt(Xs_13) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,tl_Arr921252325le_alt(Xs_13)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,hd_Arr274000865le_alt(Xs_13)),nil_Ar1741995278le_alt)) ) ) ).

tff(fact_465_listrel_Osimps,axiom,
    ! [A1: list_l1735481012le_alt,A2: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool] :
      ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,A1),A2)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1)))
    <=> ( ( ( A1 = nil_li1540629731le_alt )
          & ( A2 = nil_li1540629731le_alt ) )
        | ? [X_2: list_A1748581779le_alt,Y_1: list_A1748581779le_alt,Xs_9: list_l1735481012le_alt,Ys: list_l1735481012le_alt] :
            ( ( A1 = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,X_2),Xs_9) )
            & ( A2 = hAPP_l1653688277le_alt(hAPP_l358314791le_alt(cons_l268440883le_alt,Y_1),Ys) )
            & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_1)),R_1))
            & hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs_9),Ys)),hAPP_f1428266567t_bool(listre256509371le_alt,R_1))) ) ) ) ).

tff(fact_466_listrel_Osimps,axiom,
    ! [A1: list_A1748581779le_alt,A2: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,A1),A2)),hAPP_f557837283t_bool(listre228973110le_alt,R_1)))
    <=> ( ( ( A1 = nil_Ar1741995278le_alt )
          & ( A2 = nil_Ar1741995278le_alt ) )
        | ? [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt,Xs_9: list_A1748581779le_alt,Ys: list_A1748581779le_alt] :
            ( ( A1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Xs_9) )
            & ( A2 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Ys) )
            & hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_1)),R_1))
            & hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs_9),Ys)),hAPP_f557837283t_bool(listre228973110le_alt,R_1))) ) ) ) ).

tff(fact_467_hd_Osimps,axiom,
    ! [X_8: arrow_931160158le_alt,Xs_12: list_A1748581779le_alt] : ( hd_Arr274000865le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_8),Xs_12)) = X_8 ) ).

tff(fact_468_listrelp_OCons,axiom,
    ! [Xs: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Ar1414184139t_bool,X_1: arrow_931160158le_alt,Y_2: arrow_931160158le_alt] :
      ( hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(R_1,X_1),Y_2))
     => ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(R_1),Xs),Ys_1))
       => hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(R_1),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1))) ) ) ).

tff(fact_469_listrelp_ONil,axiom,
    ! [R_1: fun_Ar1414184139t_bool] : hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(R_1),nil_Ar1741995278le_alt),nil_Ar1741995278le_alt)) ).

tff(fact_470_hd__append,axiom,
    ! [Ys_4: list_A1748581779le_alt,Xs_11: list_A1748581779le_alt] :
      ( ( ( Xs_11 = nil_Ar1741995278le_alt )
       => ( hd_Arr274000865le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_11),Ys_4)) = hd_Arr274000865le_alt(Ys_4) ) )
      & ( ( Xs_11 != nil_Ar1741995278le_alt )
       => ( hd_Arr274000865le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_11),Ys_4)) = hd_Arr274000865le_alt(Xs_11) ) ) ) ).

tff(fact_471_hd__append2,axiom,
    ! [Ys_3: list_A1748581779le_alt,Xs_10: list_A1748581779le_alt] :
      ( ( Xs_10 != nil_Ar1741995278le_alt )
     => ( hd_Arr274000865le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_10),Ys_3)) = hd_Arr274000865le_alt(Xs_10) ) ) ).

tff(fact_472_hd__dropWhile,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ( dropWh1772583087le_alt(Pa,Xs) != nil_Ar1741995278le_alt )
     => ~ hBOOL(hAPP_A674791462t_bool(Pa,hd_Arr274000865le_alt(dropWh1772583087le_alt(Pa,Xs)))) ) ).

tff(fact_473_listrelp_Osimps,axiom,
    ! [R_1: fun_Ar1414184139t_bool,A1: list_A1748581779le_alt,A2: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(R_1),A1),A2))
    <=> ( ( ( A1 = nil_Ar1741995278le_alt )
          & ( A2 = nil_Ar1741995278le_alt ) )
        | ? [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt,Xs_9: list_A1748581779le_alt,Ys: list_A1748581779le_alt] :
            ( ( A1 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Xs_9) )
            & ( A2 = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_1),Ys) )
            & hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(R_1,X_2),Y_1))
            & hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(listre1668963176le_alt(R_1),Xs_9),Ys)) ) ) ) ).

tff(fact_474_equal,axiom,
    equal_117954737le_alt = fequal414630996le_alt ).

tff(fact_475_equal__refl,axiom,
    ! [X_7: list_A1748581779le_alt] : hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(equal_117954737le_alt,X_7),X_7)) ).

tff(fact_476_equal__eq,axiom,
    ! [X_1: list_A1748581779le_alt,Y_2: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(equal_117954737le_alt,X_1),Y_2))
    <=> ( X_1 = Y_2 ) ) ).

tff(fact_477_eq__equal,axiom,
    fequal414630996le_alt = equal_117954737le_alt ).

tff(fact_478_last__rev,axiom,
    ! [Xs_8: list_A1748581779le_alt] :
      ( ( Xs_8 != nil_Ar1741995278le_alt )
     => ( last_A1673116455le_alt(rev_Ar1562208110le_alt(Xs_8)) = hd_Arr274000865le_alt(Xs_8) ) ) ).

tff(fact_479_hd__rev,axiom,
    ! [Xs_7: list_A1748581779le_alt] :
      ( ( Xs_7 != nil_Ar1741995278le_alt )
     => ( hd_Arr274000865le_alt(rev_Ar1562208110le_alt(Xs_7)) = last_A1673116455le_alt(Xs_7) ) ) ).

tff(fact_480_replicate__append__same,axiom,
    ! [I_3: nat,X_6: arrow_931160158le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,replic1967339976le_alt(I_3,X_6)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_6),nil_Ar1741995278le_alt)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_6),replic1967339976le_alt(I_3,X_6)) ) ).

tff(fact_481_dropWhile__eq__drop,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] : ( dropWh1772583087le_alt(Pa,Xs) = hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,size_s1492124157le_alt(takeWh4609031le_alt(Pa,Xs))),Xs) ) ).

tff(fact_482_butlast__drop,axiom,
    ! [N_6: nat,Xs_6: list_A1748581779le_alt] : ( butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N_6),Xs_6)) = hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N_6),butlas730749018le_alt(Xs_6)) ) ).

tff(fact_483_drop__butlast,axiom,
    ! [N_5: nat,Xs_5: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N_5),butlas730749018le_alt(Xs_5)) = butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N_5),Xs_5)) ) ).

tff(fact_484_drop__Nil,axiom,
    ! [N_4: nat] : ( hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N_4),nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ) ).

tff(fact_485_distinct__drop,axiom,
    ! [I_2: nat,Xs_4: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs_4))
     => hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,I_2),Xs_4))) ) ).

tff(fact_486_rev__append,axiom,
    ! [Xs_3: list_A1748581779le_alt,Ys_2: list_A1748581779le_alt] : ( rev_Ar1562208110le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs_3),Ys_2)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,rev_Ar1562208110le_alt(Ys_2)),rev_Ar1562208110le_alt(Xs_3)) ) ).

tff(fact_487_rev__is__Nil__conv,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( rev_Ar1562208110le_alt(Xs) = nil_Ar1741995278le_alt )
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_488_Nil__is__rev__conv,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( nil_Ar1741995278le_alt = rev_Ar1562208110le_alt(Xs) )
    <=> ( Xs = nil_Ar1741995278le_alt ) ) ).

tff(fact_489_rev_Osimps_I1_J,axiom,
    rev_Ar1562208110le_alt(nil_Ar1741995278le_alt) = nil_Ar1741995278le_alt ).

tff(fact_490_append__replicate__commute,axiom,
    ! [N_3: nat,X_5: arrow_931160158le_alt,K_1: nat] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,replic1967339976le_alt(N_3,X_5)),replic1967339976le_alt(K_1,X_5)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,replic1967339976le_alt(K_1,X_5)),replic1967339976le_alt(N_3,X_5)) ) ).

tff(fact_491_distinct__rev,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,rev_Ar1562208110le_alt(Xs)))
    <=> hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs)) ) ).

tff(fact_492_rev__singleton__conv,axiom,
    ! [Xs: list_A1748581779le_alt,X_1: arrow_931160158le_alt] :
      ( ( rev_Ar1562208110le_alt(Xs) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt) )
    <=> ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt) ) ) ).

tff(fact_493_singleton__rev__conv,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( ( hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt) = rev_Ar1562208110le_alt(Xs) )
    <=> ( Xs = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),nil_Ar1741995278le_alt) ) ) ).

tff(fact_494_replicate__app__Cons__same,axiom,
    ! [N_2: nat,X_4: arrow_931160158le_alt,Xs_2: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,replic1967339976le_alt(N_2,X_4)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_4),Xs_2)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_4),hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,replic1967339976le_alt(N_2,X_4)),Xs_2)) ) ).

tff(fact_495_rev_Osimps_I2_J,axiom,
    ! [X_3: arrow_931160158le_alt,Xs_1: list_A1748581779le_alt] : ( rev_Ar1562208110le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_3),Xs_1)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,rev_Ar1562208110le_alt(Xs_1)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_3),nil_Ar1741995278le_alt)) ) ).

tff(fact_496_rev__eq__Cons__iff,axiom,
    ! [Xs: list_A1748581779le_alt,Y_2: arrow_931160158le_alt,Ys_1: list_A1748581779le_alt] :
      ( ( rev_Ar1562208110le_alt(Xs) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),Ys_1) )
    <=> ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,rev_Ar1562208110le_alt(Ys_1)),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,Y_2),nil_Ar1741995278le_alt)) ) ) ).

tff(fact_497_takeWhile__neq__rev,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
       => ( takeWh4609031le_alt(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,fNot),hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,fequal628352221le_alt),X_1)),rev_Ar1562208110le_alt(Xs)) = rev_Ar1562208110le_alt(tl_Arr921252325le_alt(dropWh1772583087le_alt(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,fNot),hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,fequal628352221le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_498_takeWhile__neq__rev,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_l2093488478t_bool(distin2008613906le_alt,Xs))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
       => ( takeWh871442828le_alt(hAPP_f842237845t_bool(hAPP_f208471283t_bool(cOMBB_2059950425le_alt,fNot),hAPP_P1710235071t_bool(hAPP_f498121449t_bool(cOMBC_662543858t_bool,fequal1128546102le_alt),X_1)),rev_Pr919241317le_alt(Xs)) = rev_Pr919241317le_alt(tl_Pro747896878le_alt(dropWh2059627236le_alt(hAPP_f842237845t_bool(hAPP_f208471283t_bool(cOMBB_2059950425le_alt,fNot),hAPP_P1710235071t_bool(hAPP_f498121449t_bool(cOMBC_662543858t_bool,fequal1128546102le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_499_takeWhile__neq__rev,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_l878728062i_bool(distin455238322e_indi,Xs))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
       => ( takeWh1517834028e_indi(hAPP_f1282576021i_bool(hAPP_f694179955i_bool(cOMBB_238582393e_indi,fNot),hAPP_A643541183i_bool(hAPP_f470111209i_bool(cOMBC_112876850i_bool,fequal293925846e_indi),X_1)),rev_Ar1187845509e_indi(Xs)) = rev_Ar1187845509e_indi(tl_Arr711649486e_indi(dropWh1846039684e_indi(hAPP_f1282576021i_bool(hAPP_f694179955i_bool(cOMBB_238582393e_indi,fNot),hAPP_A643541183i_bool(hAPP_f470111209i_bool(cOMBC_112876850i_bool,fequal293925846e_indi),X_1)),Xs))) ) ) ) ).

tff(fact_500_takeWhile__neq__rev,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
       => ( takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),rev_bool(Xs)) = rev_bool(tl_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),Xs))) ) ) ) ).

