TPTP Problem File: SCT171_1.p
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%------------------------------------------------------------------------------
% File : SCT171_1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_100_tff_l309 [Bla11]
% Status : Theorem
% Rating : 0.00 v5.3.0
% Syntax : Number of formulae : 558 ( 92 unt; 319 typ; 0 def)
% Number of atoms : 565 ( 145 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 443 ( 117 ~; 9 |; 14 &)
% ( 50 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 110 ( 109 usr)
% Number of type conns : 275 ( 151 >; 124 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 209 ( 209 usr; 59 con; 0-2 aty)
% Number of variables : 569 ( 568 !; 1 ?; 569 :)
% SPC : TF0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:38:02
%------------------------------------------------------------------------------
%----Should-be-implicit typings (109)
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%----Explicit typings (210)
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hAPP_f90330565l_bool: ( fun_fu350122099l_bool * fun_Ar1871347069i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___104,type,
hAPP_f1993665755l_bool: ( fun_fu892925833l_bool * fun_Ar1871347069i_bool ) > fun_fu350122099l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___105,type,
hAPP_f823592631i_bool: ( fun_fu341524965i_bool * fun_Ar1871347069i_bool ) > fun_fu23838287i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___106,type,
hAPP_f1224613979i_bool: ( fun_fu932525193i_bool * fun_Ar1871347069i_bool ) > fun_fu1950461939i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___107,type,
hAPP_f1364159657i_bool: ( fun_fu1845530641i_bool * fun_Ar1871347069i_bool ) > fun_fu1867632401i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___108,type,
hAPP_f1561296623i_bool: ( fun_fu1605010205i_bool * fun_Ar1871347069i_bool ) > fun_Pr123985543i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___109,type,
hAPP_f1631746589e_indi: ( fun_fu2069019647e_indi * fun_Ar2047178847t_bool ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___110,type,
hAPP_f1095388607l_bool: ( fun_fu103733537l_bool * fun_Ar2047178847t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___111,type,
hAPP_f1511451035i_bool: ( fun_fu23838287i_bool * fun_Ar2047178847t_bool ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___112,type,
hAPP_f1418708797l_bool: ( fun_fu658952305l_bool * fun_Ar2047178847t_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___113,type,
hAPP_f1265202753l_bool: ( fun_fu746839971l_bool * fun_Ar2047178847t_bool ) > fun_fu383145951l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc___114,type,
hAPP_f718157575t_bool: ( fun_fu50365883t_bool * fun_Ar2047178847t_bool ) > fun_Pr1639951081t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,type,
hAPP_f387058535l_bool: ( fun_fu1255657237l_bool * fun_bool_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc__,type,
hAPP_f1325493883l_bool: ( fun_fu1159982633l_bool * fun_bool_bool ) > fun_fu658952305l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___115,type,
hAPP_f1364914207l_bool: ( fun_fu797886669l_bool * fun_bool_bool ) > fun_fu1734842389l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc___116,type,
hAPP_f1230984105l_bool: ( fun_fu1940222097l_bool * fun_bool_bool ) > fun_fu1903211571l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__prod_Itc_,type,
hAPP_f1601816755l_bool: ( fun_fu1791463777l_bool * fun_bool_bool ) > fun_Pr534938793l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi,type,
hAPP_f1753158741l_bool: ( fun_fu243829175l_bool * fun_fu1103697397l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_117,type,
hAPP_f598211249l_bool: ( fun_fu1019918867l_bool * fun_fu682929745l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_118,type,
hAPP_f1237345129l_bool: ( fun_fu386577431l_bool * fun_fu103733537l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_119,type,
hAPP_f466810275l_bool: ( fun_fu337461969l_bool * fun_fu103733537l_bool ) > fun_Ar1784032663l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_120,type,
hAPP_f2013855105l_bool: ( fun_fu123258927l_bool * fun_fu103733537l_bool ) > fun_bo1613497205l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_121,type,
hAPP_f786935331l_bool: ( fun_fu698697681l_bool * fun_fu103733537l_bool ) > fun_fu386577431l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_122,type,
hAPP_f87993209e_indi: ( fun_fu1743730523e_indi * fun_fu50365883t_bool ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_123,type,
hAPP_f725100827l_bool: ( fun_fu1251737213l_bool * fun_fu50365883t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_124,type,
hAPP_f1559864639i_bool: ( fun_fu1950461939i_bool * fun_fu50365883t_bool ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_125,type,
hAPP_f626809057l_bool: ( fun_fu1734842389l_bool * fun_fu50365883t_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_126,type,
hAPP_f748921117l_bool: ( fun_fu1904749695l_bool * fun_fu2085524157t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mi,type,
hAPP_f1481710327l_bool: ( fun_fu376055641l_bool * fun_fu132047767l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Or,type,
hAPP_f759862099l_bool: ( fun_fu1037822389l_bool * fun_fu1655311859l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____O,type,
hAPP_f639792199l_bool: ( fun_fu664235509l_bool * fun_fu897278719l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____M,type,
hAPP_f899216831l_bool: ( fun_fu582883361l_bool * fun_fu2114498143t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr,type,
hAPP_f243652437l_bool: ( fun_fu881806519l_bool * fun_fu1884117237i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_127,type,
hAPP_f1394256759l_bool: ( fun_fu288602073l_bool * fun_fu386577431l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_128,type,
hAPP_f1435434693l_bool: ( fun_fu304973171l_bool * fun_fu1251737213l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_129,type,
hAPP_f544895323l_bool: ( fun_fu1740763529l_bool * fun_fu1251737213l_bool ) > fun_Ar884201459l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_130,type,
hAPP_f989466937l_bool: ( fun_fu1786351335l_bool * fun_fu1251737213l_bool ) > fun_bo2138151889l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_131,type,
hAPP_f1303771867l_bool: ( fun_fu1536608137l_bool * fun_fu1251737213l_bool ) > fun_fu304973171l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
hAPP_f174050481l_bool: ( fun_fu595758099l_bool * fun_fu1123909713i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_132,type,
hAPP_f1827424979l_bool: ( fun_fu2105385269l_bool * fun_fu304973171l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,type,
hAPP_f359017159l_bool: ( fun_fu1655733109l_bool * fun_fu1083074431i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell_133,type,
hAPP_f1347377641l_bool: ( fun_fu1371820951l_bool * fun_fu2011759009l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr,type,
hAPP_f1270259485l_bool: ( fun_fu278604415l_bool * fun_fu662212797i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_134,type,
hAPP_f180608831l_bool: ( fun_fu2011759009l_bool * fun_fu383145951l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_135,type,
hAPP_f1651042461l_bool: ( fun_fu491357777l_bool * fun_fu383145951l_bool ) > fun_Ar1821573119l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_136,type,
hAPP_f71505983l_bool: ( fun_fu1479273075l_bool * fun_fu383145951l_bool ) > fun_bo1803678369l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_137,type,
hAPP_f459175489l_bool: ( fun_fu890127093l_bool * fun_fu383145951l_bool ) > fun_fu746839971l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_138,type,
hAPP_f279586623l_bool: ( fun_fu66812275l_bool * fun_fu383145951l_bool ) > fun_fu2011759009l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O,type,
hAPP_f671542927e_indi: ( fun_fu334384573e_indi * fun_Pr1639951081t_bool ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_139,type,
hAPP_f1944886577l_bool: ( fun_fu383145951l_bool * fun_Pr1639951081t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_140,type,
hAPP_f1560118175t_bool: ( fun_fu193278215t_bool * fun_Pr1639951081t_bool ) > fun_Ar154839667t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_141,type,
hAPP_f1699392794t_bool: ( fun_fu1760369922t_bool * fun_Pr1639951081t_bool ) > fun_Ar1822233582t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_142,type,
hAPP_f906860201i_bool: ( fun_fu1867632401i_bool * fun_Pr1639951081t_bool ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_143,type,
hAPP_f1172974131t_bool: ( fun_fu1917018721t_bool * fun_Pr1639951081t_bool ) > fun_Ar2047178847t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_144,type,
hAPP_f2128533835l_bool: ( fun_fu1903211571l_bool * fun_Pr1639951081t_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_145,type,
hAPP_f1758973969t_bool: ( fun_fu1008469439t_bool * fun_Pr1639951081t_bool ) > fun_bo230129725t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_146,type,
hAPP_f1911990195l_bool: ( fun_fu1157966945l_bool * fun_Pr1639951081t_bool ) > fun_fu383145951l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_147,type,
hAPP_f910728105t_bool: ( fun_fu1965119761t_bool * fun_Pr1639951081t_bool ) > fun_fu148272765t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_148,type,
hAPP_f727188501t_bool: ( fun_fu148272765t_bool * fun_Pr1639951081t_bool ) > fun_Pr1639951081t_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc__,type,
hAPP_P163170789e_indi: ( fun_Pr506339783e_indi * produc624534567le_alt ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___149,type,
hAPP_P751176071t_bool: ( fun_Pr1639951081t_bool * produc624534567le_alt ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___150,type,
hAPP_P259956691i_bool: ( fun_Pr123985543i_bool * produc624534567le_alt ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___151,type,
hAPP_P2005668213l_bool: ( fun_Pr534938793l_bool * produc624534567le_alt ) > fun_bool_bool ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi,type,
member1124131880e_indi: arrow_501706939e_indi > fun_fu350122099l_bool ).