tff(fact_501_takeWhile__neq__rev,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_l1036944766l_bool(distin1125305010t_bool,Xs))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
       => ( takeWh1450838828t_bool(hAPP_f1077478037l_bool(hAPP_f2053120627l_bool(cOMBB_593231993t_bool,fNot),hAPP_f926158015l_bool(hAPP_f1147912169l_bool(cOMBC_2092631346l_bool,fequal730162134t_bool),X_1)),rev_fu762704773t_bool(Xs)) = rev_fu762704773t_bool(tl_fun1694877902t_bool(dropWh1304379524t_bool(hAPP_f1077478037l_bool(hAPP_f2053120627l_bool(cOMBB_593231993t_bool,fNot),hAPP_f926158015l_bool(hAPP_f1147912169l_bool(cOMBC_2092631346l_bool,fequal730162134t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_502_takeWhile__neq__rev,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_l971282430l_bool(distin1251351564t_bool,Xs))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
       => ( takeWh1072801554t_bool(hAPP_f1050277569l_bool(hAPP_f925342873l_bool(cOMBB_2017616773t_bool,fNot),hAPP_f314169011l_bool(hAPP_f5916613l_bool(cOMBC_2092631450l_bool,fequal818396648t_bool),X_1)),rev_fu601479545t_bool(Xs)) = rev_fu601479545t_bool(tl_fun1631474416t_bool(dropWh693679034t_bool(hAPP_f1050277569l_bool(hAPP_f925342873l_bool(cOMBB_2017616773t_bool,fNot),hAPP_f314169011l_bool(hAPP_f5916613l_bool(cOMBC_2092631450l_bool,fequal818396648t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_503_takeWhile__neq__rev,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_l1132755054l_bool(distin420467362t_bool,Xs))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
       => ( takeWh1707174172t_bool(hAPP_f626396309l_bool(hAPP_f1078200691l_bool(cOMBB_1270085993t_bool,fNot),hAPP_f1839818431l_bool(hAPP_f1270395369l_bool(cOMBC_422512914l_bool,fequal1183344582t_bool),X_1)),rev_fu207962229t_bool(Xs)) = rev_fu207962229t_bool(tl_fun436180158t_bool(dropWh1950353012t_bool(hAPP_f626396309l_bool(hAPP_f1078200691l_bool(cOMBB_1270085993t_bool,fNot),hAPP_f1839818431l_bool(hAPP_f1270395369l_bool(cOMBC_422512914l_bool,fequal1183344582t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_504_takeWhile__neq__rev,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_l108838032t_bool(distin2115974596le_alt,Xs))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
       => ( takeWh641303102le_alt(hAPP_f70231061t_bool(hAPP_f1056396531t_bool(cOMBB_1693113739le_alt,fNot),hAPP_P339234111t_bool(hAPP_f182135529t_bool(cOMBC_1001276758t_bool,fequal1713866472le_alt),X_1)),rev_Pr1555478679le_alt(Xs)) = rev_Pr1555478679le_alt(tl_Pro1271790560le_alt(dropWh1019479958le_alt(hAPP_f70231061t_bool(hAPP_f1056396531t_bool(cOMBB_1693113739le_alt,fNot),hAPP_P339234111t_bool(hAPP_f182135529t_bool(cOMBC_1001276758t_bool,fequal1713866472le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_505_dropWhile__neq__rev,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
       => ( dropWh1772583087le_alt(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,fNot),hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,fequal628352221le_alt),X_1)),rev_Ar1562208110le_alt(Xs)) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),rev_Ar1562208110le_alt(takeWh4609031le_alt(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,fNot),hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,fequal628352221le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_506_dropWhile__neq__rev,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_l2093488478t_bool(distin2008613906le_alt,Xs))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
       => ( dropWh2059627236le_alt(hAPP_f842237845t_bool(hAPP_f208471283t_bool(cOMBB_2059950425le_alt,fNot),hAPP_P1710235071t_bool(hAPP_f498121449t_bool(cOMBC_662543858t_bool,fequal1128546102le_alt),X_1)),rev_Pr919241317le_alt(Xs)) = hAPP_l1876658005le_alt(hAPP_P59114565le_alt(cons_P1348035861le_alt,X_1),rev_Pr919241317le_alt(takeWh871442828le_alt(hAPP_f842237845t_bool(hAPP_f208471283t_bool(cOMBB_2059950425le_alt,fNot),hAPP_P1710235071t_bool(hAPP_f498121449t_bool(cOMBC_662543858t_bool,fequal1128546102le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_507_dropWhile__neq__rev,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_l878728062i_bool(distin455238322e_indi,Xs))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
       => ( dropWh1846039684e_indi(hAPP_f1282576021i_bool(hAPP_f694179955i_bool(cOMBB_238582393e_indi,fNot),hAPP_A643541183i_bool(hAPP_f470111209i_bool(cOMBC_112876850i_bool,fequal293925846e_indi),X_1)),rev_Ar1187845509e_indi(Xs)) = hAPP_l221792213e_indi(hAPP_A1717387813e_indi(cons_A1348960309e_indi,X_1),rev_Ar1187845509e_indi(takeWh1517834028e_indi(hAPP_f1282576021i_bool(hAPP_f694179955i_bool(cOMBB_238582393e_indi,fNot),hAPP_A643541183i_bool(hAPP_f470111209i_bool(cOMBC_112876850i_bool,fequal293925846e_indi),X_1)),Xs))) ) ) ) ).

tff(fact_508_dropWhile__neq__rev,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
       => ( dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),rev_bool(Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),rev_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),Xs))) ) ) ) ).

tff(fact_509_dropWhile__neq__rev,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_l1036944766l_bool(distin1125305010t_bool,Xs))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
       => ( dropWh1304379524t_bool(hAPP_f1077478037l_bool(hAPP_f2053120627l_bool(cOMBB_593231993t_bool,fNot),hAPP_f926158015l_bool(hAPP_f1147912169l_bool(cOMBC_2092631346l_bool,fequal730162134t_bool),X_1)),rev_fu762704773t_bool(Xs)) = hAPP_l137391573t_bool(hAPP_f812806181t_bool(cons_f1295695413t_bool,X_1),rev_fu762704773t_bool(takeWh1450838828t_bool(hAPP_f1077478037l_bool(hAPP_f2053120627l_bool(cOMBB_593231993t_bool,fNot),hAPP_f926158015l_bool(hAPP_f1147912169l_bool(cOMBC_2092631346l_bool,fequal730162134t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_510_dropWhile__neq__rev,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_l971282430l_bool(distin1251351564t_bool,Xs))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
       => ( dropWh693679034t_bool(hAPP_f1050277569l_bool(hAPP_f925342873l_bool(cOMBB_2017616773t_bool,fNot),hAPP_f314169011l_bool(hAPP_f5916613l_bool(cOMBC_2092631450l_bool,fequal818396648t_bool),X_1)),rev_fu601479545t_bool(Xs)) = hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),rev_fu601479545t_bool(takeWh1072801554t_bool(hAPP_f1050277569l_bool(hAPP_f925342873l_bool(cOMBB_2017616773t_bool,fNot),hAPP_f314169011l_bool(hAPP_f5916613l_bool(cOMBC_2092631450l_bool,fequal818396648t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_511_dropWhile__neq__rev,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_l1132755054l_bool(distin420467362t_bool,Xs))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
       => ( dropWh1950353012t_bool(hAPP_f626396309l_bool(hAPP_f1078200691l_bool(cOMBB_1270085993t_bool,fNot),hAPP_f1839818431l_bool(hAPP_f1270395369l_bool(cOMBC_422512914l_bool,fequal1183344582t_bool),X_1)),rev_fu207962229t_bool(Xs)) = hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),rev_fu207962229t_bool(takeWh1707174172t_bool(hAPP_f626396309l_bool(hAPP_f1078200691l_bool(cOMBB_1270085993t_bool,fNot),hAPP_f1839818431l_bool(hAPP_f1270395369l_bool(cOMBC_422512914l_bool,fequal1183344582t_bool),X_1)),Xs))) ) ) ) ).

tff(fact_512_dropWhile__neq__rev,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_l108838032t_bool(distin2115974596le_alt,Xs))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
       => ( dropWh1019479958le_alt(hAPP_f70231061t_bool(hAPP_f1056396531t_bool(cOMBB_1693113739le_alt,fNot),hAPP_P339234111t_bool(hAPP_f182135529t_bool(cOMBC_1001276758t_bool,fequal1713866472le_alt),X_1)),rev_Pr1555478679le_alt(Xs)) = hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),rev_Pr1555478679le_alt(takeWh641303102le_alt(hAPP_f70231061t_bool(hAPP_f1056396531t_bool(cOMBB_1693113739le_alt,fNot),hAPP_P339234111t_bool(hAPP_f182135529t_bool(cOMBC_1001276758t_bool,fequal1713866472le_alt),X_1)),Xs))) ) ) ) ).

tff(fact_513_drop__Cons,axiom,
    ! [N: nat,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)) = nat_ca1780707935le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs),hAPP_l1844587084le_alt(hAPP_f1168703685le_alt(cOMBC_723368737le_alt,drop_A1802510926le_alt),Xs),N) ) ).

tff(fact_514_rev__foldl__cons,axiom,
    ! [Xs: list_A1748581779le_alt] : ( rev_Ar1562208110le_alt(Xs) = foldl_971653884le_alt(hAPP_f1593322349le_alt(cOMBC_1067846133le_alt,cons_A684544190le_alt),nil_Ar1741995278le_alt,Xs) ) ).

tff(fact_515_in__set__dropD,axiom,
    ! [X_1: arrow_931160158le_alt,N: nat,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(hAPP_l2085326633le_alt(hAPP_n447277270le_alt(drop_A1802510926le_alt,N),Xs))))
     => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs))) ) ).

tff(fact_516_in__set__dropD,axiom,
    ! [X_1: produc662089077le_alt,N: nat,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(hAPP_l1876658005le_alt(hAPP_n108239496le_alt(drop_P738054021le_alt,N),Xs))))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs))) ) ).

tff(fact_517_in__set__dropD,axiom,
    ! [X_1: arrow_2115524757e_indi,N: nat,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(hAPP_l221792213e_indi(hAPP_n1577580168e_indi(drop_A134812325e_indi,N),Xs))))
     => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs))) ) ).

tff(fact_518_in__set__dropD,axiom,
    ! [X_1: bool,N: nat,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N),Xs))))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) ) ).

tff(fact_519_in__set__dropD,axiom,
    ! [X_1: fun_fu1595299477t_bool,N: nat,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(hAPP_l137391573t_bool(hAPP_n366487176t_bool(drop_f1457139877t_bool,N),Xs))))
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs))) ) ).

tff(fact_520_in__set__dropD,axiom,
    ! [X_1: fun_Pr1055212137t_bool,N: nat,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(hAPP_l943674815t_bool(hAPP_n875739372t_bool(drop_f202273881t_bool,N),Xs))))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs))) ) ).

tff(fact_521_in__set__dropD,axiom,
    ! [X_1: fun_Ar500372357t_bool,N: nat,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(hAPP_l1831878357t_bool(hAPP_n140868232t_bool(drop_f1478843797t_bool,N),Xs))))
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs))) ) ).

tff(fact_522_in__set__dropD,axiom,
    ! [X_1: produc1840315303le_alt,N: nat,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(hAPP_l1141483861le_alt(hAPP_n152084232le_alt(drop_P1273017783le_alt,N),Xs))))
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs))) ) ).

tff(fact_523_set__takeWhileD,axiom,
    ! [X_1: arrow_931160158le_alt,Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(takeWh4609031le_alt(Pa,Xs))))
     => ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
        & hBOOL(hAPP_A674791462t_bool(Pa,X_1)) ) ) ).

tff(fact_524_set__takeWhileD,axiom,
    ! [X_1: produc662089077le_alt,Pa: fun_Pr1013460023t_bool,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(takeWh871442828le_alt(Pa,Xs))))
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
        & hBOOL(hAPP_P274047445t_bool(Pa,X_1)) ) ) ).

tff(fact_525_set__takeWhileD,axiom,
    ! [X_1: arrow_2115524757e_indi,Pa: fun_Ar552120407i_bool,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(takeWh1517834028e_indi(Pa,Xs))))
     => ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
        & hBOOL(hAPP_A1888055029i_bool(Pa,X_1)) ) ) ).

tff(fact_526_set__takeWhileD,axiom,
    ! [X_1: bool,Pa: fun_bool_bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(takeWhile_bool(Pa,Xs))))
     => ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
        & hBOOL(hAPP_bool_bool(Pa,X_1)) ) ) ).

tff(fact_527_set__takeWhileD,axiom,
    ! [X_1: fun_fu1595299477t_bool,Pa: fun_fu1138137687l_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(takeWh1450838828t_bool(Pa,Xs))))
     => ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
        & hBOOL(hAPP_f611501301l_bool(Pa,X_1)) ) ) ).

tff(fact_528_set__takeWhileD,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Pa: fun_fu1015689055l_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(takeWh1072801554t_bool(Pa,Xs))))
     => ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
        & hBOOL(hAPP_f429946033l_bool(Pa,X_1)) ) ) ).

tff(fact_529_set__takeWhileD,axiom,
    ! [X_1: fun_Ar500372357t_bool,Pa: fun_fu775006535l_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(takeWh1707174172t_bool(Pa,Xs))))
     => ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
        & hBOOL(hAPP_f1766661605l_bool(Pa,X_1)) ) ) ).

tff(fact_530_set__takeWhileD,axiom,
    ! [X_1: produc1840315303le_alt,Pa: fun_Pr1055212137t_bool,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(takeWh641303102le_alt(Pa,Xs))))
     => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
        & hBOOL(hAPP_P166437127t_bool(Pa,X_1)) ) ) ).