tff(sy_c_member_000tc__HOL__Obool,type,
member_bool: bool > fun_fu1255657237l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc,type,
member1701178322t_bool: fun_Ar1200683263t_bool > fun_fu243829175l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_152,type,
member2069173038t_bool: fun_Ar1570071899t_bool > fun_fu1019918867l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_153,type,
member558395596t_bool: fun_Ar2047178847t_bool > fun_fu386577431l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_154,type,
member844573594le_alt: fun_Ar795681735le_alt > fun_fu1904749695l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mirabelle,type,
member1494646772t_bool: fun_bo478202017t_bool > fun_fu376055641l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Order____,type,
member1211611472t_bool: fun_bo2136393469t_bool > fun_fu1037822389l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____Order___,type,
member2079888426t_bool: fun_bo230129725t_bool > fun_fu664235509l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____Mirabell,type,
member158436796le_alt: fun_bo1156530537le_alt > fun_fu582883361l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__,type,
member422031058e_indi: fun_fu2069019647e_indi > fun_fu881806519l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___155,type,
member1120178292l_bool: fun_fu103733537l_bool > fun_fu288602073l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___156,type,
member256508712t_bool: fun_fu50365883t_bool > fun_fu304973171l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv,type,
member95348014e_indi: fun_fu1743730523e_indi > fun_fu595758099l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_157,type,
member326955216l_bool: fun_fu1251737213l_bool > fun_fu2105385269l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,type,
member993084970e_indi: fun_fu334384573e_indi > fun_fu1655733109l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_158,type,
member85421004l_bool: fun_fu383145951l_bool > fun_fu1371820951l_bool ).
tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb_,type,
member555231642e_indi: fun_Pr506339783e_indi > fun_fu278604415l_bool ).
tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__159,type,
member641857340t_bool: fun_Pr1639951081t_bool > fun_fu2011759009l_bool ).
tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc,type,
member1484933012le_alt: produc624534567le_alt > fun_fu383145951l_bool ).
tff(sy_v_F,type,
f: fun_fu50365883t_bool ).
tff(sy_v_Lab____,type,
lab: fun_Pr1639951081t_bool ).
tff(sy_v_Lba____,type,
lba: fun_Pr1639951081t_bool ).
tff(sy_v_P____,type,
p: fun_Ar2047178847t_bool ).
tff(sy_v_a____,type,
a: arrow_1621810872le_alt ).
tff(sy_v_b____,type,
b: arrow_1621810872le_alt ).
tff(sy_v_c____,type,
c: arrow_1621810872le_alt ).
tff(sy_v_d____,type,
d: arrow_1621810872le_alt ).
tff(sy_v_e____,type,
e: arrow_1621810872le_alt ).
tff(sy_v_h____,type,
h: fun_Ar2035712896di_nat ).
tff(sy_v_n____,type,
n: nat ).
%----Relevant facts (198)
tff(fact_0_assms_I3_J,axiom,
hBOOL(hAPP_f725100827l_bool(arrow_981905126le_IIA,f)) ).
tff(fact_1_u,axiom,
hBOOL(hAPP_f725100827l_bool(arrow_807483785nimity,f)) ).
tff(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
tff(fact_3__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(p),arrow_1880704820e_Prof)) ).
tff(fact_4_in__mkbot,axiom,
! [X_2: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool,Z_1: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1126550734_mkbot,L),Z_1)))
<=> ( ( Y_1 != Z_1 )
& ( ( X_2 = Z_1 )
=> ( X_2 != Y_1 ) )
& ( ( X_2 != Z_1 )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),L)) ) ) ) ).
tff(fact_5_in__mktop,axiom,
! [X_2: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool,Z_1: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1275257820_mktop,L),Z_1)))
<=> ( ( X_2 != Z_1 )
& ( ( Y_1 = Z_1 )
=> ( X_2 != Y_1 ) )
& ( ( Y_1 != Z_1 )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),L)) ) ) ) ).
tff(fact_6__C2_C,axiom,
! [P_1: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,A_8: arrow_1621810872le_alt,B_8: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( A_8 != B_8 )
=> ( ( Aa != B_8 )
=> ( ( Ba != A_8 )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_1),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_A2044747691t_bool(P_1,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_f718157575t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).
tff(fact_7__C1_C,axiom,
! [P_1: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,A_8: arrow_1621810872le_alt,B_8: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( A_8 != B_8 )
=> ( ( Aa != B_8 )
=> ( ( Ba != A_8 )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_1),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_A2044747691t_bool(P_1,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_f718157575t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).
tff(fact_8__C4_C,axiom,
! [P_1: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,Ca: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( Ba != Ca )
=> ( ( Aa != Ca )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_1),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Ca)),hAPP_A2044747691t_bool(P_1,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Ca)),hAPP_f718157575t_bool(f,P_1))) ) ) ) ) ) ) ) ).
tff(fact_9_pairwise__neutrality,axiom,
! [P_1: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,A_8: arrow_1621810872le_alt,B_8: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( A_8 != B_8 )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_1),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_A2044747691t_bool(P_1,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_8,B_8)),hAPP_f718157575t_bool(f,P_1))) ) ) ) ) ) ) ).