tff(fact_531_takeWhile__eq__all__conv,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ( takeWh4609031le_alt(Pa,Xs) = Xs )
    <=> ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
         => hBOOL(hAPP_A674791462t_bool(Pa,X_2)) ) ) ).

tff(fact_532_in__set__butlastD,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(butlas730749018le_alt(Xs))))
     => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs))) ) ).

tff(fact_533_in__set__butlastD,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(butlas1911524985le_alt(Xs))))
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs))) ) ).

tff(fact_534_in__set__butlastD,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(butlas92561305e_indi(Xs))))
     => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs))) ) ).

tff(fact_535_in__set__butlastD,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs))))
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) ) ).

tff(fact_536_in__set__butlastD,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(butlas606086553t_bool(Xs))))
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs))) ) ).

tff(fact_537_in__set__butlastD,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(butlas717559397t_bool(Xs))))
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs))) ) ).

tff(fact_538_in__set__butlastD,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(butlas707526281t_bool(Xs))))
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs))) ) ).

tff(fact_539_in__set__butlastD,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(butlas1000653483le_alt(Xs))))
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs))) ) ).

tff(fact_540_set__ConsD,axiom,
    ! [Y_2: arrow_931160158le_alt,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,Y_2),set_Ar1033255471le_alt(hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,Y_2),set_Ar1033255471le_alt(Xs))) ) ) ).

tff(fact_541_set__ConsD,axiom,
    ! [Y_2: produc662089077le_alt,X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,Y_2),set_Pr1859340644le_alt(hAPP_l1876658005le_alt(hAPP_P59114565le_alt(cons_P1348035861le_alt,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,Y_2),set_Pr1859340644le_alt(Xs))) ) ) ).

tff(fact_542_set__ConsD,axiom,
    ! [Y_2: arrow_2115524757e_indi,X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_2),set_Ar1464464132e_indi(hAPP_l221792213e_indi(hAPP_A1717387813e_indi(cons_A1348960309e_indi,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,Y_2),set_Ar1464464132e_indi(Xs))) ) ) ).

tff(fact_543_set__ConsD,axiom,
    ! [Y_2: bool,X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))))
     => ( ( hBOOL(Y_2)
        <=> hBOOL(X_1) )
        | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(Xs))) ) ) ).

tff(fact_544_set__ConsD,axiom,
    ! [Y_2: fun_fu1595299477t_bool,X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Y_2),set_fu1616240388t_bool(hAPP_l137391573t_bool(hAPP_f812806181t_bool(cons_f1295695413t_bool,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,Y_2),set_fu1616240388t_bool(Xs))) ) ) ).

tff(fact_545_set__ConsD,axiom,
    ! [Y_2: fun_Pr1055212137t_bool,X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Y_2),set_fu945091898t_bool(hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,Y_2),set_fu945091898t_bool(Xs))) ) ) ).

tff(fact_546_set__ConsD,axiom,
    ! [Y_2: fun_Ar500372357t_bool,X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Y_2),set_fu116139252t_bool(hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,Y_2),set_fu116139252t_bool(Xs))) ) ) ).

tff(fact_547_set__ConsD,axiom,
    ! [Y_2: produc1840315303le_alt,X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Y_2),set_Pr1864214038le_alt(hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),Xs))))
     => ( ( Y_2 = X_1 )
        | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,Y_2),set_Pr1864214038le_alt(Xs))) ) ) ).

tff(fact_548_in__set__insert,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
     => ( insert428884260le_alt(X_1,Xs) = Xs ) ) ).

tff(fact_549_in__set__insert,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
     => ( insert633788207le_alt(X_1,Xs) = Xs ) ) ).

tff(fact_550_in__set__insert,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
     => ( insert13019471e_indi(X_1,Xs) = Xs ) ) ).

tff(fact_551_in__set__insert,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
     => ( insert_bool(X_1,Xs) = Xs ) ) ).

tff(fact_552_in__set__insert,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
     => ( insert1079671631t_bool(X_1,Xs) = Xs ) ) ).

tff(fact_553_in__set__insert,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
     => ( insert1909791023t_bool(X_1,Xs) = Xs ) ) ).

tff(fact_554_in__set__insert,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
     => ( insert2063552063t_bool(X_1,Xs) = Xs ) ) ).

tff(fact_555_in__set__insert,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
     => ( insert1516219489le_alt(X_1,Xs) = Xs ) ) ).

tff(fact_556_distinct_Osimps_I2_J,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
        & hBOOL(hAPP_l713721587t_bool(distin692125441le_alt,Xs)) ) ) ).

tff(fact_557_distinct_Osimps_I2_J,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_l2093488478t_bool(distin2008613906le_alt,hAPP_l1876658005le_alt(hAPP_P59114565le_alt(cons_P1348035861le_alt,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
        & hBOOL(hAPP_l2093488478t_bool(distin2008613906le_alt,Xs)) ) ) ).

tff(fact_558_distinct_Osimps_I2_J,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_l878728062i_bool(distin455238322e_indi,hAPP_l221792213e_indi(hAPP_A1717387813e_indi(cons_A1348960309e_indi,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
        & hBOOL(hAPP_l878728062i_bool(distin455238322e_indi,Xs)) ) ) ).

tff(fact_559_distinct_Osimps_I2_J,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
        & hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) ) ) ).

tff(fact_560_distinct_Osimps_I2_J,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_l1036944766l_bool(distin1125305010t_bool,hAPP_l137391573t_bool(hAPP_f812806181t_bool(cons_f1295695413t_bool,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
        & hBOOL(hAPP_l1036944766l_bool(distin1125305010t_bool,Xs)) ) ) ).

tff(fact_561_distinct_Osimps_I2_J,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_l971282430l_bool(distin1251351564t_bool,hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
        & hBOOL(hAPP_l971282430l_bool(distin1251351564t_bool,Xs)) ) ) ).

tff(fact_562_distinct_Osimps_I2_J,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_l1132755054l_bool(distin420467362t_bool,hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
        & hBOOL(hAPP_l1132755054l_bool(distin420467362t_bool,Xs)) ) ) ).

tff(fact_563_distinct_Osimps_I2_J,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_l108838032t_bool(distin2115974596le_alt,hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),Xs)))
    <=> ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
        & hBOOL(hAPP_l108838032t_bool(distin2115974596le_alt,Xs)) ) ) ).

tff(fact_564_takeWhile__append1,axiom,
    ! [Ys_1: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
     => ( ~ hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( takeWh4609031le_alt(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1)) = takeWh4609031le_alt(Pa,Xs) ) ) ) ).

tff(fact_565_takeWhile__append1,axiom,
    ! [Ys_1: list_P1493174166le_alt,Pa: fun_Pr1013460023t_bool,X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
     => ( ~ hBOOL(hAPP_P274047445t_bool(Pa,X_1))
       => ( takeWh871442828le_alt(Pa,hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),Ys_1)) = takeWh871442828le_alt(Pa,Xs) ) ) ) ).

tff(fact_566_takeWhile__append1,axiom,
    ! [Ys_1: list_A964264886e_indi,Pa: fun_Ar552120407i_bool,X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
     => ( ~ hBOOL(hAPP_A1888055029i_bool(Pa,X_1))
       => ( takeWh1517834028e_indi(Pa,hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),Ys_1)) = takeWh1517834028e_indi(Pa,Xs) ) ) ) ).

tff(fact_567_takeWhile__append1,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
     => ( ~ hBOOL(hAPP_bool_bool(Pa,X_1))
       => ( takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = takeWhile_bool(Pa,Xs) ) ) ) ).

tff(fact_568_takeWhile__append1,axiom,
    ! [Ys_1: list_f1301614006t_bool,Pa: fun_fu1138137687l_bool,X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f611501301l_bool(Pa,X_1))
       => ( takeWh1450838828t_bool(Pa,hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),Ys_1)) = takeWh1450838828t_bool(Pa,Xs) ) ) ) ).

tff(fact_569_takeWhile__append1,axiom,
    ! [Ys_1: list_f418358302t_bool,Pa: fun_fu1015689055l_bool,X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(Pa,X_1))
       => ( takeWh1072801554t_bool(Pa,hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),Ys_1)) = takeWh1072801554t_bool(Pa,Xs) ) ) ) ).

tff(fact_570_takeWhile__append1,axiom,
    ! [Ys_1: list_f767102118t_bool,Pa: fun_fu775006535l_bool,X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f1766661605l_bool(Pa,X_1))
       => ( takeWh1707174172t_bool(Pa,hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),Ys_1)) = takeWh1707174172t_bool(Pa,Xs) ) ) ) ).

tff(fact_571_takeWhile__append1,axiom,
    ! [Ys_1: list_P1216503240le_alt,Pa: fun_Pr1055212137t_bool,X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
     => ( ~ hBOOL(hAPP_P166437127t_bool(Pa,X_1))
       => ( takeWh641303102le_alt(Pa,hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),Ys_1)) = takeWh641303102le_alt(Pa,Xs) ) ) ) ).

tff(fact_572_last__in__set,axiom,
    ! [As: list_A1748581779le_alt] :
      ( ( As != nil_Ar1741995278le_alt )
     => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,last_A1673116455le_alt(As)),set_Ar1033255471le_alt(As))) ) ).

tff(fact_573_last__in__set,axiom,
    ! [As: list_P1493174166le_alt] :
      ( ( As != nil_Pr1812858053le_alt )
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,last_P1178810988le_alt(As)),set_Pr1859340644le_alt(As))) ) ).

tff(fact_574_last__in__set,axiom,
    ! [As: list_A964264886e_indi] :
      ( ( As != nil_Ar1066084325e_indi )
     => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,last_A989769740e_indi(As)),set_Ar1464464132e_indi(As))) ) ).

tff(fact_575_last__in__set,axiom,
    ! [As: list_bool] :
      ( ( As != nil_bool )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,last_bool(As)),set_bool(As))) ) ).

tff(fact_576_last__in__set,axiom,
    ! [As: list_f1301614006t_bool] :
      ( ( As != nil_fu1362281957t_bool )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,last_f766782476t_bool(As)),set_fu1616240388t_bool(As))) ) ).

tff(fact_577_last__in__set,axiom,
    ! [As: list_f418358302t_bool] :
      ( ( As != nil_fu67358489t_bool )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,last_f1672818226t_bool(As)),set_fu945091898t_bool(As))) ) ).

tff(fact_578_last__in__set,axiom,
    ! [As: list_f767102118t_bool] :
      ( ( As != nil_fu141734613t_bool )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,last_f1815194108t_bool(As)),set_fu116139252t_bool(As))) ) ).

tff(fact_579_last__in__set,axiom,
    ! [As: list_P1216503240le_alt] :
      ( ( As != nil_Pr1200540407le_alt )
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,last_P1995563806le_alt(As)),set_Pr1864214038le_alt(As))) ) ).

tff(fact_580_dropWhile__eq__Nil__conv,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ( dropWh1772583087le_alt(Pa,Xs) = nil_Ar1741995278le_alt )
    <=> ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
         => hBOOL(hAPP_A674791462t_bool(Pa,X_2)) ) ) ).

tff(fact_581_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_A1748581779le_alt,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(butlas730749018le_alt(Xs))))
        | hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(butlas730749018le_alt(Ys_1)))) )
     => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(butlas730749018le_alt(hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1))))) ) ).

tff(fact_582_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_P1493174166le_alt,X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(butlas1911524985le_alt(Xs))))
        | hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(butlas1911524985le_alt(Ys_1)))) )
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(butlas1911524985le_alt(hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),Ys_1))))) ) ).

tff(fact_583_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_A964264886e_indi,X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(butlas92561305e_indi(Xs))))
        | hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(butlas92561305e_indi(Ys_1)))) )
     => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(butlas92561305e_indi(hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),Ys_1))))) ) ).

tff(fact_584_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_bool,X_1: bool,Xs: list_bool] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs))))
        | hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Ys_1)))) )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1))))) ) ).

tff(fact_585_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f1301614006t_bool,X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(butlas606086553t_bool(Xs))))
        | hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(butlas606086553t_bool(Ys_1)))) )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(butlas606086553t_bool(hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),Ys_1))))) ) ).

tff(fact_586_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f418358302t_bool,X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(butlas717559397t_bool(Xs))))
        | hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(butlas717559397t_bool(Ys_1)))) )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(butlas717559397t_bool(hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),Ys_1))))) ) ).

tff(fact_587_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_f767102118t_bool,X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(butlas707526281t_bool(Xs))))
        | hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(butlas707526281t_bool(Ys_1)))) )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(butlas707526281t_bool(hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),Ys_1))))) ) ).

tff(fact_588_in__set__butlast__appendI,axiom,
    ! [Ys_1: list_P1216503240le_alt,X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(butlas1000653483le_alt(Xs))))
        | hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(butlas1000653483le_alt(Ys_1)))) )
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(butlas1000653483le_alt(hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),Ys_1))))) ) ).

tff(fact_589_hd__in__set,axiom,
    ! [Xs: list_A1748581779le_alt] :
      ( ( Xs != nil_Ar1741995278le_alt )
     => hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,hd_Arr274000865le_alt(Xs)),set_Ar1033255471le_alt(Xs))) ) ).

tff(fact_590_hd__in__set,axiom,
    ! [Xs: list_P1493174166le_alt] :
      ( ( Xs != nil_Pr1812858053le_alt )
     => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hd_Pro156409650le_alt(Xs)),set_Pr1859340644le_alt(Xs))) ) ).

tff(fact_591_hd__in__set,axiom,
    ! [Xs: list_A964264886e_indi] :
      ( ( Xs != nil_Ar1066084325e_indi )
     => hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,hd_Arr1709813202e_indi(Xs)),set_Ar1464464132e_indi(Xs))) ) ).

tff(fact_592_hd__in__set,axiom,
    ! [Xs: list_bool] :
      ( ( Xs != nil_bool )
     => hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hd_bool(Xs)),set_bool(Xs))) ) ).

tff(fact_593_hd__in__set,axiom,
    ! [Xs: list_f1301614006t_bool] :
      ( ( Xs != nil_fu1362281957t_bool )
     => hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,hd_fun1472091602t_bool(Xs)),set_fu1616240388t_bool(Xs))) ) ).

tff(fact_594_hd__in__set,axiom,
    ! [Xs: list_f418358302t_bool] :
      ( ( Xs != nil_fu67358489t_bool )
     => hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,hd_fun290318572t_bool(Xs)),set_fu945091898t_bool(Xs))) ) ).

tff(fact_595_hd__in__set,axiom,
    ! [Xs: list_f767102118t_bool] :
      ( ( Xs != nil_fu141734613t_bool )
     => hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,hd_fun674840002t_bool(Xs)),set_fu116139252t_bool(Xs))) ) ).

tff(fact_596_hd__in__set,axiom,
    ! [Xs: list_P1216503240le_alt] :
      ( ( Xs != nil_Pr1200540407le_alt )
     => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hd_Pro636780772le_alt(Xs)),set_Pr1864214038le_alt(Xs))) ) ).

tff(fact_597_dropWhile__append1,axiom,
    ! [Ys_1: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
     => ( ~ hBOOL(hAPP_A674791462t_bool(Pa,X_1))
       => ( dropWh1772583087le_alt(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,dropWh1772583087le_alt(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_598_dropWhile__append1,axiom,
    ! [Ys_1: list_P1493174166le_alt,Pa: fun_Pr1013460023t_bool,X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
     => ( ~ hBOOL(hAPP_P274047445t_bool(Pa,X_1))
       => ( dropWh2059627236le_alt(Pa,hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),Ys_1)) = hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,dropWh2059627236le_alt(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_599_dropWhile__append1,axiom,
    ! [Ys_1: list_A964264886e_indi,Pa: fun_Ar552120407i_bool,X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
     => ( ~ hBOOL(hAPP_A1888055029i_bool(Pa,X_1))
       => ( dropWh1846039684e_indi(Pa,hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),Ys_1)) = hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,dropWh1846039684e_indi(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_600_dropWhile__append1,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,X_1: bool,Xs: list_bool] :
      ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
     => ( ~ hBOOL(hAPP_bool_bool(Pa,X_1))
       => ( dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,dropWhile_bool(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_601_dropWhile__append1,axiom,
    ! [Ys_1: list_f1301614006t_bool,Pa: fun_fu1138137687l_bool,X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f611501301l_bool(Pa,X_1))
       => ( dropWh1304379524t_bool(Pa,hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),Ys_1)) = hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,dropWh1304379524t_bool(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_602_dropWhile__append1,axiom,
    ! [Ys_1: list_f418358302t_bool,Pa: fun_fu1015689055l_bool,X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f429946033l_bool(Pa,X_1))
       => ( dropWh693679034t_bool(Pa,hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),Ys_1)) = hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,dropWh693679034t_bool(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_603_dropWhile__append1,axiom,
    ! [Ys_1: list_f767102118t_bool,Pa: fun_fu775006535l_bool,X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
     => ( ~ hBOOL(hAPP_f1766661605l_bool(Pa,X_1))
       => ( dropWh1950353012t_bool(Pa,hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),Ys_1)) = hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,dropWh1950353012t_bool(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_604_dropWhile__append1,axiom,
    ! [Ys_1: list_P1216503240le_alt,Pa: fun_Pr1055212137t_bool,X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
     => ( ~ hBOOL(hAPP_P166437127t_bool(Pa,X_1))
       => ( dropWh1019479958le_alt(Pa,hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),Ys_1)) = hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,dropWh1019479958le_alt(Pa,Xs)),Ys_1) ) ) ) ).

tff(fact_605_List_Oinsert__def,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
       => ( insert428884260le_alt(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
       => ( insert428884260le_alt(X_1,Xs) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) ) ) ) ).

tff(fact_606_List_Oinsert__def,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
       => ( insert633788207le_alt(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
       => ( insert633788207le_alt(X_1,Xs) = hAPP_l1876658005le_alt(hAPP_P59114565le_alt(cons_P1348035861le_alt,X_1),Xs) ) ) ) ).

tff(fact_607_List_Oinsert__def,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
       => ( insert13019471e_indi(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
       => ( insert13019471e_indi(X_1,Xs) = hAPP_l221792213e_indi(hAPP_A1717387813e_indi(cons_A1348960309e_indi,X_1),Xs) ) ) ) ).

tff(fact_608_List_Oinsert__def,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
       => ( insert_bool(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
       => ( insert_bool(X_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) ) ) ) ).

tff(fact_609_List_Oinsert__def,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
       => ( insert1079671631t_bool(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
       => ( insert1079671631t_bool(X_1,Xs) = hAPP_l137391573t_bool(hAPP_f812806181t_bool(cons_f1295695413t_bool,X_1),Xs) ) ) ) ).

tff(fact_610_List_Oinsert__def,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
       => ( insert1909791023t_bool(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
       => ( insert1909791023t_bool(X_1,Xs) = hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),Xs) ) ) ) ).

tff(fact_611_List_Oinsert__def,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
       => ( insert2063552063t_bool(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
       => ( insert2063552063t_bool(X_1,Xs) = hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),Xs) ) ) ) ).

tff(fact_612_List_Oinsert__def,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
       => ( insert1516219489le_alt(X_1,Xs) = Xs ) )
      & ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
       => ( insert1516219489le_alt(X_1,Xs) = hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),Xs) ) ) ) ).

tff(fact_613_not__in__set__insert,axiom,
    ! [X_1: arrow_931160158le_alt,Xs: list_A1748581779le_alt] :
      ( ~ hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_1),set_Ar1033255471le_alt(Xs)))
     => ( insert428884260le_alt(X_1,Xs) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_1),Xs) ) ) ).

tff(fact_614_not__in__set__insert,axiom,
    ! [X_1: produc662089077le_alt,Xs: list_P1493174166le_alt] :
      ( ~ hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_1),set_Pr1859340644le_alt(Xs)))
     => ( insert633788207le_alt(X_1,Xs) = hAPP_l1876658005le_alt(hAPP_P59114565le_alt(cons_P1348035861le_alt,X_1),Xs) ) ) ).

tff(fact_615_not__in__set__insert,axiom,
    ! [X_1: arrow_2115524757e_indi,Xs: list_A964264886e_indi] :
      ( ~ hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_1),set_Ar1464464132e_indi(Xs)))
     => ( insert13019471e_indi(X_1,Xs) = hAPP_l221792213e_indi(hAPP_A1717387813e_indi(cons_A1348960309e_indi,X_1),Xs) ) ) ).

tff(fact_616_not__in__set__insert,axiom,
    ! [X_1: bool,Xs: list_bool] :
      ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
     => ( insert_bool(X_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) ) ) ).

tff(fact_617_not__in__set__insert,axiom,
    ! [X_1: fun_fu1595299477t_bool,Xs: list_f1301614006t_bool] :
      ( ~ hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_1),set_fu1616240388t_bool(Xs)))
     => ( insert1079671631t_bool(X_1,Xs) = hAPP_l137391573t_bool(hAPP_f812806181t_bool(cons_f1295695413t_bool,X_1),Xs) ) ) ).

tff(fact_618_not__in__set__insert,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( ~ hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
     => ( insert1909791023t_bool(X_1,Xs) = hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),Xs) ) ) ).

tff(fact_619_not__in__set__insert,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( ~ hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
     => ( insert2063552063t_bool(X_1,Xs) = hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),Xs) ) ) ).

tff(fact_620_not__in__set__insert,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
     => ( insert1516219489le_alt(X_1,Xs) = hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),Xs) ) ) ).

tff(fact_621_partition__P,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt,Yes: list_A1748581779le_alt,No: list_A1748581779le_alt] :
      ( ( partit1943378951le_alt(Pa,Xs) = hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Yes),No) )
     => ( ! [X_2: arrow_931160158le_alt] :
            ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Yes)))
           => hBOOL(hAPP_A674791462t_bool(Pa,X_2)) )
        & ! [X_2: arrow_931160158le_alt] :
            ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(No)))
           => ~ hBOOL(hAPP_A674791462t_bool(Pa,X_2)) ) ) ) ).

tff(fact_622_lexord__partial__trans,axiom,
    ! [Zs_1: list_A1748581779le_alt,Ys_1: list_A1748581779le_alt,R_1: fun_Pr1055212137t_bool,Xs: list_A1748581779le_alt] :
      ( ! [X_2: arrow_931160158le_alt,Y_1: arrow_931160158le_alt,Z: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
         => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,Y_1),Z)),R_1))
             => hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Ys_1)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
       => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Ys_1),Zs_1)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1)))
         => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Xs),Zs_1)),hAPP_f557837283t_bool(lexord1413896571le_alt,R_1))) ) ) ) ).

tff(fact_623_lexord__partial__trans,axiom,
    ! [Zs_1: list_l1735481012le_alt,Ys_1: list_l1735481012le_alt,R_1: fun_Pr1013460023t_bool,Xs: list_l1735481012le_alt] :
      ( ! [X_2: list_A1748581779le_alt,Y_1: list_A1748581779le_alt,Z: list_A1748581779le_alt] :
          ( hBOOL(hAPP_f902378909l_bool(hAPP_l462777825l_bool(member631477888le_alt,X_2),set_li1265325186le_alt(Xs)))
         => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,Y_1),Z)),R_1))
             => hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,hAPP_l1128853771le_alt(hAPP_l1949544791le_alt(produc1596656747le_alt,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Ys_1)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1)))
       => ( hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Ys_1),Zs_1)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1)))
         => hBOOL(hAPP_f1655666225l_bool(hAPP_P456721929l_bool(member302274452le_alt,hAPP_l2013461446le_alt(hAPP_l601007891le_alt(produc1935847959le_alt,Xs),Zs_1)),hAPP_f1428266567t_bool(lexord103259702le_alt,R_1))) ) ) ) ).

tff(fact_624_lexord__partial__trans,axiom,
    ! [Zs_1: list_P1493174166le_alt,Ys_1: list_P1493174166le_alt,R_1: fun_Pr2049153787t_bool,Xs: list_P1493174166le_alt] :
      ( ! [X_2: produc662089077le_alt,Y_1: produc662089077le_alt,Z: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),set_Pr1859340644le_alt(Xs)))
         => ( hBOOL(hAPP_f1791116867l_bool(hAPP_P467663149l_bool(member1834889254le_alt,hAPP_P1169232561le_alt(hAPP_P850038171le_alt(produc1477938991le_alt,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f1791116867l_bool(hAPP_P467663149l_bool(member1834889254le_alt,hAPP_P1169232561le_alt(hAPP_P850038171le_alt(produc1477938991le_alt,Y_1),Z)),R_1))
             => hBOOL(hAPP_f1791116867l_bool(hAPP_P467663149l_bool(member1834889254le_alt,hAPP_P1169232561le_alt(hAPP_P850038171le_alt(produc1477938991le_alt,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f293321137l_bool(hAPP_P2065070345l_bool(member1590082836le_alt,hAPP_l1906066472le_alt(hAPP_l1522056279le_alt(produc45587863le_alt,Xs),Ys_1)),hAPP_f1090350595t_bool(lexord272977688le_alt,R_1)))
       => ( hBOOL(hAPP_f293321137l_bool(hAPP_P2065070345l_bool(member1590082836le_alt,hAPP_l1906066472le_alt(hAPP_l1522056279le_alt(produc45587863le_alt,Ys_1),Zs_1)),hAPP_f1090350595t_bool(lexord272977688le_alt,R_1)))
         => hBOOL(hAPP_f293321137l_bool(hAPP_P2065070345l_bool(member1590082836le_alt,hAPP_l1906066472le_alt(hAPP_l1522056279le_alt(produc45587863le_alt,Xs),Zs_1)),hAPP_f1090350595t_bool(lexord272977688le_alt,R_1))) ) ) ) ).