tff(fact_10__C3_C,axiom,
! [P_1: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_1),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Aa)),hAPP_A2044747691t_bool(P_1,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Aa)),hAPP_f718157575t_bool(f,P_1))) ) ) ) ) ) ).
tff(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_A2044747691t_bool(p,I)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1275257820_mktop,hAPP_A2044747691t_bool(p,I)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> ( ( ( hAPP_A1741215436di_nat(h,I) = n )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_2009189698_above,hAPP_A2044747691t_bool(p,I)),c),e))) )
& ( ( hAPP_A1741215436di_nat(h,I) != n )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1126550734_mkbot,hAPP_A2044747691t_bool(p,I)),e))) ) ) ) ) ) ).
tff(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_A2044747691t_bool(p,hAPP_n1582158000e_indi(hilber797233813di_nat(top_to850136695i_bool,h),n)))) ).
tff(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ).
tff(fact_14_PW,axiom,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ) ).
tff(fact_15_split__paired__All,axiom,
! [Pa: fun_Pr1639951081t_bool] :
( ! [X1: produc624534567le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,X1))
<=> ! [A_1: arrow_1621810872le_alt,B_1: arrow_1621810872le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,produc170576535le_alt(A_1,B_1))) ) ).
tff(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))),arrow_1880704820e_Prof)) ).
tff(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,e)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ).
tff(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(e,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ).
tff(fact_19_n_I1_J,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite1317065577e_indi(top_to850136695i_bool))) ).
tff(fact_20_injh,axiom,
hBOOL(inj_on1177549232di_nat(h,top_to850136695i_bool)) ).
tff(fact_21_Pair__inject,axiom,
! [A_10: arrow_1621810872le_alt,B_10: arrow_1621810872le_alt,A_9: arrow_1621810872le_alt,B_9: arrow_1621810872le_alt] :
( ( produc170576535le_alt(A_10,B_10) = produc170576535le_alt(A_9,B_9) )
=> ~ ( ( A_10 = A_9 )
=> ( B_10 != B_9 ) ) ) ).
tff(fact_22_Pair__eq,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt,A_8: arrow_1621810872le_alt,B_8: arrow_1621810872le_alt] :
( ( produc170576535le_alt(Aa,Ba) = produc170576535le_alt(A_8,B_8) )
<=> ( ( Aa = A_8 )
& ( Ba = B_8 ) ) ) ).
tff(fact_23_IIA__def,axiom,
! [Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(arrow_981905126le_IIA,Fa))
<=> ! [X_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),arrow_1880704820e_Prof))
=> ! [Xa: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Xa),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B_1: arrow_1621810872le_alt] :
( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_A2044747691t_bool(X_1,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_A2044747691t_bool(Xa,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_f718157575t_bool(Fa,X_1)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_f718157575t_bool(Fa,Xa))) ) ) ) ) ) ).
tff(fact_24_unanimity__def,axiom,
! [Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(arrow_807483785nimity,Fa))
<=> ! [X_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B_1: arrow_1621810872le_alt] :
( ! [I: arrow_501706939e_indi] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_A2044747691t_bool(X_1,I)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_f718157575t_bool(Fa,X_1))) ) ) ) ).
tff(fact_25_top1I,axiom,
! [X_2: fun_Pr1639951081t_bool] : hBOOL(hAPP_f1944886577l_bool(top_to1057791589l_bool,X_2)) ).
tff(fact_26_top1I,axiom,
! [X_2: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1095388607l_bool(top_to653038619l_bool,X_2)) ).
tff(fact_27_top1I,axiom,
! [X_2: fun_fu50365883t_bool] : hBOOL(hAPP_f725100827l_bool(top_to2127553399l_bool,X_2)) ).
tff(fact_28_top1I,axiom,
! [X_2: produc624534567le_alt] : hBOOL(hAPP_P751176071t_bool(top_to710777827t_bool,X_2)) ).
tff(fact_29_top1I,axiom,
! [X_2: arrow_501706939e_indi] : hBOOL(hAPP_A1059798043i_bool(top_to850136695i_bool,X_2)) ).
tff(fact_30_UNIV__I,axiom,
! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool)) ).
tff(fact_31_UNIV__I,axiom,
! [X_2: arrow_501706939e_indi] : hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),top_to850136695i_bool)) ).
tff(fact_32_UNIV__I,axiom,
! [X_2: produc624534567le_alt] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),top_to710777827t_bool)) ).
tff(fact_33_UNIV__I,axiom,
! [X_2: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),top_to653038619l_bool)) ).
tff(fact_34_UNIV__I,axiom,
! [X_2: fun_fu50365883t_bool] : hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),top_to2127553399l_bool)) ).
tff(fact_35_UNIV__I,axiom,
! [X_2: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),top_to1057791589l_bool)) ).
tff(fact_36_iso__tuple__UNIV__I,axiom,
! [X_2: bool] : hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool)) ).
tff(fact_37_iso__tuple__UNIV__I,axiom,
! [X_2: arrow_501706939e_indi] : hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),top_to850136695i_bool)) ).
tff(fact_38_iso__tuple__UNIV__I,axiom,
! [X_2: produc624534567le_alt] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),top_to710777827t_bool)) ).
tff(fact_39_iso__tuple__UNIV__I,axiom,
! [X_2: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),top_to653038619l_bool)) ).
tff(fact_40_iso__tuple__UNIV__I,axiom,
! [X_2: fun_fu50365883t_bool] : hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),top_to2127553399l_bool)) ).
tff(fact_41_iso__tuple__UNIV__I,axiom,
! [X_2: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),top_to1057791589l_bool)) ).
tff(fact_42_top__apply,axiom,
! [X_2: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f1944886577l_bool(top_to1057791589l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
tff(fact_43_top__apply,axiom,
! [X_2: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1095388607l_bool(top_to653038619l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
tff(fact_44_top__apply,axiom,
! [X_2: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(top_to2127553399l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
tff(fact_45_top__apply,axiom,
! [X_2: produc624534567le_alt] :
( hBOOL(hAPP_P751176071t_bool(top_to710777827t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
tff(fact_46_top__apply,axiom,
! [X_2: arrow_501706939e_indi] :
( hBOOL(hAPP_A1059798043i_bool(top_to850136695i_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
tff(fact_47_not__top__less,axiom,
! [Aa: fun_fu383145951l_bool] : ~ hBOOL(hAPP_f180608831l_bool(hAPP_f279586623l_bool(ord_le1472193545l_bool,top_to1057791589l_bool),Aa)) ).
tff(fact_48_not__top__less,axiom,
! [Aa: fun_fu103733537l_bool] : ~ hBOOL(hAPP_f1237345129l_bool(hAPP_f786935331l_bool(ord_le2059466615l_bool,top_to653038619l_bool),Aa)) ).
tff(fact_49_not__top__less,axiom,
! [Aa: fun_fu1251737213l_bool] : ~ hBOOL(hAPP_f1435434693l_bool(hAPP_f1303771867l_bool(ord_le1419690707l_bool,top_to2127553399l_bool),Aa)) ).
tff(fact_50_not__top__less,axiom,
! [Aa: bool] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)) ).
tff(fact_51_not__top__less,axiom,
! [Aa: fun_Pr1639951081t_bool] : ~ hBOOL(hAPP_f1944886577l_bool(hAPP_f1911990195l_bool(ord_le1051050815t_bool,top_to710777827t_bool),Aa)) ).