tff(fact_625_lexord__partial__trans,axiom,
    ! [Zs_1: list_A964264886e_indi,Ys_1: list_A964264886e_indi,R_1: fun_Pr811923643i_bool,Xs: list_A964264886e_indi] :
      ( ! [X_2: arrow_2115524757e_indi,Y_1: arrow_2115524757e_indi,Z: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),set_Ar1464464132e_indi(Xs)))
         => ( hBOOL(hAPP_f568680451l_bool(hAPP_P1644193965l_bool(member938783462e_indi,hAPP_A957051793e_indi(hAPP_A1993750875e_indi(produc609333615e_indi,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f568680451l_bool(hAPP_P1644193965l_bool(member938783462e_indi,hAPP_A957051793e_indi(hAPP_A1993750875e_indi(produc609333615e_indi,Y_1),Z)),R_1))
             => hBOOL(hAPP_f568680451l_bool(hAPP_P1644193965l_bool(member938783462e_indi,hAPP_A957051793e_indi(hAPP_A1993750875e_indi(produc609333615e_indi,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f103239857l_bool(hAPP_P93441289l_bool(member1920957716e_indi,hAPP_l1124485704e_indi(hAPP_l915221271e_indi(produc514409495e_indi,Xs),Ys_1)),hAPP_f550841667i_bool(lexord200124088e_indi,R_1)))
       => ( hBOOL(hAPP_f103239857l_bool(hAPP_P93441289l_bool(member1920957716e_indi,hAPP_l1124485704e_indi(hAPP_l915221271e_indi(produc514409495e_indi,Ys_1),Zs_1)),hAPP_f550841667i_bool(lexord200124088e_indi,R_1)))
         => hBOOL(hAPP_f103239857l_bool(hAPP_P93441289l_bool(member1920957716e_indi,hAPP_l1124485704e_indi(hAPP_l915221271e_indi(produc514409495e_indi,Xs),Zs_1)),hAPP_f550841667i_bool(lexord200124088e_indi,R_1))) ) ) ) ).

tff(fact_626_lexord__partial__trans,axiom,
    ! [Zs_1: list_bool,Ys_1: list_bool,R_1: fun_Pr754217419l_bool,Xs: list_bool] :
      ( ! [X_2: bool,Y_1: bool,Z: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
         => ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,Y_1),Z)),R_1))
             => hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Ys_1)),hAPP_f1114274611l_bool(lexord_bool,R_1)))
       => ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Ys_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_1)))
         => hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_1))) ) ) ) ).

tff(fact_627_lexord__partial__trans,axiom,
    ! [Zs_1: list_f1301614006t_bool,Ys_1: list_f1301614006t_bool,R_1: fun_Pr119656123l_bool,Xs: list_f1301614006t_bool] :
      ( ! [X_2: fun_fu1595299477t_bool,Y_1: fun_fu1595299477t_bool,Z: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),set_fu1616240388t_bool(Xs)))
         => ( hBOOL(hAPP_f1862698499l_bool(hAPP_P671450285l_bool(member710460646t_bool,hAPP_f1250830225t_bool(hAPP_f1703384923t_bool(produc1397390703t_bool,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f1862698499l_bool(hAPP_P671450285l_bool(member710460646t_bool,hAPP_f1250830225t_bool(hAPP_f1703384923t_bool(produc1397390703t_bool,Y_1),Z)),R_1))
             => hBOOL(hAPP_f1862698499l_bool(hAPP_P671450285l_bool(member710460646t_bool,hAPP_f1250830225t_bool(hAPP_f1703384923t_bool(produc1397390703t_bool,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f414270641l_bool(hAPP_P1176599817l_bool(member2127060244t_bool,hAPP_l1628744776t_bool(hAPP_l1627811095t_bool(produc1183986199t_bool,Xs),Ys_1)),hAPP_f1726370627l_bool(lexord1327872696t_bool,R_1)))
       => ( hBOOL(hAPP_f414270641l_bool(hAPP_P1176599817l_bool(member2127060244t_bool,hAPP_l1628744776t_bool(hAPP_l1627811095t_bool(produc1183986199t_bool,Ys_1),Zs_1)),hAPP_f1726370627l_bool(lexord1327872696t_bool,R_1)))
         => hBOOL(hAPP_f414270641l_bool(hAPP_P1176599817l_bool(member2127060244t_bool,hAPP_l1628744776t_bool(hAPP_l1627811095t_bool(produc1183986199t_bool,Xs),Zs_1)),hAPP_f1726370627l_bool(lexord1327872696t_bool,R_1))) ) ) ) ).

tff(fact_628_lexord__partial__trans,axiom,
    ! [Zs_1: list_f418358302t_bool,Ys_1: list_f418358302t_bool,R_1: fun_Pr811948841l_bool,Xs: list_f418358302t_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool,Y_1: fun_Pr1055212137t_bool,Z: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),set_fu945091898t_bool(Xs)))
         => ( hBOOL(hAPP_f820729201l_bool(hAPP_P463482505l_bool(member1092949460t_bool,hAPP_f1050248635t_bool(hAPP_f243222077t_bool(produc1735284823t_bool,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f820729201l_bool(hAPP_P463482505l_bool(member1092949460t_bool,hAPP_f1050248635t_bool(hAPP_f243222077t_bool(produc1735284823t_bool,Y_1),Z)),R_1))
             => hBOOL(hAPP_f820729201l_bool(hAPP_P463482505l_bool(member1092949460t_bool,hAPP_f1050248635t_bool(hAPP_f243222077t_bool(produc1735284823t_bool,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f1843355029l_bool(hAPP_P269910993l_bool(member294755704t_bool,hAPP_l213528876t_bool(hAPP_l1306343341t_bool(produc1735751425t_bool,Xs),Ys_1)),hAPP_f976656953l_bool(lexord45138054t_bool,R_1)))
       => ( hBOOL(hAPP_f1843355029l_bool(hAPP_P269910993l_bool(member294755704t_bool,hAPP_l213528876t_bool(hAPP_l1306343341t_bool(produc1735751425t_bool,Ys_1),Zs_1)),hAPP_f976656953l_bool(lexord45138054t_bool,R_1)))
         => hBOOL(hAPP_f1843355029l_bool(hAPP_P269910993l_bool(member294755704t_bool,hAPP_l213528876t_bool(hAPP_l1306343341t_bool(produc1735751425t_bool,Xs),Zs_1)),hAPP_f976656953l_bool(lexord45138054t_bool,R_1))) ) ) ) ).

tff(fact_629_lexord__partial__trans,axiom,
    ! [Zs_1: list_f767102118t_bool,Ys_1: list_f767102118t_bool,R_1: fun_Pr1660699547l_bool,Xs: list_f767102118t_bool] :
      ( ! [X_2: fun_Ar500372357t_bool,Y_1: fun_Ar500372357t_bool,Z: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),set_fu116139252t_bool(Xs)))
         => ( hBOOL(hAPP_f409297635l_bool(hAPP_P72218221l_bool(member1904937926t_bool,hAPP_f605725025t_bool(hAPP_f1863504955t_bool(produc775282511t_bool,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f409297635l_bool(hAPP_P72218221l_bool(member1904937926t_bool,hAPP_f605725025t_bool(hAPP_f1863504955t_bool(produc775282511t_bool,Y_1),Z)),R_1))
             => hBOOL(hAPP_f409297635l_bool(hAPP_P72218221l_bool(member1904937926t_bool,hAPP_f605725025t_bool(hAPP_f1863504955t_bool(produc775282511t_bool,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f2109978289l_bool(hAPP_P767196425l_bool(member1166104852t_bool,hAPP_l1542720312t_bool(hAPP_l197443575t_bool(produc1138073367t_bool,Xs),Ys_1)),hAPP_f560116835l_bool(lexord267119784t_bool,R_1)))
       => ( hBOOL(hAPP_f2109978289l_bool(hAPP_P767196425l_bool(member1166104852t_bool,hAPP_l1542720312t_bool(hAPP_l197443575t_bool(produc1138073367t_bool,Ys_1),Zs_1)),hAPP_f560116835l_bool(lexord267119784t_bool,R_1)))
         => hBOOL(hAPP_f2109978289l_bool(hAPP_P767196425l_bool(member1166104852t_bool,hAPP_l1542720312t_bool(hAPP_l197443575t_bool(produc1138073367t_bool,Xs),Zs_1)),hAPP_f560116835l_bool(lexord267119784t_bool,R_1))) ) ) ) ).

tff(fact_630_lexord__partial__trans,axiom,
    ! [Zs_1: list_P1216503240le_alt,Ys_1: list_P1216503240le_alt,R_1: fun_Pr666765279t_bool,Xs: list_P1216503240le_alt] :
      ( ! [X_2: produc1840315303le_alt,Y_1: produc1840315303le_alt,Z: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),set_Pr1864214038le_alt(Xs)))
         => ( hBOOL(hAPP_f1052511527l_bool(hAPP_P142038773l_bool(member92652554le_alt,hAPP_P1318503111le_alt(hAPP_P1832869119le_alt(produc1783421843le_alt,X_2),Y_1)),R_1))
           => ( hBOOL(hAPP_f1052511527l_bool(hAPP_P142038773l_bool(member92652554le_alt,hAPP_P1318503111le_alt(hAPP_P1832869119le_alt(produc1783421843le_alt,Y_1),Z)),R_1))
             => hBOOL(hAPP_f1052511527l_bool(hAPP_P142038773l_bool(member92652554le_alt,hAPP_P1318503111le_alt(hAPP_P1832869119le_alt(produc1783421843le_alt,X_2),Z)),R_1)) ) ) )
     => ( hBOOL(hAPP_f220748081l_bool(hAPP_P1381588489l_bool(member1552328084le_alt,hAPP_l191462618le_alt(hAPP_l196402619le_alt(produc2078958999le_alt,Xs),Ys_1)),hAPP_f1826601375t_bool(lexord840833482le_alt,R_1)))
       => ( hBOOL(hAPP_f220748081l_bool(hAPP_P1381588489l_bool(member1552328084le_alt,hAPP_l191462618le_alt(hAPP_l196402619le_alt(produc2078958999le_alt,Ys_1),Zs_1)),hAPP_f1826601375t_bool(lexord840833482le_alt,R_1)))
         => hBOOL(hAPP_f220748081l_bool(hAPP_P1381588489l_bool(member1552328084le_alt,hAPP_l191462618le_alt(hAPP_l196402619le_alt(produc2078958999le_alt,Xs),Zs_1)),hAPP_f1826601375t_bool(lexord840833482le_alt,R_1))) ) ) ) ).

tff(fact_631_dropWhile__append2,axiom,
    ! [Ys_1: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
         => hBOOL(hAPP_A674791462t_bool(Pa,X_2)) )
     => ( dropWh1772583087le_alt(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1)) = dropWh1772583087le_alt(Pa,Ys_1) ) ) ).

tff(fact_632_dropWhile__append2,axiom,
    ! [Ys_1: list_P1493174166le_alt,Pa: fun_Pr1013460023t_bool,Xs: list_P1493174166le_alt] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),set_Pr1859340644le_alt(Xs)))
         => hBOOL(hAPP_P274047445t_bool(Pa,X_2)) )
     => ( dropWh2059627236le_alt(Pa,hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),Ys_1)) = dropWh2059627236le_alt(Pa,Ys_1) ) ) ).

tff(fact_633_dropWhile__append2,axiom,
    ! [Ys_1: list_A964264886e_indi,Pa: fun_Ar552120407i_bool,Xs: list_A964264886e_indi] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),set_Ar1464464132e_indi(Xs)))
         => hBOOL(hAPP_A1888055029i_bool(Pa,X_2)) )
     => ( dropWh1846039684e_indi(Pa,hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),Ys_1)) = dropWh1846039684e_indi(Pa,Ys_1) ) ) ).

tff(fact_634_dropWhile__append2,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,Xs: list_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
         => hBOOL(hAPP_bool_bool(Pa,X_2)) )
     => ( dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = dropWhile_bool(Pa,Ys_1) ) ) ).

tff(fact_635_dropWhile__append2,axiom,
    ! [Ys_1: list_f1301614006t_bool,Pa: fun_fu1138137687l_bool,Xs: list_f1301614006t_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),set_fu1616240388t_bool(Xs)))
         => hBOOL(hAPP_f611501301l_bool(Pa,X_2)) )
     => ( dropWh1304379524t_bool(Pa,hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),Ys_1)) = dropWh1304379524t_bool(Pa,Ys_1) ) ) ).

tff(fact_636_dropWhile__append2,axiom,
    ! [Ys_1: list_f418358302t_bool,Pa: fun_fu1015689055l_bool,Xs: list_f418358302t_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),set_fu945091898t_bool(Xs)))
         => hBOOL(hAPP_f429946033l_bool(Pa,X_2)) )
     => ( dropWh693679034t_bool(Pa,hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),Ys_1)) = dropWh693679034t_bool(Pa,Ys_1) ) ) ).

tff(fact_637_dropWhile__append2,axiom,
    ! [Ys_1: list_f767102118t_bool,Pa: fun_fu775006535l_bool,Xs: list_f767102118t_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),set_fu116139252t_bool(Xs)))
         => hBOOL(hAPP_f1766661605l_bool(Pa,X_2)) )
     => ( dropWh1950353012t_bool(Pa,hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),Ys_1)) = dropWh1950353012t_bool(Pa,Ys_1) ) ) ).

tff(fact_638_dropWhile__append2,axiom,
    ! [Ys_1: list_P1216503240le_alt,Pa: fun_Pr1055212137t_bool,Xs: list_P1216503240le_alt] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),set_Pr1864214038le_alt(Xs)))
         => hBOOL(hAPP_P166437127t_bool(Pa,X_2)) )
     => ( dropWh1019479958le_alt(Pa,hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),Ys_1)) = dropWh1019479958le_alt(Pa,Ys_1) ) ) ).

tff(fact_639_takeWhile__append2,axiom,
    ! [Ys_1: list_A1748581779le_alt,Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ! [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
         => hBOOL(hAPP_A674791462t_bool(Pa,X_2)) )
     => ( takeWh4609031le_alt(Pa,hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),Ys_1)) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Xs),takeWh4609031le_alt(Pa,Ys_1)) ) ) ).

tff(fact_640_takeWhile__append2,axiom,
    ! [Ys_1: list_P1493174166le_alt,Pa: fun_Pr1013460023t_bool,Xs: list_P1493174166le_alt] :
      ( ! [X_2: produc662089077le_alt] :
          ( hBOOL(hAPP_f686625151l_bool(hAPP_P518621093l_bool(member1475736930le_alt,X_2),set_Pr1859340644le_alt(Xs)))
         => hBOOL(hAPP_P274047445t_bool(Pa,X_2)) )
     => ( takeWh871442828le_alt(Pa,hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),Ys_1)) = hAPP_l1876658005le_alt(hAPP_l627553532le_alt(append1870889072le_alt,Xs),takeWh871442828le_alt(Pa,Ys_1)) ) ) ).

tff(fact_641_takeWhile__append2,axiom,
    ! [Ys_1: list_A964264886e_indi,Pa: fun_Ar552120407i_bool,Xs: list_A964264886e_indi] :
      ( ! [X_2: arrow_2115524757e_indi] :
          ( hBOOL(hAPP_f1397511071l_bool(hAPP_A605074405l_bool(member590466050e_indi,X_2),set_Ar1464464132e_indi(Xs)))
         => hBOOL(hAPP_A1888055029i_bool(Pa,X_2)) )
     => ( takeWh1517834028e_indi(Pa,hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),Ys_1)) = hAPP_l221792213e_indi(hAPP_l378231516e_indi(append1397857296e_indi,Xs),takeWh1517834028e_indi(Pa,Ys_1)) ) ) ).

tff(fact_642_takeWhile__append2,axiom,
    ! [Ys_1: list_bool,Pa: fun_bool_bool,Xs: list_bool] :
      ( ! [X_2: bool] :
          ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
         => hBOOL(hAPP_bool_bool(Pa,X_2)) )
     => ( takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),takeWhile_bool(Pa,Ys_1)) ) ) ).

tff(fact_643_takeWhile__append2,axiom,
    ! [Ys_1: list_f1301614006t_bool,Pa: fun_fu1138137687l_bool,Xs: list_f1301614006t_bool] :
      ( ! [X_2: fun_fu1595299477t_bool] :
          ( hBOOL(hAPP_f361555359l_bool(hAPP_f1709225957l_bool(member1801442306t_bool,X_2),set_fu1616240388t_bool(Xs)))
         => hBOOL(hAPP_f611501301l_bool(Pa,X_2)) )
     => ( takeWh1450838828t_bool(Pa,hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),Ys_1)) = hAPP_l137391573t_bool(hAPP_l475965660t_bool(append1662967824t_bool,Xs),takeWh1450838828t_bool(Pa,Ys_1)) ) ) ).

tff(fact_644_takeWhile__append2,axiom,
    ! [Ys_1: list_f418358302t_bool,Pa: fun_fu1015689055l_bool,Xs: list_f418358302t_bool] :
      ( ! [X_2: fun_Pr1055212137t_bool] :
          ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_2),set_fu945091898t_bool(Xs)))
         => hBOOL(hAPP_f429946033l_bool(Pa,X_2)) )
     => ( takeWh1072801554t_bool(Pa,hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),Ys_1)) = hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Xs),takeWh1072801554t_bool(Pa,Ys_1)) ) ) ).

tff(fact_645_takeWhile__append2,axiom,
    ! [Ys_1: list_f767102118t_bool,Pa: fun_fu775006535l_bool,Xs: list_f767102118t_bool] :
      ( ! [X_2: fun_Ar500372357t_bool] :
          ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_2),set_fu116139252t_bool(Xs)))
         => hBOOL(hAPP_f1766661605l_bool(Pa,X_2)) )
     => ( takeWh1707174172t_bool(Pa,hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),Ys_1)) = hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Xs),takeWh1707174172t_bool(Pa,Ys_1)) ) ) ).

tff(fact_646_takeWhile__append2,axiom,
    ! [Ys_1: list_P1216503240le_alt,Pa: fun_Pr1055212137t_bool,Xs: list_P1216503240le_alt] :
      ( ! [X_2: produc1840315303le_alt] :
          ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_2),set_Pr1864214038le_alt(Xs)))
         => hBOOL(hAPP_P166437127t_bool(Pa,X_2)) )
     => ( takeWh641303102le_alt(Pa,hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),Ys_1)) = hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Xs),takeWh641303102le_alt(Pa,Ys_1)) ) ) ).

tff(fact_647_split__list__propE,axiom,
    ! [Pa: fun_Ar1091019988t_bool,Xs: list_A1748581779le_alt] :
      ( ? [X_2: arrow_931160158le_alt] :
          ( hBOOL(hAPP_f939114932l_bool(hAPP_A449046541l_bool(member540164529le_alt,X_2),set_Ar1033255471le_alt(Xs)))
          & hBOOL(hAPP_A674791462t_bool(Pa,X_2)) )
     => ~ ! [Ys: list_A1748581779le_alt,X_2: arrow_931160158le_alt] :
            ( ? [Zs: list_A1748581779le_alt] : ( Xs = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(append634883619le_alt,Ys),hAPP_l2085326633le_alt(hAPP_A662984834le_alt(cons_A684544190le_alt,X_2),Zs)) )
           => ~ hBOOL(hAPP_A674791462t_bool(Pa,X_2)) ) ) ).

tff(fact_648_in__set__conv__decomp,axiom,
    ! [X_1: fun_Pr1055212137t_bool,Xs: list_f418358302t_bool] :
      ( hBOOL(hAPP_f1021703871l_bool(hAPP_f1370368205l_bool(member57118396t_bool,X_1),set_fu945091898t_bool(Xs)))
    <=> ? [Ys: list_f418358302t_bool,Zs: list_f418358302t_bool] : ( Xs = hAPP_l943674815t_bool(hAPP_l598805184t_bool(append483908910t_bool,Ys),hAPP_l943674815t_bool(hAPP_f1402999885t_bool(cons_f976589513t_bool,X_1),Zs)) ) ) ).

tff(fact_649_in__set__conv__decomp,axiom,
    ! [X_1: fun_Ar500372357t_bool,Xs: list_f767102118t_bool] :
      ( hBOOL(hAPP_f1465510031l_bool(hAPP_f2029708741l_bool(member1159072754t_bool,X_1),set_fu116139252t_bool(Xs)))
    <=> ? [Ys: list_f767102118t_bool,Zs: list_f767102118t_bool] : ( Xs = hAPP_l1831878357t_bool(hAPP_l1251560940t_bool(append246315520t_bool,Ys),hAPP_l1831878357t_bool(hAPP_f523382069t_bool(cons_f54319909t_bool,X_1),Zs)) ) ) ).

tff(fact_650_in__set__conv__decomp,axiom,
    ! [X_1: produc1840315303le_alt,Xs: list_P1216503240le_alt] :
      ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,X_1),set_Pr1864214038le_alt(Xs)))
    <=> ? [Ys: list_P1216503240le_alt,Zs: list_P1216503240le_alt] : ( Xs = hAPP_l1141483861le_alt(hAPP_l1749636298le_alt(append1568444194le_alt,Ys),hAPP_l1141483861le_alt(hAPP_P74814227le_alt(cons_P105259847le_alt,X_1),Zs)) ) ) ).

tff(fact_651_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_652_lessI,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(N_1))) ).

tff(fact_653_Suc__mono,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),suc(N_1))) ) ).

tff(fact_654_n__not__Suc__n,axiom,
    ! [N_1: nat] : ( N_1 != suc(N_1) ) ).

tff(fact_655_Suc__n__not__n,axiom,
    ! [N_1: nat] : ( suc(N_1) != N_1 ) ).

tff(fact_656_nat_Oinject,axiom,
    ! [Nat_1: nat,Nat: nat] :
      ( ( suc(Nat_1) = suc(Nat) )
    <=> ( Nat_1 = Nat ) ) ).

tff(fact_657_Suc__inject,axiom,
    ! [X: nat,Y: nat] :
      ( ( suc(X) = suc(Y) )
     => ( X = Y ) ) ).

tff(fact_658_less__not__refl,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).

tff(fact_659_nat__neq__iff,axiom,
    ! [M: nat,N: nat] :
      ( ( M != N )
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ) ) ).

tff(fact_660_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_661_less__irrefl__nat,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).

tff(fact_662_less__not__refl2,axiom,
    ! [N_1: nat,M_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
     => ( M_1 != N_1 ) ) ).

tff(fact_663_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => ( S != T ) ) ).

tff(fact_664_nat__less__cases,axiom,
    ! [Pa: fun_nat_fun_nat_bool,M: nat,N: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
     => ( ( ( M = N )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) ) ) ) ).

tff(fact_665_le__refl,axiom,
    ! [N_1: nat] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).

tff(fact_666_nat__le__linear,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) ) ).

tff(fact_667_eq__imp__le,axiom,
    ! [M_1: nat,N_1: nat] :
      ( ( M_1 = N_1 )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).

tff(fact_668_le__trans,axiom,
    ! [K: nat,I_1: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K)) ) ) ).

tff(fact_669_le__antisym,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
       => ( M_1 = N_1 ) ) ) ).

tff(fact_670_Suc__less__SucD,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),suc(N_1)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).

tff(fact_671_Suc__lessD,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).

tff(fact_672_less__SucE,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
       => ( M_1 = N_1 ) ) ) ).

tff(fact_673_less__trans__Suc,axiom,
    ! [K: nat,I_1: nat,J: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(I_1)),K)) ) ) ).

tff(fact_674_Suc__lessI,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
     => ( ( suc(M_1) != N_1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1)) ) ) ).

tff(fact_675_less__SucI,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))) ) ).

tff(fact_676_less__antisym,axiom,
    ! [N_1: nat,M_1: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(M_1)))
       => ( M_1 = N_1 ) ) ) ).

tff(fact_677_not__less__less__Suc__eq,axiom,
    ! [N: nat,M: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M)))
      <=> ( N = M ) ) ) ).

tff(fact_678_Suc__less__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M)),suc(N)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).

tff(fact_679_less__Suc__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),suc(N)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
        | ( M = N ) ) ) ).

tff(fact_680_not__less__eq,axiom,
    ! [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,N),suc(M))) ) ).

tff(fact_681_Suc__n__not__le__n,axiom,
    ! [N_1: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N_1)),N_1)) ).

tff(fact_682_not__less__eq__eq,axiom,
    ! [M: nat,N: nat] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),M)) ) ).

tff(fact_683_le__Suc__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),suc(N)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
        | ( M = suc(N) ) ) ) ).

tff(fact_684_Suc__le__mono,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),suc(M)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ).

tff(fact_685_le__SucI,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1))) ) ).

tff(fact_686_le__SucE,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
       => ( M_1 = suc(N_1) ) ) ) ).

tff(fact_687_Suc__leD,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).

tff(fact_688_less__or__eq__imp__le,axiom,
    ! [M_1: nat,N_1: nat] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
        | ( M_1 = N_1 ) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).

tff(fact_689_le__neq__implies__less,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
     => ( ( M_1 != N_1 )
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ) ).

tff(fact_690_less__imp__le__nat,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).

tff(fact_691_le__eq__less__or__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
        | ( M = N ) ) ) ).

tff(fact_692_nat__less__le,axiom,
    ! [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_eq_nat,M),N))
        & ( M != N ) ) ) ).

tff(fact_693_Suc__le__lessD,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).

tff(fact_694_le__less__Suc__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M)))
      <=> ( N = M ) ) ) ).

tff(fact_695_Suc__leI,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1)) ) ).

tff(fact_696_le__imp__less__Suc,axiom,
    ! [M_1: nat,N_1: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))) ) ).

tff(fact_697_Suc__le__eq,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M)),N))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).

tff(fact_698_less__Suc__eq__le,axiom,
    ! [M: nat,N: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),suc(N)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).

tff(fact_699_less__eq__Suc__le,axiom,
    ! [N: nat,M: nat] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),M)) ) ).