tff(fact_52_not__top__less,axiom,
! [Aa: fun_Ar1871347069i_bool] : ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,top_to850136695i_bool),Aa)) ).
tff(fact_53_linorder__cases,axiom,
! [X_14: nat,Y_13: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_13))
=> ( ( X_14 != Y_13 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_14)) ) ) ).
tff(fact_54_order__less__asym,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),X_2)) ) ).
tff(fact_55_order__less__asym,axiom,
! [X_13: nat,Y_12: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_12))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_13)) ) ).
tff(fact_56_xt1_I10_J,axiom,
! [Z_1: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool,X_2: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),X_2))
=> ( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Z_1),Y_1))
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Z_1),X_2)) ) ) ).
tff(fact_57_xt1_I10_J,axiom,
! [Z_2: nat,Y_11: nat,X_12: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_11),X_12))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_12)) ) ) ).
tff(fact_58_order__less__trans,axiom,
! [Z_1: fun_Ar1871347069i_bool,X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),Z_1))
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Z_1)) ) ) ).
tff(fact_59_order__less__trans,axiom,
! [Z: nat,X_11: nat,Y_10: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_10),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Z)) ) ) ).
tff(fact_60_xt1_I2_J,axiom,
! [Ca: fun_Ar1871347069i_bool,Ba: fun_Ar1871347069i_bool,Aa: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ba),Aa))
=> ( ( Ba = Ca )
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ca),Aa)) ) ) ).
tff(fact_61_xt1_I2_J,axiom,
! [C_3: nat,B_7: nat,A_7: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),A_7))
=> ( ( B_7 = C_3 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),A_7)) ) ) ).
tff(fact_62_ord__less__eq__trans,axiom,
! [Ca: fun_Ar1871347069i_bool,Aa: fun_Ar1871347069i_bool,Ba: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),Ba))
=> ( ( Ba = Ca )
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),Ca)) ) ) ).
tff(fact_63_ord__less__eq__trans,axiom,
! [C_2: nat,A_6: nat,B_6: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_6))
=> ( ( B_6 = C_2 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),C_2)) ) ) ).
tff(fact_64_xt1_I1_J,axiom,
! [Ca: fun_Ar1871347069i_bool,Aa: fun_Ar1871347069i_bool,Ba: fun_Ar1871347069i_bool] :
( ( Aa = Ba )
=> ( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ca),Ba))
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ca),Aa)) ) ) ).
tff(fact_65_xt1_I1_J,axiom,
! [C_1: nat,A_5: nat,B_5: nat] :
( ( A_5 = B_5 )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),B_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),A_5)) ) ) ).
tff(fact_66_ord__eq__less__trans,axiom,
! [Ca: fun_Ar1871347069i_bool,Aa: fun_Ar1871347069i_bool,Ba: fun_Ar1871347069i_bool] :
( ( Aa = Ba )
=> ( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ba),Ca))
=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),Ca)) ) ) ).
tff(fact_67_ord__eq__less__trans,axiom,
! [C: nat,A_4: nat,B_4: nat] :
( ( A_4 = B_4 )
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),C))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),C)) ) ) ).
tff(fact_68_xt1_I9_J,axiom,
! [Ba: fun_Ar1871347069i_bool,Aa: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),Ba)) ) ).
tff(fact_69_xt1_I9_J,axiom,
! [B_3: nat,A_3: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_3),A_3))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_3)) ) ).
tff(fact_70_order__less__asym_H,axiom,
! [Aa: fun_Ar1871347069i_bool,Ba: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Ba),Aa)) ) ).
tff(fact_71_order__less__asym_H,axiom,
! [A_2: nat,B_2: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_2),A_2)) ) ).
tff(fact_72_order__less__imp__triv,axiom,
! [Pa: bool,X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),X_2))
=> hBOOL(Pa) ) ) ).
tff(fact_73_order__less__imp__triv,axiom,
! [Pa: bool,X_2: nat,Y_1: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
=> hBOOL(Pa) ) ) ).
tff(fact_74_order__less__imp__not__eq2,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ( Y_1 != X_2 ) ) ).
tff(fact_75_order__less__imp__not__eq2,axiom,
! [X_10: nat,Y_9: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_9))
=> ( Y_9 != X_10 ) ) ).
tff(fact_76_order__less__imp__not__eq,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ( X_2 != Y_1 ) ) ).
tff(fact_77_order__less__imp__not__eq,axiom,
! [X_9: nat,Y_8: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_8))
=> ( X_9 != Y_8 ) ) ).
tff(fact_78_order__less__imp__not__less,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),X_2)) ) ).
tff(fact_79_order__less__imp__not__less,axiom,
! [X_8: nat,Y_7: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_7))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),X_8)) ) ).
tff(fact_80_order__less__not__sym,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Y_1),X_2)) ) ).
tff(fact_81_order__less__not__sym,axiom,
! [X_7: nat,Y_6: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_6))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_6),X_7)) ) ).
tff(fact_82_less__imp__neq,axiom,
! [X_2: fun_Ar1871347069i_bool,Y_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),Y_1))
=> ( X_2 != Y_1 ) ) ).
tff(fact_83_less__imp__neq,axiom,
! [X_6: nat,Y_5: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_5))
=> ( X_6 != Y_5 ) ) ).
tff(fact_84_linorder__neqE,axiom,
! [X_5: nat,Y_4: nat] :
( ( X_5 != Y_4 )
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_5),Y_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),X_5)) ) ) ).
tff(fact_85_linorder__antisym__conv3,axiom,
! [Y_1: nat,X_2: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
<=> ( X_2 = Y_1 ) ) ) ).
tff(fact_86_linorder__less__linear,axiom,
! [X_4: nat,Y_3: nat] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Y_3))
| ( X_4 = Y_3 )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_4)) ) ).
tff(fact_87_not__less__iff__gr__or__eq,axiom,
! [X_2: nat,Y_1: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
| ( X_2 = Y_1 ) ) ) ).
tff(fact_88_linorder__neq__iff,axiom,
! [X_2: nat,Y_1: nat] :
( ( X_2 != Y_1 )
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)) ) ) ).
tff(fact_89_order__less__irrefl,axiom,
! [X_2: fun_Ar1871347069i_bool] : ~ hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,X_2),X_2)) ).
tff(fact_90_order__less__irrefl,axiom,
! [X_3: nat] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_3),X_3)) ).
tff(fact_91_UNIV__def,axiom,
top_to1057791589l_bool = collec1697917566t_bool(hAPP_b1017527359l_bool(cOMBK_1801013008t_bool,fTrue)) ).
tff(fact_92_UNIV__def,axiom,
top_to653038619l_bool = collec861220362t_bool(hAPP_b1178471617l_bool(cOMBK_70145528t_bool,fTrue)) ).
tff(fact_93_UNIV__def,axiom,
top_to2127553399l_bool = collec154865254t_bool(hAPP_b930206237l_bool(cOMBK_1362474068t_bool,fTrue)) ).
tff(fact_94_UNIV__def,axiom,
top_to710777827t_bool = collec2140722898le_alt(hAPP_b1848524425t_bool(cOMBK_350462144le_alt,fTrue)) ).
tff(fact_95_UNIV__def,axiom,
top_to850136695i_bool = collec1241994086e_indi(hAPP_b611520797i_bool(cOMBK_206372180e_indi,fTrue)) ).