%----Helper facts (107)
tff(help_fNot_1_1_U,axiom,
    ! [P: bool] :
      ( ~ hBOOL(hAPP_bool_bool(fNot,P))
      | ~ hBOOL(P) ) ).

tff(help_fNot_2_1_U,axiom,
    ! [P: bool] :
      ( hBOOL(P)
      | hBOOL(hAPP_bool_bool(fNot,P)) ) ).

tff(help_fTrue_1_1_U,axiom,
    hBOOL(fTrue) ).

tff(help_fTrue_1_1_T,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_fequal_1_1_fequal_000tc__HOL__Obool_T,axiom,
    ! [X: bool,Y: bool] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__HOL__Obool_T,axiom,
    ! [X: bool,Y: bool] :
      ( ( X != Y )
      | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_bool_bool,Q: fun_bool_bool,R: bool] : ( hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_bool_bool(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P: fun_bo1549164019l_bool,Q: bool,R: bool] : ( hAPP_bool_bool(hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_T,axiom,
    ! [X: arrow_931160158le_alt,Y: arrow_931160158le_alt] :
      ( ~ hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(fequal628352221le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_T,axiom,
    ! [X: arrow_931160158le_alt,Y: arrow_931160158le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_A674791462t_bool(hAPP_A1858212765t_bool(fequal628352221le_alt,X),Y)) ) ).

tff(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_T,axiom,
    ! [X: arrow_2115524757e_indi,Y: arrow_2115524757e_indi] :
      ( ~ hBOOL(hAPP_A1888055029i_bool(hAPP_A643541183i_bool(fequal293925846e_indi,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_T,axiom,
    ! [X: arrow_2115524757e_indi,Y: arrow_2115524757e_indi] :
      ( ( X != Y )
      | hBOOL(hAPP_A1888055029i_bool(hAPP_A643541183i_bool(fequal293925846e_indi,X),Y)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctu,axiom,
    ! [P: bool,Q: arrow_931160158le_alt] : ( hAPP_A674791462t_bool(hAPP_b1990207796t_bool(cOMBK_1114709381le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____ctu_724,axiom,
    ! [P: bool,Q: arrow_2115524757e_indi] : ( hAPP_A1888055029i_bool(hAPP_b1439777783i_bool(cOMBK_1820189998e_indi,P),Q) = P ) ).

tff(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [X: list_A1748581779le_alt,Y: list_A1748581779le_alt] :
      ( ~ hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(fequal414630996le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [X: list_A1748581779le_alt,Y: list_A1748581779le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_l713721587t_bool(hAPP_l1173894719t_bool(fequal414630996le_alt,X),Y)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar1091019988t_bool,R: arrow_931160158le_alt] : ( hAPP_A674791462t_bool(hAPP_f1892578603t_bool(hAPP_f1567951747t_bool(cOMBB_1573225850le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_A674791462t_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order___725,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar552120407i_bool,R: arrow_2115524757e_indi] : ( hAPP_A1888055029i_bool(hAPP_f1282576021i_bool(hAPP_f694179955i_bool(cOMBB_238582393e_indi,P),Q),R) = hAPP_bool_bool(P,hAPP_A1888055029i_bool(Q,R)) ) ).

tff(help_fequal_1_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,axiom,
    ! [X: produc1840315303le_alt,Y: produc1840315303le_alt] :
      ( ~ hBOOL(hAPP_P166437127t_bool(hAPP_P339234111t_bool(fequal1713866472le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqn,axiom,
    ! [X: produc1840315303le_alt,Y: produc1840315303le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_P166437127t_bool(hAPP_P339234111t_bool(fequal1713866472le_alt,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t,axiom,
    ! [P: fun_Ar1414184139t_bool,Q: arrow_931160158le_alt,R: arrow_931160158le_alt] : ( hAPP_A674791462t_bool(hAPP_A1858212765t_bool(hAPP_f117812633t_bool(cOMBC_1674187866t_bool,P),Q),R) = hAPP_A674791462t_bool(hAPP_A1858212765t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000,axiom,
    ! [P: fun_Ar1906539123i_bool,Q: arrow_2115524757e_indi,R: arrow_2115524757e_indi] : ( hAPP_A1888055029i_bool(hAPP_A643541183i_bool(hAPP_f470111209i_bool(cOMBC_112876850i_bool,P),Q),R) = hAPP_A1888055029i_bool(hAPP_A643541183i_bool(P,R),Q) ) ).

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_fequal_1_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: fun_Pr1055212137t_bool,Y: fun_Pr1055212137t_bool] :
      ( ~ hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(fequal818396648t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: fun_Pr1055212137t_bool,Y: fun_Pr1055212137t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f429946033l_bool(hAPP_f314169011l_bool(fequal818396648t_bool,X),Y)) ) ).

tff(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: produc662089077le_alt,Y: produc662089077le_alt] : ( hAPP_P1208706541le_alt(hAPP_P443881687le_alt(if_Pro1761812485le_alt(fTrue),X),Y) = X ) ).

tff(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [X: produc662089077le_alt,Y: produc662089077le_alt] : ( hAPP_P1208706541le_alt(hAPP_P443881687le_alt(if_Pro1761812485le_alt(fFalse),X),Y) = Y ) ).

tff(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
    ! [P: bool] :
      ( ( P = fTrue )
      | ( P = fFalse ) ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Arrow_,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr1055212137t_bool,R: produc1840315303le_alt] : ( hAPP_P166437127t_bool(hAPP_f70231061t_bool(hAPP_f1056396531t_bool(cOMBB_1693113739le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P166437127t_bool(Q,R)) ) ).

tff(help_fequal_1_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
    ! [X: produc662089077le_alt,Y: produc662089077le_alt] :
      ( ~ hBOOL(hAPP_P274047445t_bool(hAPP_P1710235071t_bool(fequal1128546102le_alt,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
    ! [X: produc662089077le_alt,Y: produc662089077le_alt] :
      ( ( X != Y )
      | hBOOL(hAPP_P274047445t_bool(hAPP_P1710235071t_bool(fequal1128546102le_alt,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____,axiom,
    ! [P: fun_na1791315646le_alt,Q: list_A1748581779le_alt,R: nat] : ( hAPP_n1493999368le_alt(hAPP_l1844587084le_alt(hAPP_f1168703685le_alt(cOMBC_723368737le_alt,P),Q),R) = hAPP_l2085326633le_alt(hAPP_n447277270le_alt(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_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__prod_It,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1015689055l_bool,R: fun_Pr1055212137t_bool] : ( hAPP_f429946033l_bool(hAPP_f1050277569l_bool(hAPP_f925342873l_bool(cOMBB_2017616773t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f429946033l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr1055212137t_bool] : ( hAPP_f269590987l_bool(hAPP_f1519524905l_bool(cOMBK_1253994904t_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: bool] : ( hAPP_b1650070463l_bool(hAPP_f259799103l_bool(cOMBK_1489759608l_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__List__,axiom,
    ! [P: fun_bool_bool,Q: fun_Pr1013460023t_bool,R: produc662089077le_alt] : ( hAPP_P274047445t_bool(hAPP_f842237845t_bool(hAPP_f208471283t_bool(cOMBB_2059950425le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P274047445t_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,axiom,
    ! [P: fun_Ar1091019988t_bool,Q: produc1840315303le_alt] : ( hAPP_P1239753854t_bool(hAPP_f651702217t_bool(cOMBK_350001591le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_726,axiom,
    ! [P: fun_Pr1055212137t_bool,Q: arrow_931160158le_alt] : ( hAPP_A606737888t_bool(hAPP_f786530292t_bool(cOMBK_82914883le_alt,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t_727,axiom,
    ! [P: fun_Ar283682666le_alt,Q: list_A1748581779le_alt,R: arrow_931160158le_alt] : ( hAPP_A1866301020le_alt(hAPP_l1542090656le_alt(hAPP_f1593322349le_alt(cOMBC_1067846133le_alt,P),Q),R) = hAPP_l2085326633le_alt(hAPP_A662984834le_alt(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___728,axiom,
    ! [P: fun_Ar552120407i_bool,Q: produc1840315303le_alt] : ( hAPP_P1326783277i_bool(hAPP_f324402723i_bool(cOMBK_646689008le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_729,axiom,
    ! [P: fun_Pr1055212137t_bool,Q: arrow_2115524757e_indi] : ( hAPP_A1174518481t_bool(hAPP_f311418073t_bool(cOMBK_1522533360e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
    ! [P: fun_li165117579le_alt,Q: arrow_931160158le_alt] : ( hAPP_A662984834le_alt(hAPP_f2067535732le_alt(cOMBK_313903393le_alt,P),Q) = P ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,axiom,
    ! [X: fun_Ar500372357t_bool,Y: fun_Ar500372357t_bool] :
      ( ~ hBOOL(hAPP_f1766661605l_bool(hAPP_f1839818431l_bool(fequal1183344582t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm,axiom,
    ! [X: fun_Ar500372357t_bool,Y: fun_Ar500372357t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f1766661605l_bool(hAPP_f1839818431l_bool(fequal1183344582t_bool,X),Y)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t_730,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_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,axiom,
    ! [P: fun_li973302697le_alt,Q: list_A1748581779le_alt,R: list_A1748581779le_alt] : ( hAPP_l2085326633le_alt(hAPP_l38598005le_alt(hAPP_f1762369621le_alt(cOMBC_67621220le_alt,P),Q),R) = hAPP_l2085326633le_alt(hAPP_l38598005le_alt(P,R),Q) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___731,axiom,
    ! [P: fun_Ar1091019988t_bool,Q: fun_Pr1055212137t_bool] : ( hAPP_f1099651112t_bool(hAPP_f5211821t_bool(cOMBK_1771409497t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_732,axiom,
    ! [P: fun_fu1015689055l_bool,Q: arrow_931160158le_alt] : ( hAPP_A1787768616l_bool(hAPP_f377423160l_bool(cOMBK_433524227le_alt,P),Q) = P ) ).

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___733,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_734,axiom,
    ! [P: fun_fu1015689055l_bool,Q: arrow_2115524757e_indi] : ( hAPP_A1279849719l_bool(hAPP_f1793492343l_bool(cOMBK_1595020336e_indi,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Arrow__,axiom,
    ! [P: fun_bool_bool,Q: fun_fu775006535l_bool,R: fun_Ar500372357t_bool] : ( hAPP_f1766661605l_bool(hAPP_f626396309l_bool(hAPP_f1078200691l_bool(cOMBB_1270085993t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f1766661605l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_735,axiom,
    ! [P: fun_bool_bool,Q: fun_Ar500372357t_bool] : ( hAPP_f84039575l_bool(hAPP_f2138308309l_bool(cOMBK_768188438t_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: bool] : ( hAPP_b1849744615l_bool(hAPP_f126479309l_bool(cOMBK_1709453334l_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_736,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__prod_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm_,axiom,
    ! [P: fun_Pr973555187t_bool,Q: produc1840315303le_alt,R: produc1840315303le_alt] : ( hAPP_P166437127t_bool(hAPP_P339234111t_bool(hAPP_f182135529t_bool(cOMBC_1001276758t_bool,P),Q),R) = hAPP_P166437127t_bool(hAPP_P339234111t_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_737,axiom,
    ! [P: fun_li1990043301l_bool,Q: fun_Pr1013460023t_bool,R: list_A1748581779le_alt] : ( hAPP_l713721587t_bool(hAPP_f137643187t_bool(hAPP_f441886219t_bool(cOMBC_307006084l_bool,P),Q),R) = hAPP_f686625151l_bool(hAPP_l896015811l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oalt_000t_738,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_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,axiom,
    ! [P: fun_li973302697le_alt,Q: fun_Ar1553825290le_alt,R: arrow_931160158le_alt] : ( hAPP_A662984834le_alt(hAPP_f566168733le_alt(hAPP_f293521405le_alt(cOMBB_764295458le_alt,P),Q),R) = hAPP_l38598005le_alt(P,hAPP_A1866301020le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___739,axiom,
    ! [P: fun_Ar1091019988t_bool,Q: fun_Ar500372357t_bool] : ( hAPP_f87867740t_bool(hAPP_f1528883111t_bool(cOMBK_841302421t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_740,axiom,
    ! [P: fun_fu775006535l_bool,Q: arrow_931160158le_alt] : ( hAPP_A2111843262l_bool(hAPP_f1837403508l_bool(cOMBK_1262239973le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___741,axiom,
    ! [P: fun_Ar552120407i_bool,Q: fun_Ar500372357t_bool] : ( hAPP_f109229519i_bool(hAPP_f1845592261i_bool(cOMBK_1865603534t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_742,axiom,
    ! [P: fun_fu775006535l_bool,Q: arrow_2115524757e_indi] : ( hAPP_A182831535l_bool(hAPP_f2099786901l_bool(cOMBK_970693070e_indi,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct_743,axiom,
    ! [P: fun_Pr1055212137t_bool,Q: produc662089077le_alt] : ( hAPP_P385761265t_bool(hAPP_f303577849t_bool(cOMBK_1603999824le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,axiom,
    ! [P: fun_Pr1013460023t_bool,Q: produc1840315303le_alt] : ( hAPP_P1279976973t_bool(hAPP_f1545334371t_bool(cOMBK_1927707728le_alt,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_744,axiom,
    ! [P: fun_li352365677le_alt,Q: fun_li165117579le_alt,R: list_A1748581779le_alt] : ( hAPP_l1128853771le_alt(hAPP_f900901495le_alt(hAPP_f1292327175le_alt(cOMBB_1257018821le_alt,P),Q),R) = hAPP_l1128853771le_alt(P,hAPP_l2085326633le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____ct,axiom,
    ! [P: fun_fu1515494241l_bool,Q: fun_Pr1055212137t_bool,R: fun_Pr1055212137t_bool] : ( hAPP_f429946033l_bool(hAPP_f314169011l_bool(hAPP_f5916613l_bool(cOMBC_2092631450l_bool,P),Q),R) = hAPP_f429946033l_bool(hAPP_f314169011l_bool(P,R),Q) ) ).

tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____ctuiwsvqnm__Oindi_000_745,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_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_746,axiom,
    ! [P: fun_fu1015689055l_bool,Q: produc662089077le_alt] : ( hAPP_P272697303l_bool(hAPP_f1115980887l_bool(cOMBK_2034944144le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___747,axiom,
    ! [P: fun_Pr1013460023t_bool,Q: fun_Pr1055212137t_bool] : ( hAPP_f557837283t_bool(hAPP_f2035600681t_bool(cOMBK_1082115712t_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_Pr2138751219t_bool,Q: produc662089077le_alt,R: produc662089077le_alt] : ( hAPP_P274047445t_bool(hAPP_P1710235071t_bool(hAPP_f498121449t_bool(cOMBC_662543858t_bool,P),Q),R) = hAPP_P274047445t_bool(hAPP_P1710235071t_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(hAPP_f1650801283l_bool(cOMBB_480104238le_alt,P),Q),R) = hAPP_P840149257l_bool(P,hAPP_A1313367280le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_748,axiom,
    ! [P: fun_li1761430841t_bool,Q: fun_Pr1013460023t_bool,R: list_A1748581779le_alt] : ( hAPP_l1173894719t_bool(hAPP_f615584405t_bool(hAPP_f1269493503t_bool(cOMBC_1004503918t_bool,P),Q),R) = hAPP_f137643187t_bool(hAPP_l189416837t_bool(P,R),Q) ) ).

tff(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____c,axiom,
    ! [X: fun_fu1595299477t_bool,Y: fun_fu1595299477t_bool] :
      ( ~ hBOOL(hAPP_f611501301l_bool(hAPP_f926158015l_bool(fequal730162134t_bool,X),Y))
      | ( X = Y ) ) ).

tff(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____c,axiom,
    ! [X: fun_fu1595299477t_bool,Y: fun_fu1595299477t_bool] :
      ( ( X != Y )
      | hBOOL(hAPP_f611501301l_bool(hAPP_f926158015l_bool(fequal730162134t_bool,X),Y)) ) ).

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__prod_Itc__Arrow____Order____Mirabe_749,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__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_750,axiom,
    ! [P: fun_li1598912907le_alt,Q: fun_li165117579le_alt,R: list_A1748581779le_alt] : ( hAPP_l1949544791le_alt(hAPP_f2007624449le_alt(hAPP_f760536509le_alt(cOMBB_991641265le_alt,P),Q),R) = hAPP_l1949544791le_alt(P,hAPP_l2085326633le_alt(Q,R)) ) ).

tff(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui,axiom,
    ! [P: fun_li1019735149le_alt,Q: fun_li352365677le_alt,R: list_A1748581779le_alt] : ( hAPP_l1128853771le_alt(hAPP_f1535045909le_alt(hAPP_f1060117389le_alt(cOMBS_1384849976le_alt,P),Q),R) = hAPP_P1208706541le_alt(hAPP_l724324921le_alt(P,R),hAPP_l1128853771le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu_751,axiom,
    ! [P: fun_fu775006535l_bool,Q: produc662089077le_alt] : ( hAPP_P725642959l_bool(hAPP_f1405662645l_bool(cOMBK_1129525550le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___752,axiom,
    ! [P: fun_Pr1013460023t_bool,Q: fun_Ar500372357t_bool] : ( hAPP_f1203715503t_bool(hAPP_f1701776901t_bool(cOMBK_851707182t_bool,P),Q) = P ) ).

tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1138137687l_bool,R: fun_fu1595299477t_bool] : ( hAPP_f611501301l_bool(hAPP_f1077478037l_bool(hAPP_f2053120627l_bool(cOMBB_593231993t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f611501301l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_753,axiom,
    ! [P: fun_bool_bool,Q: fun_fu1595299477t_bool] : ( hAPP_f352672903l_bool(hAPP_f1090778053l_bool(cOMBK_1251240998t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_fu1138137687l_bool,Q: bool] : ( hAPP_b816606711l_bool(hAPP_f1922499821l_bool(cOMBK_1417083942l_bool,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm__,axiom,
    ! [P: fun_fu2072229747l_bool,Q: fun_Ar500372357t_bool,R: fun_Ar500372357t_bool] : ( hAPP_f1766661605l_bool(hAPP_f1839818431l_bool(hAPP_f1270395369l_bool(cOMBC_422512914l_bool,P),Q),R) = hAPP_f1766661605l_bool(hAPP_f1839818431l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
    ! [P: fun_Pr1472769671l_bool,Q: fun_li352365677le_alt,R: list_A1748581779le_alt] : ( hAPP_l896015811l_bool(hAPP_f1660849997l_bool(hAPP_f270961347l_bool(cOMBB_2055762783le_alt,P),Q),R) = hAPP_P518621093l_bool(P,hAPP_l1128853771le_alt(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___754,axiom,
    ! [P: fun_Ar1091019988t_bool,Q: fun_fu1595299477t_bool] : ( hAPP_f735144044t_bool(hAPP_f2020309431t_bool(cOMBK_1604195493t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_755,axiom,
    ! [P: fun_fu1138137687l_bool,Q: arrow_931160158le_alt] : ( hAPP_A1313889230l_bool(hAPP_f2030964596l_bool(cOMBK_289343701le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___756,axiom,
    ! [P: fun_Ar552120407i_bool,Q: fun_fu1595299477t_bool] : ( hAPP_f740807359i_bool(hAPP_f301073845i_bool(cOMBK_189636062t_bool,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_757,axiom,
    ! [P: fun_fu1138137687l_bool,Q: arrow_2115524757e_indi] : ( hAPP_A1538515647l_bool(hAPP_f1639366069l_bool(cOMBK_1014681054e_indi,P),Q) = P ) ).

tff(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_758,axiom,
    ! [P: fun_li897167357le_alt,Q: fun_li165117579le_alt,R: list_A1748581779le_alt] : ( hAPP_l1949544791le_alt(hAPP_f2007624449le_alt(hAPP_f724120879le_alt(cOMBC_1169880370le_alt,P),Q),R) = hAPP_f900901495le_alt(hAPP_l869353033le_alt(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(hAPP_f695996419l_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,axiom,
    ! [P: fun_fu699199419t_bool,Q: fun_Ar500372357t_bool,R: arrow_2115524757e_indi] : ( hAPP_A131904271t_bool(hAPP_f576849227t_bool(hAPP_f2044798215t_bool(cOMBB_656639247e_indi,P),Q),R) = hAPP_f1909595219t_bool(P,hAPP_A1174518481t_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____ctuiwsvqnm___759,axiom,
    ! [P: fun_fu709917073t_bool,Q: fun_Ar1689125069l_bool,R: arrow_931160158le_alt] : ( hAPP_A1770325791t_bool(hAPP_f1435501085t_bool(hAPP_f318336003t_bool(cOMBB_1430402568le_alt,P),Q),R) = hAPP_f2087965871t_bool(P,hAPP_A1256181151l_bool(Q,R)) ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_760,axiom,
    ! [P: fun_fu1138137687l_bool,Q: produc662089077le_alt] : ( hAPP_P469411807l_bool(hAPP_f64308949l_bool(cOMBK_801230142le_alt,P),Q) = P ) ).

tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___761,axiom,
    ! [P: fun_Pr1013460023t_bool,Q: fun_fu1595299477t_bool] : ( hAPP_f1014198943t_bool(hAPP_f1729202933t_bool(cOMBK_1744775486t_bool,P),Q) = P ) ).

tff(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____ctui_762,axiom,
    ! [P: fun_li1459246747le_alt,Q: fun_li1598912907le_alt,R: list_A1748581779le_alt] : ( hAPP_l1949544791le_alt(hAPP_f186933785le_alt(hAPP_f1043429597le_alt(cOMBS_384423136le_alt,P),Q),R) = hAPP_f1535045909le_alt(hAPP_l955365607le_alt(P,R),hAPP_l1949544791le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_763,axiom,
    ! [P: fun_Pr286692619le_alt,Q: fun_li352365677le_alt,R: list_A1748581779le_alt] : ( hAPP_l724324921le_alt(hAPP_f330272197le_alt(hAPP_f675875329le_alt(cOMBB_1744225841le_alt,P),Q),R) = hAPP_P443881687le_alt(P,hAPP_l1128853771le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
    ! [P: fun_fu1464168373l_bool,Q: fun_li1598912907le_alt,R: list_A1748581779le_alt] : ( hAPP_l1385346191l_bool(hAPP_f1120297681l_bool(hAPP_f788365459l_bool(cOMBB_1398787847le_alt,P),Q),R) = hAPP_f1660849997l_bool(P,hAPP_l1949544791le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_764,axiom,
    ! [P: fun_fu1211133043t_bool,Q: fun_li971691843l_bool,R: list_A1748581779le_alt] : ( hAPP_l189416837t_bool(hAPP_f133408895t_bool(hAPP_f1802448643t_bool(cOMBB_1898463941le_alt,P),Q),R) = hAPP_f441886219t_bool(P,hAPP_l1385346191l_bool(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_765,axiom,
    ! [P: fun_fu46714991le_alt,Q: fun_li1598912907le_alt,R: list_A1748581779le_alt] : ( hAPP_l869353033le_alt(hAPP_f74494859le_alt(hAPP_f489798931le_alt(cOMBB_1371834305le_alt,P),Q),R) = hAPP_f1292327175le_alt(P,hAPP_l1949544791le_alt(Q,R)) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_766,axiom,
    ! [P: fun_fu6778611le_alt,Q: fun_li1598912907le_alt,R: list_A1748581779le_alt] : ( hAPP_l1285746947le_alt(hAPP_f1272206039le_alt(hAPP_f1730519937le_alt(cOMBB_1090121759le_alt,P),Q),R) = hAPP_f330272197le_alt(P,hAPP_l1949544791le_alt(Q,R)) ) ).

tff(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____ctu,axiom,
    ! [P: fun_fu1756482675l_bool,Q: fun_fu1595299477t_bool,R: fun_fu1595299477t_bool] : ( hAPP_f611501301l_bool(hAPP_f926158015l_bool(hAPP_f1147912169l_bool(cOMBC_2092631346l_bool,P),Q),R) = hAPP_f611501301l_bool(hAPP_f926158015l_bool(P,R),Q) ) ).

tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_767,axiom,
    ! [P: fun_fu2139722817le_alt,Q: fun_li1501328101le_alt,R: list_A1748581779le_alt] : ( hAPP_l955365607le_alt(hAPP_f1817977963le_alt(hAPP_f1428546141le_alt(cOMBB_202310119le_alt,P),Q),R) = hAPP_f1060117389le_alt(P,hAPP_l1285746947le_alt(Q,R)) ) ).

%----Conjectures (1)
% tff(conj_0,conjecture,
%     ! [I: arrow_2115524757e_indi] :
%       ( hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),b)),hAPP_A1174518481t_bool(p,I)))
%     <=> hBOOL(hAPP_f429946033l_bool(hAPP_P840149257l_bool(member553230100le_alt,hAPP_A1313367280le_alt(hAPP_A1485971815le_alt(produc362059031le_alt,a),c)),hAPP_A606737888t_bool(hAPP_A501825983t_bool(hAPP_f1909595219t_bool(arrow_636638768_below,hAPP_A1174518481t_bool(p,I)),c),b))) ) ).

%------------------------------------------------------------------------------