tff(fact_96_pred__equals__eq2,axiom,
! [S: fun_Pr1639951081t_bool,R_1: fun_Pr1639951081t_bool] :
( ! [X_1: arrow_1621810872le_alt,Xa: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Xa)),R_1))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Xa)),S)) )
<=> ( R_1 = S ) ) ).
tff(fact_97_less__top,axiom,
! [Aa: fun_fu383145951l_bool] :
( ( Aa != top_to1057791589l_bool )
<=> hBOOL(hAPP_f180608831l_bool(hAPP_f279586623l_bool(ord_le1472193545l_bool,Aa),top_to1057791589l_bool)) ) ).
tff(fact_98_less__top,axiom,
! [Aa: fun_fu103733537l_bool] :
( ( Aa != top_to653038619l_bool )
<=> hBOOL(hAPP_f1237345129l_bool(hAPP_f786935331l_bool(ord_le2059466615l_bool,Aa),top_to653038619l_bool)) ) ).
tff(fact_99_less__top,axiom,
! [Aa: fun_fu1251737213l_bool] :
( ( Aa != top_to2127553399l_bool )
<=> hBOOL(hAPP_f1435434693l_bool(hAPP_f1303771867l_bool(ord_le1419690707l_bool,Aa),top_to2127553399l_bool)) ) ).
tff(fact_100_less__top,axiom,
! [Aa: bool] :
( ~ ( hBOOL(Aa)
<=> hBOOL(top_top_bool) )
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ) ).
tff(fact_101_less__top,axiom,
! [Aa: fun_Pr1639951081t_bool] :
( ( Aa != top_to710777827t_bool )
<=> hBOOL(hAPP_f1944886577l_bool(hAPP_f1911990195l_bool(ord_le1051050815t_bool,Aa),top_to710777827t_bool)) ) ).
tff(fact_102_less__top,axiom,
! [Aa: fun_Ar1871347069i_bool] :
( ( Aa != top_to850136695i_bool )
<=> hBOOL(hAPP_f90330565l_bool(hAPP_f1993665755l_bool(ord_le287438291i_bool,Aa),top_to850136695i_bool)) ) ).
tff(fact_103_inv__f__eq,axiom,
! [X_2: arrow_501706939e_indi,Y_1: nat,F: fun_Ar2035712896di_nat] :
( hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = Y_1 )
=> ( hAPP_n1582158000e_indi(hilber797233813di_nat(top_to850136695i_bool,F),Y_1) = X_2 ) ) ) ).
tff(fact_104_inv__f__f,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar2035712896di_nat] :
( hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool))
=> ( hAPP_n1582158000e_indi(hilber797233813di_nat(top_to850136695i_bool,F),hAPP_A1741215436di_nat(F,X_2)) = X_2 ) ) ).
tff(fact_105_inv__into__f__f,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> ( hAPP_n1582158000e_indi(hilber797233813di_nat(A,F),hAPP_A1741215436di_nat(F,X_2)) = X_2 ) ) ) ).
tff(fact_106_inv__into__f__eq,axiom,
! [Y_1: nat,X_2: arrow_501706939e_indi,F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = Y_1 )
=> ( hAPP_n1582158000e_indi(hilber797233813di_nat(A,F),Y_1) = X_2 ) ) ) ) ).
tff(fact_107_inj__eq,axiom,
! [X_2: arrow_501706939e_indi,Y_1: arrow_501706939e_indi,F: fun_Ar2035712896di_nat] :
( hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = hAPP_A1741215436di_nat(F,Y_1) )
<=> ( X_2 = Y_1 ) ) ) ).
tff(fact_108_inj__on__def,axiom,
! [F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
<=> ! [X_1: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> ! [Xa: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(Xa),A))
=> ( ( hAPP_A1741215436di_nat(F,X_1) = hAPP_A1741215436di_nat(F,Xa) )
=> ( X_1 = Xa ) ) ) ) ) ).
tff(fact_109_inj__on__contraD,axiom,
! [X_2: arrow_501706939e_indi,Y_1: arrow_501706939e_indi,F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
=> ( ( X_2 != Y_1 )
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(Y_1),A))
=> ( hAPP_A1741215436di_nat(F,X_2) != hAPP_A1741215436di_nat(F,Y_1) ) ) ) ) ) ).
tff(fact_110_inj__on__iff,axiom,
! [Y_1: arrow_501706939e_indi,X_2: arrow_501706939e_indi,F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(Y_1),A))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = hAPP_A1741215436di_nat(F,Y_1) )
<=> ( X_2 = Y_1 ) ) ) ) ) ).
tff(fact_111_inj__onD,axiom,
! [X_2: arrow_501706939e_indi,Y_1: arrow_501706939e_indi,F: fun_Ar2035712896di_nat,A: fun_Ar1871347069i_bool] :
( hBOOL(inj_on1177549232di_nat(F,A))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = hAPP_A1741215436di_nat(F,Y_1) )
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(Y_1),A))
=> ( X_2 = Y_1 ) ) ) ) ) ).
tff(fact_112_injD,axiom,
! [X_2: arrow_501706939e_indi,Y_1: arrow_501706939e_indi,F: fun_Ar2035712896di_nat] :
( hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool))
=> ( ( hAPP_A1741215436di_nat(F,X_2) = hAPP_A1741215436di_nat(F,Y_1) )
=> ( X_2 = Y_1 ) ) ) ).
tff(fact_113_inj__imp__inv__eq,axiom,
! [G: fun_na1602142942e_indi,F: fun_Ar2035712896di_nat] :
( hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool))
=> ( ! [X_1: nat] : hAPP_A1741215436di_nat(F,hAPP_n1582158000e_indi(G,X_1)) = X_1
=> ( hilber797233813di_nat(top_to850136695i_bool,F) = G ) ) ) ).
tff(fact_114_injI,axiom,
! [F: fun_Ar2035712896di_nat] :
( ! [X_1: arrow_501706939e_indi,Y_2: arrow_501706939e_indi] :
( ( hAPP_A1741215436di_nat(F,X_1) = hAPP_A1741215436di_nat(F,Y_2) )
=> ( X_1 = Y_2 ) )
=> hBOOL(inj_on1177549232di_nat(F,top_to850136695i_bool)) ) ).
tff(fact_115_assms_I1_J,axiom,
hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(f),pi_fun456133649t_bool(arrow_1880704820e_Prof,hAPP_f459175489l_bool(cOMBK_639770490t_bool,arrow_1008788854le_Lin)))) ).
tff(fact_116__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP_f180608831l_bool(member641857340t_bool(lba),arrow_1008788854le_Lin)) ).
tff(fact_117__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP_f180608831l_bool(member641857340t_bool(lab),arrow_1008788854le_Lin)) ).
tff(fact_118_Lin__irrefl,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),L))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Aa)),L)) ) ) ).
tff(fact_119_notin__Lin__iff,axiom,
! [X_2: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> ( ( X_2 != Y_1 )
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),L))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Y_1,X_2)),L)) ) ) ) ).
tff(fact_120_mem__def,axiom,
! [X_2: arrow_501706939e_indi,A: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
<=> hBOOL(hAPP_A1059798043i_bool(A,X_2)) ) ).
tff(fact_121_mem__def,axiom,
! [X_2: bool,A: fun_bool_bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
<=> hBOOL(hAPP_bool_bool(A,X_2)) ) ).
tff(fact_122_mem__def,axiom,
! [X_2: produc624534567le_alt,A: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A))
<=> hBOOL(hAPP_P751176071t_bool(A,X_2)) ) ).
tff(fact_123_mem__def,axiom,
! [X_2: fun_Ar2047178847t_bool,A: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
<=> hBOOL(hAPP_f1095388607l_bool(A,X_2)) ) ).
tff(fact_124_mem__def,axiom,
! [X_2: fun_fu50365883t_bool,A: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A))
<=> hBOOL(hAPP_f725100827l_bool(A,X_2)) ) ).
tff(fact_125_mem__def,axiom,
! [X_2: fun_Pr1639951081t_bool,A: fun_fu383145951l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A))
<=> hBOOL(hAPP_f1944886577l_bool(A,X_2)) ) ).
tff(fact_126_Collect__def,axiom,
! [Pa: fun_Ar1871347069i_bool] : collec1241994086e_indi(Pa) = Pa ).
tff(fact_127_mktop__Lin,axiom,
! [X_2: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1275257820_mktop,L),X_2)),arrow_1008788854le_Lin)) ) ).
tff(fact_128_mkbot__Lin,axiom,
! [X_2: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1126550734_mkbot,L),X_2)),arrow_1008788854le_Lin)) ) ).
tff(fact_129_above__Lin,axiom,
! [L: fun_Pr1639951081t_bool,X_2: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt] :
( ( X_2 != Y_1 )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_2009189698_above,L),X_2),Y_1)),arrow_1008788854le_Lin)) ) ) ).
tff(fact_130_const__Lin__Prof,axiom,
! [L: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_f1172974131t_bool(cOMBK_164791446e_indi,L)),arrow_1880704820e_Prof)) ) ).
tff(fact_131_in__above,axiom,
! [X_2: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt,L: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_2009189698_above,L),Aa),Ba)))
<=> ( ( X_2 != Y_1 )
& ( ( X_2 = Ba )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Y_1)),L)) )
& ( ( X_2 != Ba )
=> ( ( ( Y_1 = Ba )
=> ( ( X_2 = Aa )
| hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Aa)),L)) ) )
& ( ( Y_1 != Ba )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_2,Y_1)),L)) ) ) ) ) ) ) ) ).
tff(fact_132_dictatorI,axiom,
! [I_1: arrow_501706939e_indi,Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(Fa),pi_fun456133649t_bool(arrow_1880704820e_Prof,hAPP_f459175489l_bool(cOMBK_639770490t_bool,arrow_1008788854le_Lin))))
=> ( ! [X_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B_1: arrow_1621810872le_alt] :
( ( A_1 != B_1 )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_A2044747691t_bool(X_1,I_1)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B_1)),hAPP_f718157575t_bool(Fa,X_1))) ) ) )
=> hBOOL(hAPP_A1059798043i_bool(hAPP_f1559864639i_bool(arrow_1322316103ctator,Fa),I_1)) ) ) ).
tff(fact_133_PiE,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B: fun_Pr534938793l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_2)),hAPP_P2005668213l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A)) ) ) ).
tff(fact_134_PiE,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_2)),hAPP_A2044747691t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A)) ) ) ).
tff(fact_135_PiE,axiom,
! [X_2: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B: fun_bo230129725t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_2)),hAPP_b1848524425t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
tff(fact_136_PiE,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar1784032663l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_2)),hAPP_A1790795747l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A)) ) ) ).
tff(fact_137_PiE,axiom,
! [X_2: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B: fun_bo1613497205l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_2)),hAPP_b1178471617l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
tff(fact_138_PiE,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar884201459l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_2)),hAPP_A107624255l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A)) ) ) ).
tff(fact_139_PiE,axiom,
! [X_2: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B: fun_bo2138151889l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_2)),hAPP_b930206237l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
tff(fact_140_PiE,axiom,
! [X_2: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B: fun_bo1803678369l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_2)),hAPP_b1017527359l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
tff(fact_141_PiE,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B: fun_Pr123985543i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_2)),hAPP_P259956691i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A)) ) ) ).
tff(fact_142_PiE,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B: fun_fu23838287i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_2)),hAPP_f1511451035i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A)) ) ) ).
tff(fact_143_PiE,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B: fun_fu658952305l_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_2)),hAPP_f1418708797l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A)) ) ) ).
tff(fact_144_PiE,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B: fun_fu1950461939i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_2)),hAPP_f1559864639i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A)) ) ) ).
tff(fact_145_PiE,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B: fun_fu1734842389l_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_2)),hAPP_f626809057l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A)) ) ) ).
tff(fact_146_PiE,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B: fun_fu1867632401i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_2)),hAPP_f906860201i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A)) ) ) ).
tff(fact_147_PiE,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B: fun_fu1903211571l_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_2)),hAPP_f2128533835l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A)) ) ) ).
tff(fact_148_PiE,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B: fun_fu746839971l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_2)),hAPP_f1265202753l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A)) ) ) ).
tff(fact_149_PiE,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar1821573119l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_2)),hAPP_A1710743709l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A)) ) ) ).
tff(fact_150_complete__Lin,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ? [X_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),arrow_1008788854le_Lin))
& hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),X_1)) ) ) ).
tff(fact_151_PiProf,axiom,
! [Na: nat] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(cOMBC_1257424504t_bool(cOMBC_64563468t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),Na)),lab),lba)),arrow_1880704820e_Prof)) ).
tff(fact_152_Pi__mem,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B: fun_Pr534938793l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B)))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_2)),hAPP_P2005668213l_bool(B,X_2))) ) ) ).
tff(fact_153_Pi__mem,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B: fun_Pr123985543i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B)))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_2)),hAPP_P259956691i_bool(B,X_2))) ) ) ).
tff(fact_154_Pi__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B: fun_fu23838287i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_2)),hAPP_f1511451035i_bool(B,X_2))) ) ) ).
tff(fact_155_Pi__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B: fun_fu658952305l_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_2)),hAPP_f1418708797l_bool(B,X_2))) ) ) ).
tff(fact_156_Pi__mem,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B: fun_fu1950461939i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B)))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_2)),hAPP_f1559864639i_bool(B,X_2))) ) ) ).
tff(fact_157_Pi__mem,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B: fun_fu1734842389l_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B)))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_2)),hAPP_f626809057l_bool(B,X_2))) ) ) ).
tff(fact_158_Pi__mem,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B: fun_fu1867632401i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B)))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_2)),hAPP_f906860201i_bool(B,X_2))) ) ) ).
tff(fact_159_Pi__mem,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B: fun_fu1903211571l_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B)))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_2)),hAPP_f2128533835l_bool(B,X_2))) ) ) ).
tff(fact_160_Pi__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_2)),hAPP_A2044747691t_bool(B,X_2))) ) ) ).
tff(fact_161_Pi__mem,axiom,
! [X_2: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B: fun_bo230129725t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_2)),hAPP_b1848524425t_bool(B,X_2))) ) ) ).
tff(fact_162_Pi__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar1784032663l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_2)),hAPP_A1790795747l_bool(B,X_2))) ) ) ).
tff(fact_163_Pi__mem,axiom,
! [X_2: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B: fun_bo1613497205l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_2)),hAPP_b1178471617l_bool(B,X_2))) ) ) ).
tff(fact_164_Pi__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar884201459l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_2)),hAPP_A107624255l_bool(B,X_2))) ) ) ).
tff(fact_165_Pi__mem,axiom,
! [X_2: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B: fun_bo2138151889l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_2)),hAPP_b930206237l_bool(B,X_2))) ) ) ).
tff(fact_166_Pi__mem,axiom,
! [X_2: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B: fun_bo1803678369l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_2)),hAPP_b1017527359l_bool(B,X_2))) ) ) ).
tff(fact_167_Pi__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B: fun_fu746839971l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_2)),hAPP_f1265202753l_bool(B,X_2))) ) ) ).
tff(fact_168_Pi__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B: fun_Ar1821573119l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_2)),hAPP_A1710743709l_bool(B,X_2))) ) ) ).
tff(fact_169_Prof__def,axiom,
arrow_1880704820e_Prof = pi_Arr1358199477t_bool(top_to850136695i_bool,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,arrow_1008788854le_Lin)) ).
tff(fact_170_funcset__mem,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B: fun_bool_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,hAPP_f1601816755l_bool(cOMBK_290363320le_alt,B))))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_2)),B)) ) ) ).
tff(fact_171_funcset__mem,axiom,
! [X_2: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,hAPP_f1561296623i_bool(cOMBK_328807062le_alt,B))))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_2)),B)) ) ) ).
tff(fact_172_funcset__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,hAPP_f823592631i_bool(cOMBK_269839822t_bool,B))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_2)),B)) ) ) ).
tff(fact_173_funcset__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B: fun_bool_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,hAPP_f1325493883l_bool(cOMBK_167511280t_bool,B))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_2)),B)) ) ) ).
tff(fact_174_funcset__mem,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,hAPP_f1224613979i_bool(cOMBK_519762474t_bool,B))))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_2)),B)) ) ) ).
tff(fact_175_funcset__mem,axiom,
! [X_2: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B: fun_bool_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,hAPP_f1364914207l_bool(cOMBK_1853791052t_bool,B))))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_2)),B)) ) ) ).
tff(fact_176_funcset__mem,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,hAPP_f1364159657i_bool(cOMBK_1207925178t_bool,B))))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_2)),B)) ) ) ).
tff(fact_177_funcset__mem,axiom,
! [X_2: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B: fun_bool_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,hAPP_f1230984105l_bool(cOMBK_1838733848t_bool,B))))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_2)),B)) ) ) ).
tff(fact_178_funcset__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,hAPP_f1172974131t_bool(cOMBK_164791446e_indi,B))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_2)),B)) ) ) ).
tff(fact_179_funcset__mem,axiom,
! [X_2: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,hAPP_f1758973969t_bool(cOMBK_1897375160l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_2)),B)) ) ) ).
tff(fact_180_funcset__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,hAPP_f466810275l_bool(cOMBK_30438862e_indi,B))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_2)),B)) ) ) ).
tff(fact_181_funcset__mem,axiom,
! [X_2: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,hAPP_f2013855105l_bool(cOMBK_1481288432l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_2)),B)) ) ) ).
tff(fact_182_funcset__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,hAPP_f544895323l_bool(cOMBK_869185066e_indi,B))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_2)),B)) ) ) ).
tff(fact_183_funcset__mem,axiom,
! [X_2: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,hAPP_f989466937l_bool(cOMBK_343479628l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_2)),B)) ) ) ).
tff(fact_184_funcset__mem,axiom,
! [X_2: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B: fun_fu383145951l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,hAPP_f71505983l_bool(cOMBK_648664568l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_2)),B)) ) ) ).
tff(fact_185_funcset__mem,axiom,
! [X_2: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B: fun_fu383145951l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,hAPP_f459175489l_bool(cOMBK_639770490t_bool,B))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_2)),B)) ) ) ).
tff(fact_186_funcset__mem,axiom,
! [X_2: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B: fun_fu383145951l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,B))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_2),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_2)),B)) ) ) ).
tff(fact_187_dictator__def,axiom,
! [Fa: fun_fu50365883t_bool,I_1: arrow_501706939e_indi] :
( hBOOL(hAPP_A1059798043i_bool(hAPP_f1559864639i_bool(arrow_1322316103ctator,Fa),I_1))
<=> ! [X_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),arrow_1880704820e_Prof))
=> ( hAPP_f718157575t_bool(Fa,X_1) = hAPP_A2044747691t_bool(X_1,I_1) ) ) ) ).
tff(fact_188_Pi__UNIV,axiom,
! [A: fun_Pr1639951081t_bool] : pi_Pro811330557t_bool(A,hAPP_f1601816755l_bool(cOMBK_290363320le_alt,top_to1647826457l_bool)) = top_to1057791589l_bool ).
tff(fact_189_Pi__UNIV,axiom,
! [A: fun_fu103733537l_bool] : pi_fun456133649t_bool(A,hAPP_f459175489l_bool(cOMBK_639770490t_bool,top_to1057791589l_bool)) = top_to2127553399l_bool ).
tff(fact_190_Pi__UNIV,axiom,
! [A: fun_Ar1871347069i_bool] : pi_Arr1358199477t_bool(A,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,top_to1057791589l_bool)) = top_to653038619l_bool ).
tff(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(e,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e))))))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),hAPP_f718157575t_bool(f,cOMBC_1257424504t_bool(cOMBC_64563468t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),lab),lba)))) ) ).
tff(fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I: arrow_501706939e_indi] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(e,d)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1275257820_mktop,hAPP_A2044747691t_bool(p,I)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> ( ( ( hAPP_A1741215436di_nat(h,I) = n )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(e,d)),hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_2009189698_above,hAPP_A2044747691t_bool(p,I)),c),e))) )
& ( ( hAPP_A1741215436di_nat(h,I) != n )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(e,d)),hAPP_A476679046t_bool(hAPP_f1699392794t_bool(arrow_1126550734_mkbot,hAPP_A2044747691t_bool(p,I)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A1741215436di_nat(h,I)),n))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),lba)) ) ) ) ).
tff(fact_193__096a_A_126_061_Ab_096,axiom,
a != b ).
tff(fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),lba)) ).
tff(fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(a,b)),lab)) ).
tff(fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(a,b)),lba)) ).
tff(fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),lab)) ).
%----Helper facts (40)
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__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X: nat,Y: nat] :
( ( X != Y )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____yfv,axiom,
! [P: bool,Q: arrow_501706939e_indi] : hAPP_A1059798043i_bool(hAPP_b611520797i_bool(cOMBK_206372180e_indi,P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000,axiom,
! [P: fun_Ar156616864t_bool,Q: nat,R: arrow_501706939e_indi] : hAPP_A1059798043i_bool(cOMBC_998415407t_bool(P,Q),R) = hAPP_nat_bool(hAPP_A1239621182t_bool(P,R),Q) ).
tff(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P: fun_nat_fun_nat_bool,Q: fun_Ar2035712896di_nat,R: arrow_501706939e_indi] : hAPP_A1239621182t_bool(cOMBB_1514803447e_indi(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_A1741215436di_nat(Q,R)) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P: bool,Q: produc624534567le_alt] : hAPP_P751176071t_bool(hAPP_b1848524425t_bool(cOMBK_350462144le_alt,P),Q) = P ).
tff(help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp,axiom,
! [X: fun_Pr1639951081t_bool,Y: fun_Pr1639951081t_bool] : hAPP_f727188501t_bool(hAPP_f910728105t_bool(hAPP_b1702702257t_bool(if_fun95824985t_bool,fTrue),X),Y) = X ).
tff(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp,axiom,
! [X: fun_Pr1639951081t_bool,Y: fun_Pr1639951081t_bool] : hAPP_f727188501t_bool(hAPP_f910728105t_bool(hAPP_b1702702257t_bool(if_fun95824985t_bool,fFalse),X),Y) = Y ).
tff(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwp,axiom,
! [P: bool] :
( ( P = fTrue )
| ( P = fFalse ) ) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P: bool,Q: fun_Pr1639951081t_bool] : hAPP_f1944886577l_bool(hAPP_b1017527359l_bool(cOMBK_1801013008t_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: produc624534567le_alt] : hAPP_P2005668213l_bool(hAPP_f1601816755l_bool(cOMBK_290363320le_alt,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,axiom,
! [P: fun_Pr1639951081t_bool,Q: bool] : hAPP_b1848524425t_bool(hAPP_f1758973969t_bool(cOMBK_1897375160l_bool,P),Q) = P ).
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_Pr1639951081t_bool] : hAPP_f2128533835l_bool(hAPP_f1230984105l_bool(cOMBK_1838733848t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P: fun_fu383145951l_bool,Q: bool] : hAPP_b1017527359l_bool(hAPP_f71505983l_bool(cOMBK_648664568l_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__,axiom,
! [P: fun_Ar1871347069i_bool,Q: produc624534567le_alt] : hAPP_P259956691i_bool(hAPP_f1561296623i_bool(cOMBK_328807062le_alt,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_160,axiom,
! [P: fun_Pr1639951081t_bool,Q: arrow_501706939e_indi] : hAPP_A2044747691t_bool(hAPP_f1172974131t_bool(cOMBK_164791446e_indi,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P: bool,Q: fun_Ar2047178847t_bool] : hAPP_f1095388607l_bool(hAPP_b1178471617l_bool(cOMBK_70145528t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___161,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_Pr1639951081t_bool] : hAPP_f906860201i_bool(hAPP_f1364159657i_bool(cOMBK_1207925178t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_162,axiom,
! [P: fun_fu383145951l_bool,Q: arrow_501706939e_indi] : hAPP_A1710743709l_bool(hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_163,axiom,
! [P: fun_bool_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1418708797l_bool(hAPP_f1325493883l_bool(cOMBK_167511280t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv,axiom,
! [P: fun_fu103733537l_bool,Q: bool] : hAPP_b1178471617l_bool(hAPP_f2013855105l_bool(cOMBK_1481288432l_bool,P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_164,axiom,
! [P: fun_Ar1757019876t_bool,Q: arrow_1621810872le_alt,R: arrow_501706939e_indi] : hAPP_A2044747691t_bool(cOMBC_377836265t_bool(P,Q),R) = hAPP_A476679046t_bool(hAPP_A711829680t_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___165,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1511451035i_bool(hAPP_f823592631i_bool(cOMBK_269839822t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_166,axiom,
! [P: fun_fu103733537l_bool,Q: arrow_501706939e_indi] : hAPP_A1790795747l_bool(hAPP_f466810275l_bool(cOMBK_30438862e_indi,P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_167,axiom,
! [P: fun_Ar2079322857t_bool,Q: arrow_1621810872le_alt,R: arrow_501706939e_indi] : hAPP_A711829680t_bool(cOMBC_1994570734t_bool(P,Q),R) = hAPP_A272835723t_bool(hAPP_A784015157t_bool(P,R),Q) ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_168,axiom,
! [P: fun_Ar2040671475t_bool,Q: fun_Pr1639951081t_bool,R: arrow_501706939e_indi] : hAPP_A2044747691t_bool(cOMBC_1257424504t_bool(P,Q),R) = hAPP_f727188501t_bool(hAPP_A301260095t_bool(P,R),Q) ).
tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000,axiom,
! [P: fun_Ar2040671475t_bool,Q: fun_Ar2047178847t_bool,R: arrow_501706939e_indi] : hAPP_A2044747691t_bool(cOMBS_1688227464t_bool(P,Q),R) = hAPP_f727188501t_bool(hAPP_A301260095t_bool(P,R),hAPP_A2044747691t_bool(Q,R)) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
! [P: bool,Q: fun_fu50365883t_bool] : hAPP_f725100827l_bool(hAPP_b930206237l_bool(cOMBK_1362474068t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_169,axiom,
! [P: fun_fu383145951l_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1265202753l_bool(hAPP_f459175489l_bool(cOMBK_639770490t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_170,axiom,
! [P: fun_bool_bool,Q: fun_fu50365883t_bool] : hAPP_f626809057l_bool(hAPP_f1364914207l_bool(cOMBK_1853791052t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P: fun_fu1251737213l_bool,Q: bool] : hAPP_b930206237l_bool(hAPP_f989466937l_bool(cOMBK_343479628l_bool,P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,axiom,
! [P: fun_fu1760369922t_bool,Q: fun_Ar2047178847t_bool,R: arrow_501706939e_indi] : hAPP_A711829680t_bool(cOMBB_1932856316e_indi(P,Q),R) = hAPP_f1699392794t_bool(P,hAPP_A2044747691t_bool(Q,R)) ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___171,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_fu50365883t_bool] : hAPP_f1559864639i_bool(hAPP_f1224613979i_bool(cOMBK_519762474t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_172,axiom,
! [P: fun_fu1251737213l_bool,Q: arrow_501706939e_indi] : hAPP_A107624255l_bool(hAPP_f544895323l_bool(cOMBK_869185066e_indi,P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_173,axiom,
! [P: fun_fu193278215t_bool,Q: fun_Ar2047178847t_bool,R: arrow_501706939e_indi] : hAPP_A784015157t_bool(cOMBB_715840641e_indi(P,Q),R) = hAPP_f1560118175t_bool(P,hAPP_A2044747691t_bool(Q,R)) ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_174,axiom,
! [P: fun_Ar2100459655t_bool,Q: fun_Pr1639951081t_bool,R: arrow_501706939e_indi] : hAPP_A301260095t_bool(cOMBC_64563468t_bool(P,Q),R) = hAPP_f910728105t_bool(hAPP_A1985966547t_bool(P,R),Q) ).
tff(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_175,axiom,
! [P: fun_Ar2100459655t_bool,Q: fun_Ar2047178847t_bool,R: arrow_501706939e_indi] : hAPP_A301260095t_bool(cOMBS_1833320732t_bool(P,Q),R) = hAPP_f910728105t_bool(hAPP_A1985966547t_bool(P,R),hAPP_A2044747691t_bool(Q,R)) ).
tff(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
! [P: fun_bo292969573t_bool,Q: fun_Ar1871347069i_bool,R: arrow_501706939e_indi] : hAPP_A1985966547t_bool(cOMBB_124649523e_indi(P,Q),R) = hAPP_b1702702257t_bool(P,hAPP_A1059798043i_bool(Q,R)) ).
%----Conjectures (1)
tff(conj_0,conjecture,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))) ).
%------------------------------------------------------------------------------